TSTP Solution File: SYO605+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO605+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 01:41:02 EDT 2022
% Result : Theorem 11.22s 7.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO605+1 : TPTP v8.1.0. Released v7.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 15:11:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 11.22/7.47 % SZS status Theorem
% 11.22/7.47 % SZS output start Proof
% 11.22/7.47 tff(g_true_only_type, type, (
% 11.22/7.47 g_true_only: ( $i * $i ) > $o)).
% 11.22/7.47 tff(tptp_fun_A_0_type, type, (
% 11.22/7.47 tptp_fun_A_0: $i)).
% 11.22/7.47 tff(tptp_fun_A_1_type, type, (
% 11.22/7.47 tptp_fun_A_1: $i > $i)).
% 11.22/7.47 tff(g_both_type, type, (
% 11.22/7.47 g_both: ( $i * $i ) > $o)).
% 11.22/7.47 tff(g_false_only_type, type, (
% 11.22/7.47 g_false_only: ( $i * $i ) > $o)).
% 11.22/7.47 tff(tptp_fun_C_4_type, type, (
% 11.22/7.47 tptp_fun_C_4: ( $i * $i ) > $i)).
% 11.22/7.47 tff(tptp_fun_A_5_type, type, (
% 11.22/7.47 tptp_fun_A_5: $i > $i)).
% 11.22/7.47 tff(tptp_fun_A_3_type, type, (
% 11.22/7.47 tptp_fun_A_3: $i)).
% 11.22/7.47 tff(tptp_fun_B_2_type, type, (
% 11.22/7.47 tptp_fun_B_2: $i > $i)).
% 11.22/7.47 tff(1,assumption,((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))), introduced(assumption)).
% 11.22/7.47 tff(2,plain,
% 11.22/7.47 (^[B: $i, C: $i] : refl((~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B))))))) <=> (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B))))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(3,plain,
% 11.22/7.47 (![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B))))))) <=> ![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[2])).
% 11.22/7.47 tff(4,plain,
% 11.22/7.47 (^[B: $i, C: $i] : rewrite((~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B))))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(5,plain,
% 11.22/7.47 (![B: $i, C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> ![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[4])).
% 11.22/7.47 tff(6,plain,
% 11.22/7.47 (![B: $i] : ![C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> ![B: $i, C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(pull_quant,[status(thm)],[])).
% 11.22/7.47 tff(7,plain,
% 11.22/7.47 (^[B: $i] : quant_intro(proof_bind(^[C: $i] : rewrite((~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))))), (![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> ![C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(8,plain,
% 11.22/7.47 (![B: $i] : ![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> ![B: $i] : ![C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[7])).
% 11.22/7.47 tff(9,plain,
% 11.22/7.47 (![B: $i] : ![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))) <=> ![B: $i, C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(transitivity,[status(thm)],[8, 6])).
% 11.22/7.47 tff(10,plain,
% 11.22/7.47 ((~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))) <=> (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(11,plain,
% 11.22/7.47 ((~?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B))))) <=> (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(12,axiom,(~((![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B)))) | ?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B))))) | (((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B))))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_true_only(C, A) & g_false_only(C, B)) | (g_false_only(C, A) & g_true_only(C, B)))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nc4')).
% 11.22/7.47 tff(13,plain,
% 11.22/7.47 (~(![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B)))) | ?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B)))))),
% 11.22/7.47 inference(or_elim,[status(thm)],[12])).
% 11.22/7.47 tff(14,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B))))),
% 11.22/7.47 inference(or_elim,[status(thm)],[13])).
% 11.22/7.47 tff(15,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[14, 11])).
% 11.22/7.47 tff(16,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[15, 10])).
% 11.22/7.47 tff(17,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[16, 10])).
% 11.22/7.47 tff(18,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[17, 10])).
% 11.22/7.47 tff(19,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[18, 10])).
% 11.22/7.47 tff(20,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[19, 10])).
% 11.22/7.47 tff(21,plain,
% 11.22/7.47 (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[20, 10])).
% 11.22/7.47 tff(22,plain,
% 11.22/7.47 (^[B: $i] : trans(sk($oeq((~![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))), (~?[C: $i] : ((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))))), nnf_neg(proof_bind(^[C: $i] : refl($oeq((~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))), (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))))), $oeq((~?[C: $i] : ((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))), ![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B))))))), $oeq((~![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))), ![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(23,plain,(
% 11.22/7.47 ![B: $i] : ![C: $i] : (~((g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(nnf-neg,[status(sab)],[21, 22])).
% 11.22/7.47 tff(24,plain,
% 11.22/7.47 (![B: $i, C: $i] : (~((g_true_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, tptp_fun_A_1(B)) & (g_false_only(C, B) | g_true_only(C, B))) | (g_false_only(C, tptp_fun_A_1(B)) & (g_both(C, B) | g_false_only(C, B)))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[23, 9])).
% 11.22/7.47 tff(25,plain,
% 11.22/7.47 (![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[24, 5])).
% 11.22/7.47 tff(26,plain,
% 11.22/7.47 (![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[25, 3])).
% 11.22/7.47 tff(27,plain,
% 11.22/7.47 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(28,plain,
% 11.22/7.47 ((~((~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))))) <=> (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(29,plain,
% 11.22/7.47 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))))))),
% 11.22/7.47 inference(monotonicity,[status(thm)],[28])).
% 11.22/7.47 tff(30,plain,
% 11.22/7.47 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))))))),
% 11.22/7.47 inference(transitivity,[status(thm)],[29, 27])).
% 11.22/7.47 tff(31,plain,
% 11.22/7.47 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))))))),
% 11.22/7.47 inference(quant_inst,[status(thm)],[])).
% 11.22/7.47 tff(32,plain,
% 11.22/7.47 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 11.22/7.47 tff(33,plain,
% 11.22/7.47 ($false),
% 11.22/7.47 inference(unit_resolution,[status(thm)],[32, 26, 1])).
% 11.22/7.47 tff(34,plain,(~((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))))), inference(lemma,lemma(discharge,[]))).
% 11.22/7.47 tff(35,plain,
% 11.22/7.47 (((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))) | ((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))),
% 11.22/7.47 inference(tautology,[status(thm)],[])).
% 11.22/7.47 tff(36,plain,
% 11.22/7.47 ((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))),
% 11.22/7.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 11.22/7.47 tff(37,plain,
% 11.22/7.47 (^[B: $i] : refl((~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B))))))) <=> (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B))))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(38,plain,
% 11.22/7.47 (![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B))))))) <=> ![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[37])).
% 11.22/7.47 tff(39,plain,
% 11.22/7.47 (^[B: $i] : rewrite((~((g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))))) <=> (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B))))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(40,plain,
% 11.22/7.47 (![B: $i] : (~((g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))))) <=> ![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[39])).
% 11.22/7.47 tff(41,plain,
% 11.22/7.47 (^[B: $i] : rewrite((~((g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))))) <=> (~((g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))))))),
% 11.22/7.47 inference(bind,[status(th)],[])).
% 11.22/7.47 tff(42,plain,
% 11.22/7.47 (![B: $i] : (~((g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))))) <=> ![B: $i] : (~((g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B)))))),
% 11.22/7.47 inference(quant_intro,[status(thm)],[41])).
% 11.22/7.47 tff(43,plain,
% 11.22/7.47 ((~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))) <=> (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(44,plain,
% 11.22/7.47 ((~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B))))) <=> (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(45,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B))))),
% 11.22/7.47 inference(or_elim,[status(thm)],[13])).
% 11.22/7.47 tff(46,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 11.22/7.47 tff(47,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[46, 43])).
% 11.22/7.47 tff(48,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[47, 43])).
% 11.22/7.47 tff(49,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[48, 43])).
% 11.22/7.47 tff(50,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[49, 43])).
% 11.22/7.47 tff(51,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[50, 43])).
% 11.22/7.47 tff(52,plain,
% 11.22/7.47 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[51, 43])).
% 11.22/7.47 tff(53,plain,(
% 11.22/7.47 $oeq((~?[B: $i] : ((g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))))), ![B: $i] : (~((g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))))))),
% 11.22/7.47 inference(transitivity,[status(sab)],[52])).
% 11.22/7.47 tff(54,plain,
% 11.22/7.47 (![B: $i] : (~((g_false_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_true_only(B, B) | g_false_only(B, B)))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[53, 42])).
% 11.22/7.47 tff(55,plain,
% 11.22/7.47 (![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[54, 40])).
% 11.22/7.47 tff(56,plain,
% 11.22/7.47 (![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))),
% 11.22/7.47 inference(modus_ponens,[status(thm)],[55, 38])).
% 11.22/7.47 tff(57,plain,
% 11.22/7.47 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(58,plain,
% 11.22/7.47 ((~((~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))))) <=> (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))),
% 11.22/7.47 inference(rewrite,[status(thm)],[])).
% 11.22/7.47 tff(59,plain,
% 11.22/7.47 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.47 inference(monotonicity,[status(thm)],[58])).
% 11.22/7.47 tff(60,plain,
% 11.22/7.47 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.47 inference(transitivity,[status(thm)],[59, 57])).
% 11.22/7.47 tff(61,plain,
% 11.22/7.47 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))),
% 11.22/7.47 inference(quant_inst,[status(thm)],[])).
% 11.22/7.47 tff(62,plain,
% 11.22/7.47 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 11.22/7.48 tff(63,plain,
% 11.22/7.48 (~((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[62, 56])).
% 11.22/7.48 tff(64,plain,
% 11.22/7.48 (((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(A!0), A!0)) | (~(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))) | ((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(65,plain,
% 11.22/7.48 ((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[64, 63])).
% 11.22/7.48 tff(66,assumption,(g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))), introduced(assumption)).
% 11.22/7.48 tff(67,plain,
% 11.22/7.48 ((g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(68,plain,
% 11.22/7.48 (g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[67, 66])).
% 11.22/7.48 tff(69,plain,
% 11.22/7.48 ((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(70,plain,
% 11.22/7.48 ((~((~g_true_only(tptp_fun_A_1(A!0), A!0)) | (~(g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))) | (~g_true_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[69, 68])).
% 11.22/7.48 tff(71,plain,
% 11.22/7.48 (~g_true_only(tptp_fun_A_1(A!0), A!0)),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[70, 65])).
% 11.22/7.48 tff(72,plain,
% 11.22/7.48 (((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0))))) | (~((~g_both(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0)))))) | ((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(73,plain,
% 11.22/7.48 ((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[72, 34])).
% 11.22/7.48 tff(74,plain,
% 11.22/7.48 ((~((~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))))) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(75,plain,
% 11.22/7.48 (~(g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[74, 66, 73])).
% 11.22/7.48 tff(76,plain,
% 11.22/7.48 ((g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)) | (~g_false_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(77,plain,
% 11.22/7.48 (~g_false_only(tptp_fun_A_1(A!0), A!0)),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[76, 75])).
% 11.22/7.48 tff(78,plain,
% 11.22/7.48 ((g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)) | (~g_both(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(79,plain,
% 11.22/7.48 (~g_both(tptp_fun_A_1(A!0), A!0)),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[78, 75])).
% 11.22/7.48 tff(80,plain,
% 11.22/7.48 (^[X_2: $i, X_1: $i] : refl((g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)))),
% 11.22/7.48 inference(bind,[status(th)],[])).
% 11.22/7.48 tff(81,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(quant_intro,[status(thm)],[80])).
% 11.22/7.48 tff(82,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(83,plain,
% 11.22/7.48 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)))), rewrite(((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))))),
% 11.22/7.48 inference(bind,[status(th)],[])).
% 11.22/7.48 tff(84,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(quant_intro,[status(thm)],[83])).
% 11.22/7.48 tff(85,axiom,(![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exhaustion_g')).
% 11.22/7.48 tff(86,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[85, 84])).
% 11.22/7.48 tff(87,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[86, 82])).
% 11.22/7.48 tff(88,plain,(
% 11.22/7.48 ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(skolemize,[status(sab)],[87])).
% 11.22/7.48 tff(89,plain,
% 11.22/7.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[88, 81])).
% 11.22/7.48 tff(90,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(91,plain,
% 11.22/7.48 ((g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0)) <=> (g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(92,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)))),
% 11.22/7.48 inference(monotonicity,[status(thm)],[91])).
% 11.22/7.48 tff(93,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(transitivity,[status(thm)],[92, 90])).
% 11.22/7.48 tff(94,plain,
% 11.22/7.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(A!0), A!0) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0))),
% 11.22/7.48 inference(quant_inst,[status(thm)],[])).
% 11.22/7.48 tff(95,plain,
% 11.22/7.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(A!0), A!0) | g_both(tptp_fun_A_1(A!0), A!0) | g_false_only(tptp_fun_A_1(A!0), A!0)),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 11.22/7.48 tff(96,plain,
% 11.22/7.48 ($false),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[95, 89, 79, 77, 71])).
% 11.22/7.48 tff(97,plain,(~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))), inference(lemma,lemma(discharge,[]))).
% 11.22/7.48 tff(98,plain,
% 11.22/7.48 (((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(99,plain,
% 11.22/7.48 ((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 11.22/7.48 tff(100,assumption,(~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))), introduced(assumption)).
% 11.22/7.48 tff(101,plain,
% 11.22/7.48 (((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(102,plain,
% 11.22/7.48 ((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[101, 100])).
% 11.22/7.48 tff(103,plain,
% 11.22/7.48 (((~![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B)))))) | ((~((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))) <=> ((~![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(104,plain,
% 11.22/7.48 ((~![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B)))))) | ((~((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))))),
% 11.22/7.48 inference(quant_inst,[status(thm)],[])).
% 11.22/7.48 tff(105,plain,
% 11.22/7.48 ((~![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B)))))) | (~((~g_true_only(tptp_fun_A_1(A!0), A!3)) | (~g_true_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0))))) | (~((~g_false_only(tptp_fun_A_1(A!0), A!3)) | (~g_false_only(tptp_fun_A_1(A!0), tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 11.22/7.48 tff(106,plain,
% 11.22/7.48 (~![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B)))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[105, 102, 99])).
% 11.22/7.48 tff(107,assumption,(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), introduced(assumption)).
% 11.22/7.48 tff(108,assumption,(~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), introduced(assumption)).
% 11.22/7.48 tff(109,plain,
% 11.22/7.48 ((~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(110,plain,
% 11.22/7.48 (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[109, 107, 108])).
% 11.22/7.48 tff(111,assumption,((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))), introduced(assumption)).
% 11.22/7.48 tff(112,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(113,plain,
% 11.22/7.48 ((~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))))) <=> (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(114,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.48 inference(monotonicity,[status(thm)],[113])).
% 11.22/7.48 tff(115,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.48 inference(transitivity,[status(thm)],[114, 112])).
% 11.22/7.48 tff(116,plain,
% 11.22/7.48 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))),
% 11.22/7.48 inference(quant_inst,[status(thm)],[])).
% 11.22/7.48 tff(117,plain,
% 11.22/7.48 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[116, 115])).
% 11.22/7.48 tff(118,plain,
% 11.22/7.48 ($false),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[117, 26, 111])).
% 11.22/7.48 tff(119,plain,(~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))))), inference(lemma,lemma(discharge,[]))).
% 11.22/7.48 tff(120,plain,
% 11.22/7.48 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(121,plain,
% 11.22/7.48 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 11.22/7.48 tff(122,plain,
% 11.22/7.48 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(123,plain,
% 11.22/7.48 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[122, 121])).
% 11.22/7.48 tff(124,plain,
% 11.22/7.48 (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[123, 110])).
% 11.22/7.48 tff(125,plain,
% 11.22/7.48 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(126,plain,
% 11.22/7.48 (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[125, 124])).
% 11.22/7.48 tff(127,plain,
% 11.22/7.48 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(tautology,[status(thm)],[])).
% 11.22/7.48 tff(128,plain,
% 11.22/7.48 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[127, 124])).
% 11.22/7.48 tff(129,assumption,(~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))), introduced(assumption)).
% 11.22/7.48 tff(130,assumption,(~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))), introduced(assumption)).
% 11.22/7.48 tff(131,assumption,(~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))), introduced(assumption)).
% 11.22/7.48 tff(132,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(133,plain,
% 11.22/7.48 ((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) <=> (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(134,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.22/7.48 inference(monotonicity,[status(thm)],[133])).
% 11.22/7.48 tff(135,plain,
% 11.22/7.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(transitivity,[status(thm)],[134, 132])).
% 11.22/7.48 tff(136,plain,
% 11.22/7.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.48 inference(quant_inst,[status(thm)],[])).
% 11.22/7.48 tff(137,plain,
% 11.22/7.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(modus_ponens,[status(thm)],[136, 135])).
% 11.22/7.48 tff(138,plain,
% 11.22/7.48 ($false),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[137, 89, 131, 130, 129])).
% 11.22/7.48 tff(139,plain,(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))), inference(lemma,lemma(discharge,[]))).
% 11.22/7.48 tff(140,plain,
% 11.22/7.48 (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.22/7.48 inference(unit_resolution,[status(thm)],[139, 128, 126])).
% 11.22/7.48 tff(141,assumption,((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))), introduced(assumption)).
% 11.22/7.48 tff(142,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(143,plain,
% 11.22/7.48 ((~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))))) <=> (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))),
% 11.22/7.48 inference(rewrite,[status(thm)],[])).
% 11.22/7.48 tff(144,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.48 inference(monotonicity,[status(thm)],[143])).
% 11.22/7.48 tff(145,plain,
% 11.22/7.48 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))))))),
% 11.22/7.49 inference(transitivity,[status(thm)],[144, 142])).
% 11.22/7.49 tff(146,plain,
% 11.22/7.49 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))),
% 11.22/7.49 inference(quant_inst,[status(thm)],[])).
% 11.22/7.49 tff(147,plain,
% 11.22/7.49 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))))),
% 11.22/7.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 11.22/7.49 tff(148,plain,
% 11.22/7.49 ($false),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[147, 26, 141])).
% 11.22/7.49 tff(149,plain,(~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))))), inference(lemma,lemma(discharge,[]))).
% 11.22/7.49 tff(150,plain,
% 11.22/7.49 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))) | ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(151,plain,
% 11.22/7.49 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[150, 149])).
% 11.22/7.49 tff(152,plain,
% 11.22/7.49 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(153,plain,
% 11.22/7.49 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[152, 151])).
% 11.22/7.49 tff(154,plain,
% 11.22/7.49 (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[153, 140])).
% 11.22/7.49 tff(155,plain,
% 11.22/7.49 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(156,plain,
% 11.22/7.49 (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[155, 154])).
% 11.22/7.49 tff(157,plain,
% 11.22/7.49 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(158,plain,
% 11.22/7.49 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[157, 154])).
% 11.22/7.49 tff(159,plain,
% 11.22/7.49 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))))))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(160,plain,
% 11.22/7.49 ((~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))))) <=> (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(161,plain,
% 11.22/7.49 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))))))),
% 11.22/7.49 inference(monotonicity,[status(thm)],[160])).
% 11.22/7.49 tff(162,plain,
% 11.22/7.49 (((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))) <=> ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))))))),
% 11.22/7.49 inference(transitivity,[status(thm)],[161, 159])).
% 11.22/7.49 tff(163,plain,
% 11.22/7.49 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))),
% 11.22/7.49 inference(quant_inst,[status(thm)],[])).
% 11.22/7.49 tff(164,plain,
% 11.22/7.49 ((~![B: $i, C: $i] : (~((~((~g_true_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_true_only(C, B))))) | (~((~g_both(C, tptp_fun_A_1(B))) | (~(g_false_only(C, B) | g_true_only(C, B))))) | (~((~g_false_only(C, tptp_fun_A_1(B))) | (~(g_both(C, B) | g_false_only(C, B)))))))) | (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))))),
% 11.22/7.49 inference(modus_ponens,[status(thm)],[163, 162])).
% 11.22/7.49 tff(165,plain,
% 11.22/7.49 (~((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[164, 26])).
% 11.22/7.49 tff(166,plain,
% 11.22/7.49 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))) | ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(167,plain,
% 11.22/7.49 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[166, 165])).
% 11.22/7.49 tff(168,plain,
% 11.22/7.49 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(169,plain,
% 11.22/7.49 ((~((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))) <=> (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(170,plain,
% 11.22/7.49 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))))),
% 11.22/7.49 inference(monotonicity,[status(thm)],[169])).
% 11.22/7.49 tff(171,plain,
% 11.22/7.49 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))))),
% 11.22/7.49 inference(transitivity,[status(thm)],[170, 168])).
% 11.22/7.49 tff(172,plain,
% 11.22/7.49 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.49 inference(quant_inst,[status(thm)],[])).
% 11.22/7.49 tff(173,plain,
% 11.22/7.49 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))))),
% 11.22/7.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 11.22/7.49 tff(174,plain,
% 11.22/7.49 (~((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[173, 56])).
% 11.22/7.49 tff(175,plain,
% 11.22/7.49 (((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))) | ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(176,plain,
% 11.22/7.49 ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[175, 174])).
% 11.22/7.49 tff(177,plain,
% 11.22/7.49 ((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(178,plain,
% 11.22/7.49 ((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[177, 107])).
% 11.22/7.49 tff(179,plain,
% 11.22/7.49 (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[178, 176])).
% 11.22/7.49 tff(180,plain,
% 11.22/7.49 (((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))) | ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(181,plain,
% 11.22/7.49 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[180, 174])).
% 11.22/7.49 tff(182,plain,
% 11.22/7.49 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(183,plain,
% 11.22/7.49 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[182, 110])).
% 11.22/7.49 tff(184,plain,
% 11.22/7.49 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(185,plain,
% 11.22/7.49 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[184, 183])).
% 11.22/7.49 tff(186,plain,
% 11.22/7.49 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[185, 181])).
% 11.22/7.49 tff(187,plain,
% 11.22/7.49 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(188,plain,
% 11.22/7.49 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.22/7.49 inference(quant_inst,[status(thm)],[])).
% 11.22/7.49 tff(189,plain,
% 11.22/7.49 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.22/7.49 inference(modus_ponens,[status(thm)],[188, 187])).
% 11.22/7.49 tff(190,plain,
% 11.22/7.49 (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[189, 89, 186, 179])).
% 11.22/7.49 tff(191,plain,
% 11.22/7.49 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(192,plain,
% 11.22/7.49 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[191, 190])).
% 11.22/7.49 tff(193,plain,
% 11.22/7.49 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.22/7.49 inference(tautology,[status(thm)],[])).
% 11.22/7.49 tff(194,plain,
% 11.22/7.49 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[193, 192])).
% 11.22/7.49 tff(195,plain,
% 11.22/7.49 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.22/7.49 inference(unit_resolution,[status(thm)],[194, 167])).
% 11.22/7.49 tff(196,plain,
% 11.22/7.49 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.22/7.49 inference(rewrite,[status(thm)],[])).
% 11.22/7.49 tff(197,plain,
% 11.22/7.49 ((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) <=> (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(198,plain,
% 11.33/7.50 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(monotonicity,[status(thm)],[197])).
% 11.33/7.50 tff(199,plain,
% 11.33/7.50 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(transitivity,[status(thm)],[198, 196])).
% 11.33/7.50 tff(200,plain,
% 11.33/7.50 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(quant_inst,[status(thm)],[])).
% 11.33/7.50 tff(201,plain,
% 11.33/7.50 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.33/7.50 inference(modus_ponens,[status(thm)],[200, 199])).
% 11.33/7.50 tff(202,plain,
% 11.33/7.50 ($false),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[201, 89, 195, 158, 156])).
% 11.33/7.50 tff(203,plain,((~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), inference(lemma,lemma(discharge,[]))).
% 11.33/7.50 tff(204,plain,
% 11.33/7.50 (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[203, 107])).
% 11.33/7.50 tff(205,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(206,plain,
% 11.33/7.50 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[205, 119])).
% 11.33/7.50 tff(207,plain,
% 11.33/7.50 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(208,plain,
% 11.33/7.50 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[207, 206])).
% 11.33/7.50 tff(209,plain,
% 11.33/7.50 (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[208, 204])).
% 11.33/7.50 tff(210,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(211,plain,
% 11.33/7.50 (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[210, 209])).
% 11.33/7.50 tff(212,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(213,plain,
% 11.33/7.50 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[212, 209])).
% 11.33/7.50 tff(214,plain,
% 11.33/7.50 (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[139, 213, 211])).
% 11.33/7.50 tff(215,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))))) | ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(216,plain,
% 11.33/7.50 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[215, 149])).
% 11.33/7.50 tff(217,plain,
% 11.33/7.50 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(218,plain,
% 11.33/7.50 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(A!0)))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[217, 216])).
% 11.33/7.50 tff(219,plain,
% 11.33/7.50 (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[218, 214])).
% 11.33/7.50 tff(220,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(221,plain,
% 11.33/7.50 (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[220, 219])).
% 11.33/7.50 tff(222,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))))) | ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(223,plain,
% 11.33/7.50 ((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[222, 165])).
% 11.33/7.50 tff(224,plain,
% 11.33/7.50 (((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))))) | ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(225,plain,
% 11.33/7.50 ((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[224, 174])).
% 11.33/7.50 tff(226,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(227,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[226, 204])).
% 11.33/7.50 tff(228,plain,
% 11.33/7.50 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(229,plain,
% 11.33/7.50 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[228, 227])).
% 11.33/7.50 tff(230,plain,
% 11.33/7.50 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[229, 225])).
% 11.33/7.50 tff(231,plain,
% 11.33/7.50 (g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[189, 89, 179, 230])).
% 11.33/7.50 tff(232,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(233,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[232, 231])).
% 11.33/7.50 tff(234,plain,
% 11.33/7.50 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(235,plain,
% 11.33/7.50 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[234, 233])).
% 11.33/7.50 tff(236,plain,
% 11.33/7.50 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[235, 223])).
% 11.33/7.50 tff(237,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0)))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(238,plain,
% 11.33/7.50 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[237, 219])).
% 11.33/7.50 tff(239,plain,
% 11.33/7.50 ($false),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[201, 89, 238, 236, 221])).
% 11.33/7.50 tff(240,plain,(~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))), inference(lemma,lemma(discharge,[]))).
% 11.33/7.50 tff(241,assumption,(~(g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))), introduced(assumption)).
% 11.33/7.50 tff(242,plain,
% 11.33/7.50 ((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(243,plain,
% 11.33/7.50 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[242, 241])).
% 11.33/7.50 tff(244,plain,
% 11.33/7.50 ((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(245,plain,
% 11.33/7.50 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[244, 241])).
% 11.33/7.50 tff(246,assumption,(~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), introduced(assumption)).
% 11.33/7.50 tff(247,plain,
% 11.33/7.50 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(248,plain,
% 11.33/7.50 ((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) <=> (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(249,plain,
% 11.33/7.50 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))))),
% 11.33/7.50 inference(monotonicity,[status(thm)],[248])).
% 11.33/7.50 tff(250,plain,
% 11.33/7.50 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(transitivity,[status(thm)],[249, 247])).
% 11.33/7.50 tff(251,plain,
% 11.33/7.50 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(quant_inst,[status(thm)],[])).
% 11.33/7.50 tff(252,plain,
% 11.33/7.50 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 11.33/7.50 tff(253,plain,
% 11.33/7.50 (g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[252, 89, 246])).
% 11.33/7.50 tff(254,plain,
% 11.33/7.50 ($false),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[253, 245, 243])).
% 11.33/7.50 tff(255,plain,((g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), inference(lemma,lemma(discharge,[]))).
% 11.33/7.50 tff(256,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[255, 240])).
% 11.33/7.50 tff(257,assumption,(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))), introduced(assumption)).
% 11.33/7.50 tff(258,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(259,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[258, 257])).
% 11.33/7.50 tff(260,plain,
% 11.33/7.50 ((~((~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[228, 259])).
% 11.33/7.50 tff(261,plain,
% 11.33/7.50 (~g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[260, 225])).
% 11.33/7.50 tff(262,plain,
% 11.33/7.50 ((g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(263,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[262, 257])).
% 11.33/7.50 tff(264,plain,
% 11.33/7.50 ((~((~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~(g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))) | g_false_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0)))))))) | (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[184, 263])).
% 11.33/7.50 tff(265,plain,
% 11.33/7.50 (~g_true_only(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[264, 181])).
% 11.33/7.50 tff(266,plain,
% 11.33/7.50 (g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[189, 89, 265, 261])).
% 11.33/7.50 tff(267,assumption,((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))), introduced(assumption)).
% 11.33/7.50 tff(268,plain,
% 11.33/7.50 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(269,plain,
% 11.33/7.50 ((~((~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))) <=> (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(270,plain,
% 11.33/7.50 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))))),
% 11.33/7.50 inference(monotonicity,[status(thm)],[269])).
% 11.33/7.50 tff(271,plain,
% 11.33/7.50 (((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))))),
% 11.33/7.50 inference(transitivity,[status(thm)],[270, 268])).
% 11.33/7.50 tff(272,plain,
% 11.33/7.50 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))),
% 11.33/7.50 inference(quant_inst,[status(thm)],[])).
% 11.33/7.50 tff(273,plain,
% 11.33/7.50 ((~![B: $i] : (~((~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_true_only(B, B) | g_false_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))))),
% 11.33/7.50 inference(modus_ponens,[status(thm)],[272, 271])).
% 11.33/7.50 tff(274,plain,
% 11.33/7.50 ($false),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[273, 56, 267])).
% 11.33/7.50 tff(275,plain,(~((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))), inference(lemma,lemma(discharge,[]))).
% 11.33/7.50 tff(276,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) | ((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(277,plain,
% 11.33/7.50 ((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[276, 275])).
% 11.33/7.50 tff(278,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) | ((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(279,plain,
% 11.33/7.50 ((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[278, 275])).
% 11.33/7.50 tff(280,plain,
% 11.33/7.50 (((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) | ((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))),
% 11.33/7.50 inference(tautology,[status(thm)],[])).
% 11.33/7.50 tff(281,plain,
% 11.33/7.50 ((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))),
% 11.33/7.50 inference(unit_resolution,[status(thm)],[280, 275])).
% 11.33/7.50 tff(282,assumption,(![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))), introduced(assumption)).
% 11.33/7.50 tff(283,plain,
% 11.33/7.50 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | ((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.50 inference(rewrite,[status(thm)],[])).
% 11.33/7.50 tff(284,plain,
% 11.33/7.50 (((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) <=> ((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(285,plain,
% 11.33/7.51 ((~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))) <=> (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(286,plain,
% 11.33/7.51 (((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))) <=> ((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[285])).
% 11.33/7.51 tff(287,plain,
% 11.33/7.51 ((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) <=> (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[286])).
% 11.33/7.51 tff(288,plain,
% 11.33/7.51 (((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) <=> ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[287])).
% 11.33/7.51 tff(289,plain,
% 11.33/7.51 (((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0))))))) <=> ((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.51 inference(transitivity,[status(thm)],[288, 284])).
% 11.33/7.51 tff(290,plain,
% 11.33/7.51 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | ((~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[289])).
% 11.33/7.51 tff(291,plain,
% 11.33/7.51 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)))),
% 11.33/7.51 inference(transitivity,[status(thm)],[290, 283])).
% 11.33/7.51 tff(292,plain,
% 11.33/7.51 ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | ((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0)) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))))),
% 11.33/7.51 inference(quant_inst,[status(thm)],[])).
% 11.33/7.51 tff(293,plain,
% 11.33/7.51 ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))) | (~((~g_both(tptp_fun_B_2(A!0), A!0)) | (~(g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_true_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_false_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~((~g_false_only(tptp_fun_B_2(A!0), A!0)) | (~(g_both(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)) | g_true_only(tptp_fun_B_2(A!0), tptp_fun_B_2(A!0)))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), A!0))),
% 11.33/7.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 11.33/7.51 tff(294,plain,
% 11.33/7.51 ($false),
% 11.33/7.51 inference(unit_resolution,[status(thm)],[293, 282, 281, 279, 277, 257, 266])).
% 11.33/7.51 tff(295,plain,((~g_both(tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))), tptp_fun_A_1(tptp_fun_A_1(tptp_fun_A_1(A!0))))) | (~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))))), inference(lemma,lemma(discharge,[]))).
% 11.33/7.51 tff(296,plain,
% 11.33/7.51 (~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))),
% 11.33/7.51 inference(unit_resolution,[status(thm)],[295, 256])).
% 11.33/7.51 tff(297,plain,
% 11.33/7.51 ((![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))) <=> (![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))) | ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(298,plain,
% 11.33/7.51 (^[B: $i, C_6: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) <=> ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))))), monotonicity(rewrite((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) <=> (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B))))), rewrite((~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))) <=> (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))), (((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))) <=> ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))))), (((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))) <=> (((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))))), rewrite((((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))) <=> ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))), (((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))) <=> ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))))),
% 11.33/7.51 inference(bind,[status(th)],[])).
% 11.33/7.51 tff(299,plain,
% 11.33/7.51 (![B: $i, C_6: $i, A: $i, C: $i] : ((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))) <=> ![B: $i, C_6: $i, A: $i, C: $i] : ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))),
% 11.33/7.51 inference(quant_intro,[status(thm)],[298])).
% 11.33/7.51 tff(300,plain,
% 11.33/7.51 (^[A: $i, B: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) <=> (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))), (((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))) <=> ((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))), ((~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) <=> (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))), ((((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) <=> (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))))), rewrite((((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) <=> ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))), ((((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) <=> ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))))),
% 11.33/7.51 inference(bind,[status(th)],[])).
% 11.33/7.51 tff(301,plain,
% 11.33/7.51 (![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) <=> ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))))),
% 11.33/7.51 inference(quant_intro,[status(thm)],[300])).
% 11.33/7.51 tff(302,plain,
% 11.33/7.51 ((![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))))) <=> (![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[301, 299])).
% 11.33/7.51 tff(303,plain,
% 11.33/7.51 ((![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))))) <=> (![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((~g_both(C, A)) | (~g_both(C, B)) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B))))) | ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))))),
% 11.33/7.51 inference(transitivity,[status(thm)],[302, 297])).
% 11.33/7.51 tff(304,plain,
% 11.33/7.51 ((![A: $i] : (![B: $i] : ((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i] : (![A: $i] : (![C: $i] : ((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ![C: $i] : ((~((~g_false_only(C, tptp_fun_A_5(B))) | (~g_true_only(C, B)))) | (~((~g_true_only(C, tptp_fun_A_5(B))) | (~g_false_only(C, B))))))) <=> (![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i, C_6: $i, A: $i, C: $i] : ((((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ((~((~g_false_only(C_6, tptp_fun_A_5(B))) | (~g_true_only(C_6, B)))) | (~((~g_true_only(C_6, tptp_fun_A_5(B))) | (~g_false_only(C_6, B)))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(305,plain,
% 11.33/7.51 ((![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | (g_both(tptp_fun_B_2(A), A) & (g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_true_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_false_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))) | ![B: $i] : ((g_true_only(B, A!3) & g_true_only(B, B)) | (g_false_only(B, A!3) & g_false_only(B, B))) | ![B: $i] : (![A: $i] : (![C: $i] : (~(g_both(C, A) & g_both(C, B))) | (g_both(tptp_fun_C_4(A, B), A) & (g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_true_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_false_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))) | ![C: $i] : ((g_false_only(C, tptp_fun_A_5(B)) & g_true_only(C, B)) | (g_true_only(C, tptp_fun_A_5(B)) & g_false_only(C, B))))) <=> (![A: $i] : (![B: $i] : ((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_2(A), A)) | (~(g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_true_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | (~((~g_false_only(tptp_fun_B_2(A), A)) | (~(g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!3)) | (~g_true_only(B, B)))) | (~((~g_false_only(B, A!3)) | (~g_false_only(B, B))))) | ![B: $i] : (![A: $i] : (![C: $i] : ((~g_both(C, A)) | (~g_both(C, B))) | (~((~g_both(tptp_fun_C_4(A, B), A)) | (~(g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_true_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))))) | (~((~g_false_only(tptp_fun_C_4(A, B), A)) | (~(g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))))) | ![C: $i] : ((~((~g_false_only(C, tptp_fun_A_5(B))) | (~g_true_only(C, B)))) | (~((~g_true_only(C, tptp_fun_A_5(B))) | (~g_false_only(C, B)))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(306,plain,
% 11.33/7.51 ((![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | ((g_both(tptp_fun_B_2(A), A) & (g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_true_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_false_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))))) | ![B: $i] : ((g_true_only(B, A!3) & g_true_only(B, B)) | (g_false_only(B, A!3) & g_false_only(B, B))) | ![B: $i] : (![A: $i] : (![C: $i] : (~(g_both(C, A) & g_both(C, B))) | ((g_both(tptp_fun_C_4(A, B), A) & (g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_true_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_false_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B))))) | ![C: $i] : ((g_false_only(C, tptp_fun_A_5(B)) & g_true_only(C, B)) | (g_true_only(C, tptp_fun_A_5(B)) & g_false_only(C, B))))) <=> (![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | (g_both(tptp_fun_B_2(A), A) & (g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_true_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_false_only(tptp_fun_B_2(A), tptp_fun_B_2(A)))) | (g_false_only(tptp_fun_B_2(A), A) & (g_both(tptp_fun_B_2(A), tptp_fun_B_2(A)) | g_true_only(tptp_fun_B_2(A), tptp_fun_B_2(A))))) | ![B: $i] : ((g_true_only(B, A!3) & g_true_only(B, B)) | (g_false_only(B, A!3) & g_false_only(B, B))) | ![B: $i] : (![A: $i] : (![C: $i] : (~(g_both(C, A) & g_both(C, B))) | (g_both(tptp_fun_C_4(A, B), A) & (g_false_only(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_true_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_true_only(tptp_fun_C_4(A, B), B))) | (g_false_only(tptp_fun_C_4(A, B), A) & (g_both(tptp_fun_C_4(A, B), B) | g_false_only(tptp_fun_C_4(A, B), B)))) | ![C: $i] : ((g_false_only(C, tptp_fun_A_5(B)) & g_true_only(C, B)) | (g_true_only(C, tptp_fun_A_5(B)) & g_false_only(C, B)))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(307,plain,
% 11.33/7.51 ((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B)))))) <=> (?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(308,plain,
% 11.33/7.51 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B)))))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[307])).
% 11.33/7.51 tff(309,plain,
% 11.33/7.51 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B)))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(310,plain,
% 11.33/7.51 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B)))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(311,plain,
% 11.33/7.51 ((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) <=> (?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))))),
% 11.33/7.51 inference(rewrite,[status(thm)],[])).
% 11.33/7.51 tff(312,plain,
% 11.33/7.51 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))))),
% 11.33/7.51 inference(monotonicity,[status(thm)],[311])).
% 11.33/7.51 tff(313,plain,
% 11.33/7.51 ((~(((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B))))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_true_only(C, A) & g_false_only(C, B)) | (g_false_only(C, A) & g_true_only(C, B)))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))))),
% 11.33/7.52 inference(rewrite,[status(thm)],[])).
% 11.33/7.52 tff(314,plain,
% 11.33/7.52 (~(((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B)))) | (g_false_only(B, A) & (g_true_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B))))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_true_only(C, A) & g_false_only(C, B)) | (g_false_only(C, A) & g_true_only(C, B)))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : (((g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B)))) | (g_false_only(C, A) & (g_false_only(C, B) | g_both(C, B))))))),
% 11.33/7.52 inference(or_elim,[status(thm)],[12])).
% 11.33/7.52 tff(315,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[314, 313])).
% 11.33/7.52 tff(316,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))) & (~?[B: $i] : ![A: $i] : ?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[315, 312])).
% 11.33/7.52 tff(317,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[316, 310])).
% 11.33/7.52 tff(318,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[317, 309])).
% 11.33/7.52 tff(319,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[318, 308])).
% 11.33/7.52 tff(320,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.52 inference(modus_ponens,[status(thm)],[319, 308])).
% 11.33/7.52 tff(321,plain,
% 11.33/7.52 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.53 inference(modus_ponens,[status(thm)],[320, 308])).
% 11.33/7.53 tff(322,plain,
% 11.33/7.53 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_true_only(B, B) | g_false_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_false_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_true_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_true_only(B, B)) | (g_false_only(B, A) & g_false_only(B, B)))) & ?[B: $i] : (?[A: $i] : (?[C: $i] : (g_both(C, A) & g_both(C, B)) & (~?[C: $i] : ((g_both(C, A) & (g_false_only(C, B) | g_true_only(C, B))) | (g_true_only(C, A) & (g_both(C, B) | g_true_only(C, B))) | (g_false_only(C, A) & (g_both(C, B) | g_false_only(C, B)))))) & (~?[A: $i] : ![C: $i] : ((g_false_only(C, A) & g_true_only(C, B)) | (g_true_only(C, A) & g_false_only(C, B))))))),
% 11.33/7.53 inference(modus_ponens,[status(thm)],[321, 308])).
% 11.33/7.53 unexpected number of arguments: (let ((a!1 (exists ((A $i))
% 11.33/7.53 (let ((a!1 (exists ((B $i)) (and (g_both B A) (g_both B B))))
% 11.33/7.53 (a!2 (exists ((B $i))
% 11.33/7.53 (or (and (g_both B A)
% 11.33/7.53 (or (g_true_only B B) (g_false_only B B)))
% 11.33/7.53 (and (g_true_only B A)
% 11.33/7.53 (or (g_both B B) (g_false_only B B)))
% 11.33/7.53 (and (g_false_only B A)
% 11.33/7.53 (or (g_both B B) (g_true_only B B)))))))
% 11.33/7.53 (and a!1 (not a!2)))))
% 11.33/7.53 (a!2 (forall ((A $i))
% 11.33/7.53 (let ((a!1 (forall ((B $i)) (not (and (g_both B A) (g_both B B)))))
% 11.33/7.53 (a!2 (and (g_both (B!2 A) A)
% 11.33/7.53 (or (g_true_only (B!2 A) (B!2 A))
% 11.33/7.53 (g_false_only (B!2 A) (B!2 A)))))
% 11.33/7.53 (a!3 (and (g_true_only (B!2 A) A)
% 11.33/7.53 (or (g_both (B!2 A) (B!2 A))
% 11.33/7.53 (g_false_only (B!2 A) (B!2 A)))))
% 11.33/7.53 (a!4 (and (g_false_only (B!2 A) A)
% 11.33/7.53 (or (g_both (B!2 A) (B!2 A))
% 11.33/7.53 (g_true_only (B!2 A) (B!2 A))))))
% 11.33/7.53 (or a!1 (or a!2 a!3 a!4)))))
% 11.33/7.53 (a!4 (exists ((A $i))
% 11.33/7.53 (forall ((B $i))
% 11.33/7.53 (or (and (g_true_only B A) (g_true_only B B))
% 11.33/7.53 (and (g_false_only B A) (g_false_only B B))))))
% 11.33/7.53 (a!5 (forall ((B $i))
% 11.33/7.53 (or (and (g_true_only B A!3) (g_true_only B B))
% 11.33/7.53 (and (g_false_only B A!3) (g_false_only B B)))))
% 11.33/7.53 (a!6 (proof-bind (lambda ((B $i))
% 11.33/7.53 (let ((a!1 (or (and (g_true_only B A!3)
% 11.33/7.53 (g_true_only B B))
% 11.33/7.53 (and (g_false_only B A!3)
% 11.33/7.53 (g_false_only B B)))))
% 11.33/7.53 (refl (~ a!1 a!1))))))
% 11.33/7.53 (a!8 (exists ((B $i))
% 11.33/7.53 (let ((a!1 (exists ((A $i))
% 11.33/7.53 (let ((a!1 (exists ((C $i))
% 11.33/7.53 (and (g_both C A) (g_both C B))))
% 11.33/7.53 (a!2 (exists ((C $i))
% 11.33/7.53 (or (and (g_both C A)
% 11.33/7.53 (or (g_false_only C B)
% 11.33/7.53 (g_true_only C B)))
% 11.33/7.53 (and (g_true_only C A)
% 11.33/7.53 (or (g_both C B)
% 11.33/7.53 (g_true_only C B)))
% 11.33/7.53 (and (g_false_only C A)
% 11.33/7.53 (or (g_both C B)
% 11.33/7.53 (g_false_only C B)))))))
% 11.33/7.53 (and a!1 (not a!2)))))
% 11.33/7.53 (a!2 (exists ((A $i))
% 11.33/7.53 (forall ((C $i))
% 11.33/7.53 (or (and (g_false_only C A) (g_true_only C B))
% 11.33/7.53 (and (g_true_only C A) (g_false_only C B)))))))
% 11.33/7.53 (and a!1 (not a!2)))))
% 11.33/7.53 (a!9 (forall ((B $i))
% 11.33/7.53 (let ((a!1 (forall ((A $i))
% 11.33/7.53 (let ((a!1 (forall ((C $i))
% 11.33/7.53 (not (and (g_both C A) (g_both C B)))))
% 11.33/7.53 (a!2 (and (g_both (C!4 A B) A)
% 11.33/7.53 (or (g_false_only (C!4 A B) B)
% 11.33/7.53 (g_true_only (C!4 A B) B))))
% 11.33/7.53 (a!3 (and (g_true_only (C!4 A B) A)
% 11.33/7.53 (or (g_both (C!4 A B) B)
% 11.33/7.53 (g_true_only (C!4 A B) B))))
% 11.33/7.53 (a!4 (and (g_false_only (C!4 A B) A)
% 11.33/7.53 (or (g_both (C!4 A B) B)
% 11.33/7.53 (g_false_only (C!4 A B) B)))))
% 11.33/7.53 (or a!1 (or a!2 a!3 a!4)))))
% 11.33/7.53 (a!2 (forall ((C $i))
% 11.33/7.53 (or (and (g_false_only C (A!5 B)) (g_true_only C B))
% 11.33/7.53 (and (g_true_only C (A!5 B)) (g_false_only C B))))))
% 11.33/7.53 (or a!1 a!2)))))
% 11.33/7.53 (let ((a!3 (nnf-neg (proof-bind (lambda ((A $i))
% 11.33/7.53 (let ((a!1 (exists ((B $i))
% 11.33/7.53 (and (g_both B A) (g_both B B))))
% 11.33/7.53 (a!2 (forall ((B $i))
% 11.33/7.53 (not (and (g_both B A)
% 11.33/7.53 (g_both B B)))))
% 11.33/7.53 (a!4 (exists ((B $i))
% 11.33/7.53 (or (and (g_both B A)
% 11.33/7.53 (or (g_true_only B B)
% 11.33/7.53 (g_false_only B B)))
% 11.33/7.53 (and (g_true_only B A)
% 11.33/7.53 (or (g_both B B)
% 11.33/7.53 (g_false_only B B)))
% 11.33/7.53 (and (g_false_only B A)
% 11.33/7.53 (or (g_both B B)
% 11.33/7.53 (g_true_only B B))))))
% 11.33/7.53 (a!5 (and (g_both (B!2 A) A)
% 11.33/7.53 (or (g_true_only (B!2 A)
% 11.33/7.53 (B!2 A))
% 11.33/7.53 (g_false_only (B!2 A)
% 11.33/7.53 (B!2 A)))))
% 11.33/7.53 (a!6 (and (g_true_only (B!2 A) A)
% 11.33/7.53 (or (g_both (B!2 A) (B!2 A))
% 11.33/7.53 (g_false_only (B!2 A)
% 11.33/7.53 (B!2 A)))))
% 11.33/7.53 (a!7 (and (g_false_only (B!2 A) A)
% 11.33/7.53 (or (g_both (B!2 A) (B!2 A))
% 11.33/7.53 (g_true_only (B!2 A)
% 11.33/7.53 (B!2 A))))))
% 11.33/7.53 (let ((a!3 (nnf-neg (proof-bind (lambda ((B $i))
% 11.33/7.53 (let ((a!1 (~ (not (and (g_both B
% 11.33/7.53 A)
% 11.33/7.53 (g_both B
% 11.33/7.53 B)))
% 11.33/7.53 (not (and (g_both B
% 11.33/7.53 A)
% 11.33/7.53 (g_both B
% 11.33/7.53 B))))))
% 11.33/7.53 (refl a!1))))
% 11.33/7.53 (~ (not a!1) a!2)))
% 11.33/7.53 (a!8 (nnf-neg (sk (~ a!4
% 11.33/7.53 (or a!5 a!6 a!7)))
% 11.33/7.53 (~ (not (not a!4))
% 11.33/7.53 (or a!5 a!6 a!7))))
% 11.33/7.53 (a!9 (~ (not (and a!1 (not a!4)))
% 11.33/7.53 (or a!2 (or a!5 a!6 a!7)))))
% 11.33/7.53 (nnf-neg a!3 a!8 a!9)))))
% 11.33/7.53 (~ (not a!1) a!2)))
% 11.33/7.53 (a!7 (nnf-neg (trans (sk (~ a!4 a!5))
% 11.33/7.53 (nnf-pos a!6 (~ a!5 a!5))
% 11.33/7.53 (~ a!4 a!5))
% 11.33/7.53 (~ (not (not a!4)) a!5)))
% 11.33/7.53 (a!10 (nnf-neg (proof-bind (lambda ((B $i))
% 11.33/7.53 (let ((a!1 (exists ((A $i))
% 11.33/7.53 (let ((a!1 (exists ((C $i))
% 11.33/7.53 (and (g_both C A)
% 11.33/7.53 (g_both C B))))
% 11.33/7.53 (a!2 (exists ((C $i))
% 11.33/7.53 (or (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_false_only C
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only C
% 11.33/7.53 B)))
% 11.33/7.53 (and (g_true_only C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both C
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only C
% 11.33/7.53 B)))
% 11.33/7.53 (and (g_false_only C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both C
% 11.33/7.53 B)
% 11.33/7.53 (g_false_only C
% 11.33/7.53 B)))))))
% 11.33/7.53 (and a!1 (not a!2)))))
% 11.33/7.53 (a!2 (forall ((A $i))
% 11.33/7.53 (let ((a!1 (forall ((C $i))
% 11.33/7.53 (not (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (g_both C
% 11.33/7.53 B)))))
% 11.33/7.53 (a!2 (and (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B))))
% 11.33/7.53 (a!3 (and (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B))))
% 11.33/7.53 (a!4 (and (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)))))
% 11.33/7.53 (or a!1 (or a!2 a!3 a!4)))))
% 11.33/7.53 (a!4 (exists ((A $i))
% 11.33/7.53 (forall ((C $i))
% 11.33/7.53 (or (and (g_false_only C A)
% 11.33/7.53 (g_true_only C B))
% 11.33/7.53 (and (g_true_only C A)
% 11.33/7.53 (g_false_only C B))))))
% 11.33/7.53 (a!5 (forall ((C $i))
% 11.33/7.53 (or (and (g_false_only C
% 11.33/7.53 (A!5 B))
% 11.33/7.53 (g_true_only C B))
% 11.33/7.53 (and (g_true_only C (A!5 B))
% 11.33/7.53 (g_false_only C B)))))
% 11.33/7.53 (a!6 (proof-bind (lambda ((C $i))
% 11.33/7.53 (let ((a!1 (or (and (g_false_only C
% 11.33/7.53 (A!5 B))
% 11.33/7.53 (g_true_only C
% 11.33/7.53 B))
% 11.33/7.53 (and (g_true_only C
% 11.33/7.53 (A!5 B))
% 11.33/7.53 (g_false_only C
% 11.33/7.53 B)))))
% 11.33/7.53 (refl (~ a!1 a!1)))))))
% 11.33/7.53 (let ((a!3 (nnf-neg (proof-bind (lambda ((A $i))
% 11.33/7.53 (let ((a!1 (exists ((C $i))
% 11.33/7.53 (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (g_both C
% 11.33/7.53 B))))
% 11.33/7.53 (a!2 (forall ((C $i))
% 11.33/7.53 (not (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (g_both C
% 11.33/7.53 B)))))
% 11.33/7.53 (a!4 (exists ((C $i))
% 11.33/7.53 (or (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_false_only C
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only C
% 11.33/7.53 B)))
% 11.33/7.53 (and (g_true_only C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both C
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only C
% 11.33/7.53 B)))
% 11.33/7.53 (and (g_false_only C
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both C
% 11.33/7.53 B)
% 11.33/7.53 (g_false_only C
% 11.33/7.53 B))))))
% 11.33/7.53 (a!5 (and (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B))))
% 11.33/7.53 (a!6 (and (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_true_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B))))
% 11.33/7.53 (a!7 (and (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 A)
% 11.33/7.53 (or (g_both (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)
% 11.33/7.53 (g_false_only (C!4 A
% 11.33/7.53 B)
% 11.33/7.53 B)))))
% 11.33/7.53 (let ((a!3 (nnf-neg (proof-bind (lambda ((C $i))
% 11.33/7.53 (let ((a!1 (~ (not (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (g_both C
% 11.33/7.53 B)))
% 11.33/7.53 (not (and (g_both C
% 11.33/7.53 A)
% 11.33/7.53 (g_both C
% 11.33/7.53 B))))))
% 11.33/7.53 (refl a!1))))
% 11.33/7.53 (~ (not a!1)
% 11.33/7.53 a!2)))
% 11.33/7.53 (a!8 (nnf-neg (sk (~ a!4
% 11.33/7.53 (or a!5
% 11.33/7.53 a!6
% 11.33/7.53 a!7)))
% 11.33/7.53 (~ (not (not a!4))
% 11.33/7.53 (or a!5
% 11.33/7.53 a!6
% 11.33/7.53 a!7))))
% 11.33/7.53 (a!9 (~ (not (and a!1
% 11.33/7.53 (not a!4)))
% 11.33/7.53 (or a!2
% 11.33/7.53 (or a!5
% 11.33/7.53 a!6
% 11.33/7.53 a!7)))))
% 11.33/7.53 (nnf-neg a!3
% 11.33/7.53 a!8
% 11.33/7.53 a!9)))))
% 11.33/7.53 (~ (not a!1) a!2)))
% 11.33/7.53 (a!7 (nnf-neg (trans (sk (~ a!4 a!5))
% 11.33/7.53 (nnf-pos a!6
% 11.33/7.53 (~ a!5
% 11.33/7.53 a!5))
% 11.33/7.53 (~ a!4 a!5))
% 11.33/7.53 (~ (not (not a!4)) a!5)))
% 11.33/7.53 (a!8 (~ (not (and a!1 (not a!4)))
% 11.33/7.53 (or a!2 a!5))))
% 11.33/7.53 (nnf-neg a!3 a!7 a!8)))))
% 11.33/7.53 (~ (not a!8) a!9)))
% 11.33/7.53 (a!11 (~ (not (and a!1 (not a!4) a!8)) (or a!2 a!5 a!9))))
% 11.33/7.53 (nnf-neg a!3 a!7 a!10 a!11)))
% 11.33/7.53 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------