TSTP Solution File: SEV515+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Tue Sep 20 08:12:46 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 19:13:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(g_true_only_type, type, (
% 0.12/0.40 g_true_only: ( $i * $i ) > $o)).
% 0.12/0.40 tff(g_false_only_type, type, (
% 0.12/0.40 g_false_only: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_A_2_type, type, (
% 0.12/0.40 tptp_fun_A_2: $i)).
% 0.12/0.40 tff(tptp_fun_A_0_type, type, (
% 0.12/0.40 tptp_fun_A_0: $i)).
% 0.12/0.40 tff(g_both_type, type, (
% 0.12/0.40 g_both: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_B_1_type, type, (
% 0.12/0.40 tptp_fun_B_1: $i > $i)).
% 0.12/0.40 tff(1,assumption,(g_true_only(A!0, A!0)), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 ((g_both(A!0, A!0) | g_true_only(A!0, A!0)) | (~g_true_only(A!0, A!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (g_both(A!0, A!0) | g_true_only(A!0, A!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.40 tff(4,assumption,((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))), introduced(assumption)).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (^[B: $i] : refl((~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B))))))) <=> (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B))))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (^[B: $i] : rewrite((~((g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))))) <=> (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![B: $i] : (~((g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[B: $i] : rewrite((~((g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))))) <=> (~((g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![B: $i] : (~((g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))))) <=> ![B: $i] : (~((g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ((~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))) <=> (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ((~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, B))))) <=> (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(13,axiom,(~(![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, 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_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nc1')).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, B))))),
% 0.12/0.40 inference(or_elim,[status(thm)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (~![A: $i] : ?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.12/0.40 tff(22,plain,(
% 0.12/0.40 $oeq((~?[B: $i] : ((g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))))), ![B: $i] : (~((g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))))))),
% 0.12/0.40 inference(transitivity,[status(sab)],[21])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![B: $i] : (~((g_true_only(B, A!0) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A!0) & (g_both(B, B) | g_false_only(B, B))) | (g_both(B, A!0) & (g_false_only(B, B) | g_true_only(B, B)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 8])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 6])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((~((~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0))))))) <=> (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 25, 4])).
% 0.19/0.41 tff(33,plain,(~((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))) | ((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[37, 3, 1])).
% 0.19/0.41 tff(39,plain,(~g_true_only(A!0, A!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(40,assumption,(g_false_only(A!0, A!0)), introduced(assumption)).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((g_both(A!0, A!0) | g_false_only(A!0, A!0)) | (~g_false_only(A!0, A!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (g_both(A!0, A!0) | g_false_only(A!0, A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~((~g_true_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_true_only(A!0, A!0))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, A!0) | g_true_only(A!0, A!0)))))) | ((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 33])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((~((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0))))) | (~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~g_false_only(A!0, A!0)) | (~(g_both(A!0, A!0) | g_false_only(A!0, A!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 42, 40])).
% 0.19/0.41 tff(48,plain,(~g_false_only(A!0, A!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(49,assumption,(~g_true_only(A!0, A!0)), introduced(assumption)).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0))) | g_true_only(A!0, A!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,assumption,(~g_false_only(A!0, A!0)), introduced(assumption)).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2))) | g_false_only(A!0, A!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.41 tff(55,assumption,(![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))), introduced(assumption)).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | ((~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))) <=> ((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | (~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~((~g_true_only(A!0, A!2)) | (~g_false_only(A!0, A!0)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0))))) <=> ((~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | ((~((~g_true_only(A!0, A!2)) | (~g_false_only(A!0, A!0)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))) <=> ((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | ((~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | ((~((~g_true_only(A!0, A!2)) | (~g_false_only(A!0, A!0)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))) <=> ((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | (~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | ((~((~g_true_only(A!0, A!2)) | (~g_false_only(A!0, A!0)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | (~((~g_false_only(A!0, A!0)) | (~g_true_only(A!0, A!2)))) | (~((~g_false_only(A!0, A!2)) | (~g_true_only(A!0, A!0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 55, 54, 51])).
% 0.19/0.41 tff(63,plain,(g_true_only(A!0, A!0) | (~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) | g_false_only(A!0, A!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (~![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[63, 48, 39])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[X_2: $i, X_1: $i] : refl((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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![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_true_only(X_2, X_1) | g_both(X_2, X_1) | g_false_only(X_2, X_1))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![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_true_only(X_2, X_1) | g_both(X_2, X_1) | g_false_only(X_2, X_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (^[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_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)) <=> (g_true_only(X_2, X_1) | g_both(X_2, X_1) | g_false_only(X_2, X_1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![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_true_only(X_2, X_1) | g_both(X_2, X_1) | g_false_only(X_2, X_1))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.41 tff(70,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')).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.41 tff(73,plain,(
% 0.19/0.41 ![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))),
% 0.19/0.41 inference(skolemize,[status(sab)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~![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))) | (g_true_only(A!0, A!0) | g_both(A!0, A!0) | g_false_only(A!0, A!0))) <=> ((~![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))) | g_true_only(A!0, A!0) | g_both(A!0, A!0) | g_false_only(A!0, A!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~![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))) | (g_true_only(A!0, A!0) | g_both(A!0, A!0) | g_false_only(A!0, A!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![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))) | g_true_only(A!0, A!0) | g_both(A!0, A!0) | g_false_only(A!0, A!0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (g_true_only(A!0, A!0) | g_both(A!0, A!0) | g_false_only(A!0, A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (g_both(A!0, A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 48, 39])).
% 0.19/0.41 tff(80,assumption,((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))), introduced(assumption)).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((~((~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))) <=> (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~(g_both(B, B) | g_true_only(B, B))))) | (~((~g_false_only(B, A!0)) | (~(g_both(B, B) | g_false_only(B, B))))) | (~((~g_both(B, A!0)) | (~(g_false_only(B, B) | g_true_only(B, B)))))))) | (~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 25, 80])).
% 0.19/0.42 tff(88,plain,(~((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))) | ((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))) | ((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))) | ((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.19/0.42 tff(95,assumption,(g_both(A!0, A!0)), introduced(assumption)).
% 0.19/0.42 tff(96,assumption,(![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))), introduced(assumption)).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | ((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0)))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~g_both(A!0, A!0)) | (~g_both(A!0, A!0)) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0))))))) <=> ((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | ((~g_both(A!0, A!0)) | (~g_both(A!0, A!0)) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | ((~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | ((~g_both(A!0, A!0)) | (~g_both(A!0, A!0)) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | ((~g_both(A!0, A!0)) | (~g_both(A!0, A!0)) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))) | (~((~g_both(tptp_fun_B_1(A!0), A!0)) | (~(g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_true_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_true_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~((~g_false_only(tptp_fun_B_1(A!0), A!0)) | (~(g_both(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)) | g_false_only(tptp_fun_B_1(A!0), tptp_fun_B_1(A!0)))))) | (~g_both(A!0, A!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 96, 95, 94, 92, 90])).
% 0.19/0.42 tff(104,plain,((~g_both(A!0, A!0)) | (~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (~![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 79])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) <=> (![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B))))) | ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) <=> ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) <=> ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) <=> (![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) <=> (![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B))))) | ![A: $i, B: $i] : ((~g_both(B, B)) | (~g_both(B, A)) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[109, 106])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((![A: $i] : (![B: $i] : ((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B)))))) <=> (![A: $i, B: $i] : (((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | (g_both(tptp_fun_B_1(A), A) & (g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_true_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_false_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))) | ![B: $i] : ((g_true_only(B, A!2) & g_false_only(B, B)) | (g_false_only(B, A!2) & g_true_only(B, B)))) <=> (![A: $i] : (![B: $i] : ((~g_both(B, B)) | (~g_both(B, A))) | (~((~g_both(tptp_fun_B_1(A), A)) | (~(g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_true_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | (~((~g_false_only(tptp_fun_B_1(A), A)) | (~(g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))))) | ![B: $i] : ((~((~g_true_only(B, A!2)) | (~g_false_only(B, B)))) | (~((~g_false_only(B, A!2)) | (~g_true_only(B, B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | ((g_both(tptp_fun_B_1(A), A) & (g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_true_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_false_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))))) | ![B: $i] : ((g_true_only(B, A!2) & g_false_only(B, B)) | (g_false_only(B, A!2) & g_true_only(B, B)))) <=> (![A: $i] : (![B: $i] : (~(g_both(B, A) & g_both(B, B))) | (g_both(tptp_fun_B_1(A), A) & (g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_true_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_true_only(tptp_fun_B_1(A), tptp_fun_B_1(A)))) | (g_false_only(tptp_fun_B_1(A), A) & (g_both(tptp_fun_B_1(A), tptp_fun_B_1(A)) | g_false_only(tptp_fun_B_1(A), tptp_fun_B_1(A))))) | ![B: $i] : ((g_true_only(B, A!2) & g_false_only(B, B)) | (g_false_only(B, A!2) & g_true_only(B, B))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B))))) <=> (?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : (((g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B)))) | (g_false_only(B, A) & (g_false_only(B, B) | g_both(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(or_elim,[status(thm)],[13])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[121, 115])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[123, 115])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & g_both(B, B)) & (~?[B: $i] : ((g_both(B, A) & (g_false_only(B, B) | g_true_only(B, B))) | (g_true_only(B, A) & (g_both(B, B) | g_true_only(B, B))) | (g_false_only(B, A) & (g_both(B, B) | g_false_only(B, B)))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & g_false_only(B, B)) | (g_false_only(B, A) & g_true_only(B, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[124, 115])).
% 0.19/0.44 unexpected number of arguments: (let ((a!1 (exists ((A $i))
% 0.19/0.44 (let ((a!1 (exists ((B $i)) (and (g_both B A) (g_both B B))))
% 0.19/0.44 (a!2 (exists ((B $i))
% 0.19/0.44 (or (and (g_both B A)
% 0.19/0.44 (or (g_false_only B B) (g_true_only B B)))
% 0.19/0.44 (and (g_true_only B A)
% 0.19/0.44 (or (g_both B B) (g_true_only B B)))
% 0.19/0.44 (and (g_false_only B A)
% 0.19/0.44 (or (g_both B B) (g_false_only B B)))))))
% 0.19/0.44 (and a!1 (not a!2)))))
% 0.19/0.44 (a!2 (forall ((A $i))
% 0.19/0.44 (let ((a!1 (forall ((B $i)) (not (and (g_both B A) (g_both B B)))))
% 0.19/0.44 (a!2 (and (g_both (B!1 A) A)
% 0.19/0.44 (or (g_false_only (B!1 A) (B!1 A))
% 0.19/0.44 (g_true_only (B!1 A) (B!1 A)))))
% 0.19/0.44 (a!3 (and (g_true_only (B!1 A) A)
% 0.19/0.44 (or (g_both (B!1 A) (B!1 A))
% 0.19/0.44 (g_true_only (B!1 A) (B!1 A)))))
% 0.19/0.44 (a!4 (and (g_false_only (B!1 A) A)
% 0.19/0.44 (or (g_both (B!1 A) (B!1 A))
% 0.19/0.44 (g_false_only (B!1 A) (B!1 A))))))
% 0.19/0.44 (or a!1 (or a!2 a!3 a!4)))))
% 0.19/0.44 (a!4 (exists ((A $i))
% 0.19/0.44 (forall ((B $i))
% 0.19/0.44 (or (and (g_true_only B A) (g_false_only B B))
% 0.19/0.44 (and (g_false_only B A) (g_true_only B B))))))
% 0.19/0.44 (a!5 (forall ((B $i))
% 0.19/0.44 (or (and (g_true_only B A!2) (g_false_only B B))
% 0.19/0.44 (and (g_false_only B A!2) (g_true_only B B)))))
% 0.19/0.44 (a!6 (proof-bind (lambda ((B $i))
% 0.19/0.44 (let ((a!1 (or (and (g_true_only B A!2)
% 0.19/0.44 (g_false_only B B))
% 0.19/0.44 (and (g_false_only B A!2)
% 0.19/0.44 (g_true_only B B)))))
% 0.19/0.44 (refl (~ a!1 a!1)))))))
% 0.19/0.44 (let ((a!3 (nnf-neg (proof-bind (lambda ((A $i))
% 0.19/0.44 (let ((a!1 (exists ((B $i))
% 0.19/0.44 (and (g_both B A) (g_both B B))))
% 0.19/0.44 (a!2 (forall ((B $i))
% 0.19/0.44 (not (and (g_both B A)
% 0.19/0.44 (g_both B B)))))
% 0.19/0.44 (a!4 (exists ((B $i))
% 0.19/0.44 (or (and (g_both B A)
% 0.19/0.44 (or (g_false_only B B)
% 0.19/0.44 (g_true_only B B)))
% 0.19/0.44 (and (g_true_only B A)
% 0.19/0.44 (or (g_both B B)
% 0.19/0.44 (g_true_only B B)))
% 0.19/0.44 (and (g_false_only B A)
% 0.19/0.44 (or (g_both B B)
% 0.19/0.44 (g_false_only B B))))))
% 0.19/0.44 (a!5 (and (g_both (B!1 A) A)
% 0.19/0.44 (or (g_false_only (B!1 A)
% 0.19/0.44 (B!1 A))
% 0.19/0.44 (g_true_only (B!1 A)
% 0.19/0.44 (B!1 A)))))
% 0.19/0.44 (a!6 (and (g_true_only (B!1 A) A)
% 0.19/0.44 (or (g_both (B!1 A) (B!1 A))
% 0.19/0.44 (g_true_only (B!1 A)
% 0.19/0.44 (B!1 A)))))
% 0.19/0.44 (a!7 (and (g_false_only (B!1 A) A)
% 0.19/0.44 (or (g_both (B!1 A) (B!1 A))
% 0.19/0.44 (g_false_only (B!1 A)
% 0.19/0.44 (B!1 A))))))
% 0.19/0.44 (let ((a!3 (nnf-neg (proof-bind (lambda ((B $i))
% 0.19/0.44 (let ((a!1 (~ (not (and (g_both B
% 0.19/0.44 A)
% 0.19/0.44 (g_both B
% 0.19/0.44 B)))
% 0.19/0.44 (not (and (g_both B
% 0.19/0.44 A)
% 0.19/0.44 (g_both B
% 0.19/0.44 B))))))
% 0.19/0.44 (refl a!1))))
% 0.19/0.44 (~ (not a!1) a!2)))
% 0.19/0.44 (a!8 (nnf-neg (sk (~ a!4
% 0.19/0.44 (or a!5 a!6 a!7)))
% 0.19/0.44 (~ (not (not a!4))
% 0.19/0.44 (or a!5 a!6 a!7))))
% 0.19/0.44 (a!9 (~ (not (and a!1 (not a!4)))
% 0.19/0.44 (or a!2 (or a!5 a!6 a!7)))))
% 0.19/0.44 (nnf-neg a!3 a!8 a!9)))))
% 0.19/0.44 (~ (not a!1) a!2)))
% 0.19/0.44 (a!7 (nnf-neg (trans (sk (~ a!4 a!5))
% 0.19/0.44 (nnf-pos a!6 (~ a!5 a!5))
% 0.19/0.44 (~ a!4 a!5))
% 0.19/0.44 (~ (not (not a!4)) a!5)))
% 0.19/0.44 (a!8 (~ (not (and a!1 (not a!4))) (or a!2 a!5))))
% 0.19/0.44 (nnf-neg a!3 a!7 a!8)))
% 0.19/0.44 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------