TSTP Solution File: SYO607+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 01:41:03 EDT 2022
% Result : Theorem 0.71s 0.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.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 : Mon Sep 5 15:50:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.71/0.74 % SZS status Theorem
% 0.71/0.74 % SZS output start Proof
% 0.71/0.74 tff(g_both_type, type, (
% 0.71/0.74 g_both: ( $i * $i ) > $o)).
% 0.71/0.74 tff(tptp_fun_B_0_type, type, (
% 0.71/0.74 tptp_fun_B_0: $i > $i)).
% 0.71/0.74 tff(a_type, type, (
% 0.71/0.74 a: $i)).
% 0.71/0.74 tff(g_false_only_type, type, (
% 0.71/0.74 g_false_only: ( $i * $i ) > $o)).
% 0.71/0.74 tff(tptp_fun_B_1_type, type, (
% 0.71/0.74 tptp_fun_B_1: $i > $i)).
% 0.71/0.74 tff(g_true_only_type, type, (
% 0.71/0.74 g_true_only: ( $i * $i ) > $o)).
% 0.71/0.74 tff(1,plain,
% 0.71/0.74 ((~?[A: $i] : ![B: $i] : g_true_only(A, B)) <=> (~?[A: $i] : ![B: $i] : g_true_only(A, B))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(2,axiom,(~((?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)) | ?[A: $i] : ![B: $i] : g_true_only(A, B)) | (((?[A: $i] : (((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A))) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nc6')).
% 0.71/0.74 tff(3,plain,
% 0.71/0.74 (~(?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)) | ?[A: $i] : ![B: $i] : g_true_only(A, B))),
% 0.71/0.74 inference(or_elim,[status(thm)],[2])).
% 0.71/0.74 tff(4,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(or_elim,[status(thm)],[3])).
% 0.71/0.74 tff(5,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.71/0.74 tff(6,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.71/0.74 tff(7,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.71/0.74 tff(8,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.71/0.74 tff(9,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.71/0.74 tff(10,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.71/0.74 tff(11,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.71/0.74 tff(12,plain,
% 0.71/0.74 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.71/0.74 tff(13,plain,
% 0.71/0.74 (^[A: $i] : sk($oeq((~![B: $i] : g_true_only(A, B)), (~g_true_only(A, tptp_fun_B_0(A)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(14,plain,(
% 0.71/0.74 ![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))),
% 0.71/0.74 inference(nnf-neg,[status(sab)],[12, 13])).
% 0.71/0.74 tff(15,plain,
% 0.71/0.74 ((~![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))) | (~g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(16,plain,
% 0.71/0.74 (~g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.71/0.74 tff(17,assumption,(![B: $i] : g_true_only(tptp_fun_B_0(a), B)), introduced(assumption)).
% 0.71/0.74 tff(18,plain,
% 0.71/0.74 ((~![B: $i] : g_true_only(tptp_fun_B_0(a), B)) | g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(19,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.71/0.74 tff(20,plain,(~![B: $i] : g_true_only(tptp_fun_B_0(a), B)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(21,assumption,(![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))), introduced(assumption)).
% 0.71/0.74 tff(22,assumption,(g_both(a, tptp_fun_B_0(a))), introduced(assumption)).
% 0.71/0.74 tff(23,plain,
% 0.71/0.74 (((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(a, tptp_fun_B_0(a))) | g_false_only(a, tptp_fun_B_1(a)))) <=> ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(a, tptp_fun_B_0(a))) | g_false_only(a, tptp_fun_B_1(a)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(24,plain,
% 0.71/0.74 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(a, tptp_fun_B_0(a))) | g_false_only(a, tptp_fun_B_1(a)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(25,plain,
% 0.71/0.74 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(a, tptp_fun_B_0(a))) | g_false_only(a, tptp_fun_B_1(a))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.71/0.74 tff(26,plain,
% 0.71/0.74 (g_false_only(a, tptp_fun_B_1(a))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[25, 21, 22])).
% 0.71/0.74 tff(27,plain,
% 0.71/0.74 (^[A: $i] : refl(((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))) <=> ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(28,plain,
% 0.71/0.74 (![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))) <=> ![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[27])).
% 0.71/0.74 tff(29,plain,
% 0.71/0.74 (^[A: $i] : rewrite(((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))) <=> ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(30,plain,
% 0.71/0.74 (![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))) <=> ![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[29])).
% 0.71/0.74 tff(31,plain,
% 0.71/0.74 (![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B))) <=> ![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[30, 28])).
% 0.71/0.74 tff(32,plain,
% 0.71/0.74 ((~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) <=> (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(33,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(or_elim,[status(thm)],[3])).
% 0.71/0.74 tff(34,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.71/0.74 tff(35,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.71/0.74 tff(36,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.71/0.74 tff(37,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.71/0.74 tff(38,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.71/0.74 tff(39,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.71/0.74 tff(40,plain,
% 0.71/0.74 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.71/0.74 tff(41,plain,
% 0.71/0.74 (^[A: $i] : nnf_neg(refl($oeq((~g_false_only(a, A)), (~g_false_only(a, A)))), nnf_neg(proof_bind(^[B: $i] : refl($oeq((~g_false_only(A, B)), (~g_false_only(A, B))))), $oeq((~?[B: $i] : g_false_only(A, B)), ![B: $i] : (~g_false_only(A, B)))), $oeq((~(g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))), ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(42,plain,(
% 0.71/0.74 ![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.71/0.74 inference(nnf-neg,[status(sab)],[40, 41])).
% 0.71/0.74 tff(43,plain,
% 0.71/0.74 (![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[42, 31])).
% 0.71/0.74 tff(44,plain,
% 0.71/0.74 (((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B)))) <=> ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(45,plain,
% 0.71/0.74 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(46,plain,
% 0.71/0.74 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.71/0.74 tff(47,plain,
% 0.71/0.74 (![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[46, 43, 26])).
% 0.71/0.74 tff(48,assumption,(g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))), introduced(assumption)).
% 0.71/0.74 tff(49,assumption,(![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))), introduced(assumption)).
% 0.71/0.74 tff(50,plain,
% 0.71/0.74 ((~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))) | (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(51,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[50, 49, 48])).
% 0.71/0.74 tff(52,plain,((~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))) | (~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(53,plain,
% 0.71/0.74 (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.71/0.74 tff(54,plain,
% 0.71/0.74 (((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a))))) <=> ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(55,plain,
% 0.71/0.74 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(56,plain,
% 0.71/0.74 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.71/0.74 tff(57,plain,
% 0.71/0.74 ((~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[56, 21])).
% 0.71/0.74 tff(58,plain,
% 0.71/0.74 (~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[57, 53])).
% 0.71/0.74 tff(59,plain,
% 0.71/0.74 ((~![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))) | (~g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(60,plain,
% 0.71/0.74 (~g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[59, 14])).
% 0.71/0.74 tff(61,plain,
% 0.71/0.74 (^[X_2: $i, X_1: $i] : refl((g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(62,plain,
% 0.71/0.74 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[61])).
% 0.71/0.74 tff(63,plain,
% 0.71/0.74 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(64,plain,
% 0.71/0.74 (^[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_false_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_false_only(X_2, X_1) | g_both(X_2, X_1))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(65,plain,
% 0.71/0.74 (![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_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[64])).
% 0.71/0.74 tff(66,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')).
% 0.71/0.74 tff(67,plain,
% 0.71/0.74 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.71/0.74 tff(68,plain,
% 0.71/0.74 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.71/0.74 tff(69,plain,(
% 0.71/0.74 ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(skolemize,[status(sab)],[68])).
% 0.71/0.74 tff(70,plain,
% 0.71/0.74 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.71/0.74 tff(71,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(72,plain,
% 0.71/0.74 ((g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) <=> (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(73,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[72])).
% 0.71/0.74 tff(74,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(transitivity,[status(thm)],[73, 71])).
% 0.71/0.74 tff(75,plain,
% 0.71/0.74 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(76,plain,
% 0.71/0.74 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.71/0.74 tff(77,plain,
% 0.71/0.74 (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))) | g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 0.71/0.74 tff(78,plain,
% 0.71/0.74 (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[77, 58])).
% 0.71/0.74 tff(79,plain,
% 0.71/0.74 ((~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))) | (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(80,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[79, 47, 78])).
% 0.71/0.74 tff(81,plain,((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(a, tptp_fun_B_0(a)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(82,plain,
% 0.71/0.74 (~g_both(a, tptp_fun_B_0(a))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[81, 21])).
% 0.71/0.74 tff(83,plain,
% 0.71/0.74 ((~![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))) | (~g_true_only(a, tptp_fun_B_0(a)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(84,plain,
% 0.71/0.74 (~g_true_only(a, tptp_fun_B_0(a))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[83, 14])).
% 0.71/0.74 tff(85,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(86,plain,
% 0.71/0.74 ((g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a))) <=> (g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(87,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[86])).
% 0.71/0.74 tff(88,plain,
% 0.71/0.74 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[87, 85])).
% 0.71/0.74 tff(89,plain,
% 0.71/0.74 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(90,plain,
% 0.71/0.74 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_both(a, tptp_fun_B_0(a)) | g_true_only(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.71/0.74 tff(91,plain,
% 0.71/0.74 (g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[90, 70, 84])).
% 0.71/0.74 tff(92,plain,
% 0.71/0.74 (g_false_only(a, tptp_fun_B_0(a))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[91, 82])).
% 0.71/0.74 tff(93,assumption,(~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))), introduced(assumption)).
% 0.71/0.74 tff(94,assumption,(g_false_only(a, tptp_fun_B_0(a))), introduced(assumption)).
% 0.71/0.74 tff(95,plain,
% 0.71/0.74 (((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, tptp_fun_B_0(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_0(a), B)))) <=> ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, tptp_fun_B_0(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_0(a), B)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(96,plain,
% 0.71/0.74 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, tptp_fun_B_0(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_0(a), B)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(97,plain,
% 0.71/0.75 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, tptp_fun_B_0(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.71/0.75 tff(98,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[97, 43, 94, 93])).
% 0.71/0.75 tff(99,plain,((~g_false_only(a, tptp_fun_B_0(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(100,plain,
% 0.71/0.75 (![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[99, 92])).
% 0.71/0.75 tff(101,assumption,(g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))), introduced(assumption)).
% 0.71/0.75 tff(102,assumption,(![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))), introduced(assumption)).
% 0.71/0.75 tff(103,plain,
% 0.71/0.75 ((~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))) | (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(104,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[103, 102, 101])).
% 0.71/0.75 tff(105,plain,((~g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | (~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(106,plain,
% 0.71/0.75 (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[105, 100])).
% 0.71/0.75 tff(107,plain,
% 0.71/0.75 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(108,plain,
% 0.71/0.75 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(109,plain,
% 0.71/0.75 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.71/0.75 tff(110,plain,
% 0.71/0.75 (g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))) | g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[109, 70, 16])).
% 0.71/0.75 tff(111,plain,
% 0.71/0.75 (g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.71/0.75 tff(112,assumption,(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))), introduced(assumption)).
% 0.71/0.75 tff(113,plain,
% 0.71/0.75 ((~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))) | (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(114,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[113, 112, 102])).
% 0.71/0.75 tff(115,plain,((~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))) | (~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(116,plain,
% 0.71/0.75 (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[115, 100])).
% 0.71/0.75 tff(117,plain,
% 0.71/0.75 (((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))) <=> ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(118,plain,
% 0.71/0.75 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | ((~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(119,plain,
% 0.71/0.75 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.71/0.75 tff(120,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[119, 21, 116, 111])).
% 0.71/0.75 tff(121,plain,(~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(122,plain,
% 0.71/0.75 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B)))))))) <=> (![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(123,plain,
% 0.71/0.75 (^[A: $i] : trans(monotonicity(rewrite((~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))) <=> (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))), ((![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))) <=> (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))))), rewrite((![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))) <=> (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B)))))))), ((![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))) <=> (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B)))))))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(124,plain,
% 0.71/0.75 (![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))) <=> ![A: $i] : (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B)))))))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[123])).
% 0.71/0.75 tff(125,plain,
% 0.71/0.75 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))))) <=> (![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[124])).
% 0.71/0.75 tff(126,plain,
% 0.71/0.75 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))))) <=> (![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (g_true_only(a, A) | ![B: $i] : g_true_only(A, B) | (~(g_both(a, A) | (~(g_false_only(A, tptp_fun_B_1(A)) | ![B: $i] : (~g_both(A, B))))))))),
% 0.71/0.75 inference(transitivity,[status(thm)],[125, 122])).
% 0.71/0.75 tff(127,plain,
% 0.71/0.75 ((![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))))) <=> (![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(128,plain,
% 0.71/0.75 ((![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))) <=> (![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | (~(g_both(a, A) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(129,plain,
% 0.71/0.75 ((![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) <=> (![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(130,plain,
% 0.71/0.75 (^[A: $i] : trans(monotonicity(rewrite(((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) <=> ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))), rewrite((~(~g_true_only(a, A))) <=> g_true_only(a, A)), ((((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~(~g_true_only(a, A))) | ![B: $i] : g_true_only(A, B)) <=> (((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | g_true_only(a, A) | ![B: $i] : g_true_only(A, B)))), rewrite((((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | g_true_only(a, A) | ![B: $i] : g_true_only(A, B)) <=> (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))), ((((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~(~g_true_only(a, A))) | ![B: $i] : g_true_only(A, B)) <=> (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(131,plain,
% 0.71/0.75 (![A: $i] : (((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~(~g_true_only(a, A))) | ![B: $i] : g_true_only(A, B)) <=> ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[130])).
% 0.71/0.75 tff(132,plain,
% 0.71/0.75 ((![A: $i] : (((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~(~g_true_only(a, A))) | ![B: $i] : g_true_only(A, B)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) <=> (![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[131])).
% 0.71/0.75 tff(133,plain,
% 0.71/0.75 ((![A: $i] : (((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~(~g_true_only(a, A))) | ![B: $i] : g_true_only(A, B)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) <=> (![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![A: $i] : (![B: $i] : g_true_only(A, B) | g_true_only(a, A) | ((~g_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))),
% 0.71/0.75 inference(transitivity,[status(thm)],[132, 129])).
% 0.71/0.75 tff(134,plain,
% 0.71/0.75 ((?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) <=> (?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(135,plain,
% 0.71/0.75 ((~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))) <=> (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[134])).
% 0.71/0.75 tff(136,plain,
% 0.71/0.75 ((~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))) <=> (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(137,plain,
% 0.71/0.75 ((~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))) <=> (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(138,plain,
% 0.71/0.75 ((?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B))) <=> (?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(139,plain,
% 0.71/0.75 ((~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))) <=> (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[138])).
% 0.71/0.75 tff(140,plain,
% 0.71/0.75 ((~(((?[A: $i] : (((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A))) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))) <=> (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B))))),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(141,plain,
% 0.82/0.76 (~(((?[A: $i] : (((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A))) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))),
% 0.82/0.76 inference(or_elim,[status(thm)],[2])).
% 0.82/0.76 tff(142,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.82/0.76 tff(143,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))) & (~?[A: $i] : ![B: $i] : g_true_only(A, B)))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[142, 139])).
% 0.82/0.76 tff(144,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[143, 137])).
% 0.82/0.76 tff(145,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[144, 136])).
% 0.82/0.76 tff(146,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.82/0.76 tff(147,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[146, 135])).
% 0.82/0.76 tff(148,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[147, 135])).
% 0.82/0.76 tff(149,plain,
% 0.82/0.76 (~(?[A: $i] : ((g_both(a, A) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B)))) & (~g_true_only(a, A)) & (~![B: $i] : g_true_only(A, B))) & ?[A: $i] : (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_false_only(A, B))))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[148, 135])).
% 0.82/0.76 unexpected number of arguments: (let ((a!1 (lambda ((A $i))
% 0.82/0.76 (let ((a!1 (refl (~ (not (g_both a A)) (not (g_both a A)))))
% 0.82/0.76 (a!2 (lambda ((B $i))
% 0.82/0.76 (refl (~ (not (g_both A B)) (not (g_both A B))))))
% 0.82/0.76 (a!3 (exists ((B $i)) (g_both A B)))
% 0.82/0.76 (a!4 (forall ((B $i)) (not (g_both A B))))
% 0.82/0.76 (a!5 (exists ((B $i)) (g_false_only A B)))
% 0.82/0.76 (a!12 (~ (not (not (g_true_only a A)))
% 0.82/0.76 (not (not (g_true_only a A)))))
% 0.82/0.76 (a!13 (lambda ((B $i))
% 0.82/0.76 (refl (~ (g_true_only A B) (g_true_only A B)))))
% 0.82/0.76 (a!14 (forall ((B $i)) (g_true_only A B))))
% 0.82/0.76 (let ((a!6 (sk (~ a!5 (g_false_only A (B!1 A)))))
% 0.82/0.76 (a!8 (~ (not (and a!3 (not a!5)))
% 0.82/0.76 (or a!4 (g_false_only A (B!1 A)))))
% 0.82/0.76 (a!10 (not (or (g_both a A) (and a!3 (not a!5)))))
% 0.82/0.76 (a!11 (and (not (g_both a A))
% 0.82/0.76 (or a!4 (g_false_only A (B!1 A)))))
% 0.82/0.76 (a!15 (nnf-neg (nnf-pos (proof-bind a!13) (~ a!14 a!14))
% 0.82/0.76 (~ (not (not a!14)) a!14)))
% 0.82/0.76 (a!16 (and (or (g_both a A) (and a!3 (not a!5)))
% 0.82/0.76 (not (g_true_only a A))
% 0.82/0.76 (not a!14))))
% 0.82/0.76 (let ((a!7 (nnf-neg a!6
% 0.82/0.76 (~ (not (not a!5)) (g_false_only A (B!1 A)))))
% 0.82/0.76 (a!17 (or a!11 (not (not (g_true_only a A))) a!14)))
% 0.82/0.76 (let ((a!9 (nnf-neg (nnf-neg (proof-bind a!2) (~ (not a!3) a!4))
% 0.82/0.76 a!7
% 0.82/0.76 a!8)))
% 0.82/0.76 (nnf-neg (nnf-neg a!1 a!9 (~ a!10 a!11))
% 0.82/0.76 (refl a!12)
% 0.82/0.76 a!15
% 0.82/0.76 (~ (not a!16) a!17))))))))
% 0.82/0.76 (a!2 (exists ((A $i))
% 0.82/0.76 (let ((a!1 (exists ((B $i)) (g_both A B)))
% 0.82/0.76 (a!2 (exists ((B $i)) (g_false_only A B)))
% 0.82/0.76 (a!3 (forall ((B $i)) (g_true_only A B))))
% 0.82/0.76 (and (or (g_both a A) (and a!1 (not a!2)))
% 0.82/0.76 (not (g_true_only a A))
% 0.82/0.76 (not a!3)))))
% 0.82/0.76 (a!3 (forall ((A $i))
% 0.82/0.76 (let ((a!1 (forall ((B $i)) (not (g_both A B))))
% 0.82/0.76 (a!3 (forall ((B $i)) (g_true_only A B))))
% 0.82/0.76 (let ((a!2 (and (not (g_both a A))
% 0.82/0.76 (or a!1 (g_false_only A (B!1 A))))))
% 0.82/0.76 (or a!2 (not (not (g_true_only a A))) a!3)))))
% 0.82/0.76 (a!4 (lambda ((A $i))
% 0.82/0.76 (let ((a!1 (lambda ((B $i))
% 0.82/0.76 (refl (~ (not (g_both A B)) (not (g_both A B))))))
% 0.82/0.76 (a!2 (exists ((B $i)) (g_both A B)))
% 0.82/0.76 (a!3 (forall ((B $i)) (not (g_both A B))))
% 0.82/0.76 (a!4 (exists ((B $i)) (g_false_only A B))))
% 0.82/0.76 (let ((a!5 (sk (~ a!4 (g_false_only A (B!1 A)))))
% 0.82/0.76 (a!7 (~ (not (and a!2 (not a!4)))
% 0.82/0.76 (or a!3 (g_false_only A (B!1 A))))))
% 0.82/0.76 (let ((a!6 (nnf-neg a!5
% 0.82/0.76 (~ (not (not a!4)) (g_false_only A (B!1 A))))))
% 0.82/0.76 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3)) a!6 a!7))))))
% 0.82/0.76 (a!5 (exists ((A $i))
% 0.82/0.76 (let ((a!1 (exists ((B $i)) (g_both A B)))
% 0.82/0.76 (a!2 (exists ((B $i)) (g_false_only A B))))
% 0.82/0.76 (and a!1 (not a!2)))))
% 0.82/0.76 (a!6 (forall ((A $i))
% 0.82/0.76 (let ((a!1 (forall ((B $i)) (not (g_both A B)))))
% 0.82/0.76 (or a!1 (g_false_only A (B!1 A)))))))
% 0.82/0.76 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3))
% 0.82/0.76 (nnf-neg (proof-bind a!4) (~ (not a!5) a!6))
% 0.82/0.76 (~ (not (and a!2 a!5)) (or a!3 a!6))))
% 0.82/0.76 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------