%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO607+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Sat Jun 21 05:41:58 AM UTC 2025
% Result : Theorem 0.47s 0.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO607+1 : TPTP v9.0.0. Released v7.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:18:42 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.47/0.63 % SZS status Theorem
% 0.47/0.63 % SZS output start Proof
% 0.47/0.63 tff(g_true_only_type, type, (
% 0.47/0.63 g_true_only: ( $i * $i ) > $o)).
% 0.47/0.63 tff(tptp_fun_B_0_type, type, (
% 0.47/0.63 tptp_fun_B_0: $i > $i)).
% 0.47/0.63 tff(a_type, type, (
% 0.47/0.63 a: $i)).
% 0.47/0.63 tff(g_false_only_type, type, (
% 0.47/0.63 g_false_only: ( $i * $i ) > $o)).
% 0.47/0.63 tff(g_both_type, type, (
% 0.47/0.63 g_both: ( $i * $i ) > $o)).
% 0.47/0.63 tff(tptp_fun_B_1_type, type, (
% 0.47/0.63 tptp_fun_B_1: $i > $i)).
% 0.47/0.63 tff(tptp_fun_A_4_type, type, (
% 0.47/0.63 tptp_fun_A_4: $i)).
% 0.47/0.63 tff(tptp_fun_B_3_type, type, (
% 0.47/0.63 tptp_fun_B_3: $i)).
% 0.47/0.63 tff(tptp_fun_A_2_type, type, (
% 0.47/0.63 tptp_fun_A_2: $i)).
% 0.47/0.63 tff(1,plain,
% 0.47/0.63 ((~?[A: $i] : ![B: $i] : g_true_only(A, B)) <=> (~?[A: $i] : ![B: $i] : g_true_only(A, B))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 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/sandbox/benchmark/theBenchmark.p','nc6')).
% 0.47/0.63 tff(3,plain,
% 0.47/0.63 (~(?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B)) | ?[A: $i] : ![B: $i] : g_true_only(A, B))),
% 0.47/0.63 inference(or_elim,[status(thm)],[2])).
% 0.47/0.63 tff(4,plain,
% 0.47/0.63 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.47/0.63 inference(or_elim,[status(thm)],[3])).
% 0.47/0.63 tff(5,plain,
% 0.47/0.63 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.47/0.63 tff(6,plain,
% 0.47/0.63 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.47/0.63 tff(7,plain,
% 0.47/0.63 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.47/0.63 tff(8,plain,
% 0.47/0.63 (~?[A: $i] : ![B: $i] : g_true_only(A, B)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.47/0.63 tff(9,plain,
% 0.47/0.63 (^[A: $i] : sk($oeq((~![B: $i] : g_true_only(A, B)), (~g_true_only(A, tptp_fun_B_0(A)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(10,plain,(
% 0.47/0.63 ![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))),
% 0.47/0.63 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.47/0.63 tff(11,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(12,plain,
% 0.47/0.63 (~g_true_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.47/0.63 tff(13,assumption,(![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))), introduced(assumption)).
% 0.47/0.63 tff(14,assumption,(g_both(a, tptp_fun_B_0(a))), introduced(assumption)).
% 0.47/0.63 tff(15,assumption,(![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))), introduced(assumption)).
% 0.47/0.63 tff(16,assumption,(g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))), introduced(assumption)).
% 0.47/0.63 tff(17,plain,
% 0.47/0.63 ((~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))) | (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(18,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[17, 15, 16])).
% 0.47/0.63 tff(19,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,[]))).
% 0.47/0.63 tff(20,plain,
% 0.47/0.63 (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[19, 15])).
% 0.47/0.63 tff(21,assumption,(g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))), introduced(assumption)).
% 0.47/0.63 tff(22,assumption,(~g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))), introduced(assumption)).
% 0.47/0.63 tff(23,plain,
% 0.47/0.63 (((~![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))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(24,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(25,plain,
% 0.47/0.63 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.47/0.63 tff(26,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[25, 13, 22, 21])).
% 0.47/0.63 tff(27,plain,((~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))) | (~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | g_false_only(tptp_fun_B_1(a), tptp_fun_B_1(tptp_fun_B_1(a)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(28,plain,
% 0.47/0.63 (~g_both(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[27, 20, 13])).
% 0.47/0.63 tff(29,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(30,plain,
% 0.47/0.63 (~g_true_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[29, 10])).
% 0.47/0.63 tff(31,plain,
% 0.47/0.63 (^[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)))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(32,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[31])).
% 0.47/0.63 tff(33,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(34,plain,
% 0.47/0.63 (^[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))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(35,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[34])).
% 0.47/0.63 tff(36,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/sandbox/benchmark/theBenchmark.p','exhaustion_g')).
% 0.47/0.63 tff(37,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.47/0.63 tff(38,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.47/0.63 tff(39,plain,(
% 0.47/0.63 ![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))),
% 0.47/0.63 inference(skolemize,[status(sab)],[38])).
% 0.47/0.63 tff(40,plain,
% 0.47/0.63 (![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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.47/0.63 tff(41,plain,
% 0.47/0.63 (((~![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_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))))) <=> ((~![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_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))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(42,plain,
% 0.47/0.63 ((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_true_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))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(43,plain,
% 0.47/0.63 (((~![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_true_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)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[42])).
% 0.47/0.63 tff(44,plain,
% 0.47/0.63 (((~![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_true_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))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[43, 41])).
% 0.47/0.63 tff(45,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(46,plain,
% 0.47/0.63 ((~![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_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)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.47/0.63 tff(47,plain,
% 0.47/0.63 (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)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[46, 40, 30])).
% 0.47/0.63 tff(48,plain,
% 0.47/0.63 (g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[47, 28])).
% 0.47/0.63 tff(49,plain,
% 0.47/0.63 ((~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))) | (~g_false_only(tptp_fun_B_1(a), tptp_fun_B_0(tptp_fun_B_1(a))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(50,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[49, 15, 48])).
% 0.47/0.63 tff(51,plain,((~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))) | (~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(52,plain,
% 0.47/0.63 (~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[51, 13])).
% 0.47/0.63 tff(53,assumption,(g_false_only(a, tptp_fun_B_1(a))), introduced(assumption)).
% 0.47/0.63 tff(54,assumption,(~![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))), introduced(assumption)).
% 0.47/0.63 tff(55,plain,
% 0.47/0.63 (^[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))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(56,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[55])).
% 0.47/0.63 tff(57,plain,
% 0.47/0.63 (^[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))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(58,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[57])).
% 0.47/0.63 tff(59,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[58, 56])).
% 0.47/0.63 tff(60,plain,
% 0.47/0.63 ((~?[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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(61,plain,
% 0.47/0.63 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.47/0.63 inference(or_elim,[status(thm)],[3])).
% 0.47/0.63 tff(62,plain,
% 0.47/0.63 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.47/0.63 tff(63,plain,
% 0.47/0.63 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.47/0.63 tff(64,plain,
% 0.47/0.63 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.47/0.63 tff(65,plain,
% 0.47/0.63 (~?[A: $i] : (g_false_only(a, A) & ?[B: $i] : g_false_only(A, B))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.47/0.63 tff(66,plain,
% 0.47/0.63 (^[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)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(67,plain,(
% 0.47/0.63 ![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.47/0.63 inference(nnf-neg,[status(sab)],[65, 66])).
% 0.47/0.63 tff(68,plain,
% 0.47/0.63 (![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[67, 59])).
% 0.47/0.63 tff(69,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(70,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(71,plain,
% 0.47/0.63 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.47/0.63 tff(72,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[71, 68, 54, 53])).
% 0.47/0.63 tff(73,plain,((~g_false_only(a, tptp_fun_B_1(a))) | ![B: $i] : (~g_false_only(tptp_fun_B_1(a), B))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(74,plain,
% 0.47/0.63 (~g_false_only(a, tptp_fun_B_1(a))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[73, 52])).
% 0.47/0.63 tff(75,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(76,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(77,plain,
% 0.47/0.63 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(a, tptp_fun_B_0(a))) | g_false_only(a, tptp_fun_B_1(a))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.47/0.63 tff(78,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[77, 13, 74, 14])).
% 0.47/0.63 tff(79,plain,((~g_both(a, tptp_fun_B_0(a))) | (~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(80,plain,
% 0.47/0.63 (~g_both(a, tptp_fun_B_0(a))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[79, 13])).
% 0.47/0.63 tff(81,plain,
% 0.47/0.63 ((~![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))) | (~g_true_only(a, tptp_fun_B_0(a)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(82,plain,
% 0.47/0.63 (~g_true_only(a, tptp_fun_B_0(a))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[81, 10])).
% 0.47/0.63 tff(83,plain,
% 0.47/0.63 (((~![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_both(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_true_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(84,plain,
% 0.47/0.63 ((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_true_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(85,plain,
% 0.47/0.63 (((~![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_true_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[84])).
% 0.47/0.63 tff(86,plain,
% 0.47/0.63 (((~![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_true_only(a, tptp_fun_B_0(a)) | g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[85, 83])).
% 0.47/0.63 tff(87,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(88,plain,
% 0.47/0.63 ((~![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_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.47/0.63 tff(89,plain,
% 0.47/0.63 (g_both(a, tptp_fun_B_0(a)) | g_false_only(a, tptp_fun_B_0(a))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[88, 40, 82])).
% 0.47/0.63 tff(90,plain,
% 0.47/0.63 (g_false_only(a, tptp_fun_B_0(a))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[89, 80])).
% 0.47/0.63 tff(91,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(92,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(93,plain,
% 0.47/0.63 ((~![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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.47/0.63 tff(94,plain,
% 0.47/0.63 (![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[93, 68, 90])).
% 0.47/0.63 tff(95,assumption,(![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))), introduced(assumption)).
% 0.47/0.63 tff(96,assumption,(g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))), introduced(assumption)).
% 0.47/0.63 tff(97,plain,
% 0.47/0.63 ((~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))) | (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(98,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[97, 96, 95])).
% 0.47/0.63 tff(99,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,[]))).
% 0.47/0.63 tff(100,plain,
% 0.47/0.63 (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[99, 94])).
% 0.47/0.63 tff(101,plain,
% 0.47/0.63 (((~![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_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_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_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_0(tptp_fun_B_0(a))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(102,plain,
% 0.47/0.63 ((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)))) <=> (g_true_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))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(103,plain,
% 0.47/0.63 (((~![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_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_0(tptp_fun_B_0(a)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[102])).
% 0.47/0.63 tff(104,plain,
% 0.47/0.63 (((~![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_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_0(tptp_fun_B_0(a))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[103, 101])).
% 0.47/0.63 tff(105,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(106,plain,
% 0.47/0.63 ((~![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_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_0(tptp_fun_B_0(a)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.47/0.63 tff(107,plain,
% 0.47/0.63 (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_0(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[106, 40, 12])).
% 0.47/0.64 tff(108,plain,
% 0.47/0.64 (g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[107, 100])).
% 0.47/0.64 tff(109,assumption,(~(g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B)))))), introduced(assumption)).
% 0.47/0.64 tff(110,plain,
% 0.47/0.64 ((g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))))) | (~g_both(a, tptp_fun_B_0(a)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(111,plain,
% 0.47/0.64 (~g_both(a, tptp_fun_B_0(a))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.47/0.64 tff(112,plain,
% 0.47/0.64 (g_false_only(a, tptp_fun_B_0(a))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[89, 111])).
% 0.47/0.64 tff(113,plain,
% 0.47/0.64 (![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[93, 68, 112])).
% 0.47/0.64 tff(114,plain,
% 0.47/0.64 ((g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))))) | (g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(115,plain,
% 0.47/0.64 (g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.47/0.64 tff(116,assumption,(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))), introduced(assumption)).
% 0.47/0.64 tff(117,plain,
% 0.47/0.64 ((~![B: $i] : (~g_false_only(tptp_fun_B_0(a), B))) | (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(118,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[117, 116, 95])).
% 0.47/0.64 tff(119,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,[]))).
% 0.47/0.64 tff(120,plain,
% 0.47/0.64 (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[119, 113])).
% 0.47/0.64 tff(121,plain,
% 0.47/0.64 ((~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(122,plain,
% 0.47/0.64 (![B: $i] : (~g_both(tptp_fun_B_0(a), B))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[121, 120, 115])).
% 0.47/0.64 tff(123,assumption,(g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))), introduced(assumption)).
% 0.47/0.64 tff(124,assumption,(![B: $i] : (~g_both(tptp_fun_B_0(a), B))), introduced(assumption)).
% 0.47/0.64 tff(125,plain,
% 0.47/0.64 ((~![B: $i] : (~g_both(tptp_fun_B_0(a), B))) | (~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(126,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[125, 124, 123])).
% 0.47/0.64 tff(127,plain,((~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | (~![B: $i] : (~g_both(tptp_fun_B_0(a), B)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(128,plain,
% 0.47/0.64 (~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[127, 122])).
% 0.47/0.64 tff(129,plain,
% 0.47/0.64 (g_false_only(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[107, 128])).
% 0.47/0.64 tff(130,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[97, 129, 113])).
% 0.47/0.64 tff(131,plain,(g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(132,plain,
% 0.47/0.64 ((~(g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B)))))) | g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(133,plain,
% 0.47/0.64 (g_both(a, tptp_fun_B_0(a)) | (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.47/0.64 tff(134,plain,
% 0.47/0.64 (~(g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[133, 80])).
% 0.47/0.64 tff(135,plain,
% 0.47/0.64 ((g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))) | ![B: $i] : (~g_both(tptp_fun_B_0(a), B))) | (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a))))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(136,plain,
% 0.47/0.64 (~g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.47/0.64 tff(137,plain,
% 0.47/0.64 (((~![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))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(138,plain,
% 0.47/0.64 ((~![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))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(139,plain,
% 0.47/0.64 ((~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))) | (~g_both(tptp_fun_B_0(a), tptp_fun_B_0(tptp_fun_B_0(a)))) | g_false_only(tptp_fun_B_0(a), tptp_fun_B_1(tptp_fun_B_0(a)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.47/0.64 tff(140,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[139, 13, 136, 108])).
% 0.47/0.64 tff(141,plain,(~![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(142,plain,
% 0.47/0.64 ((~![A: $i] : (~g_true_only(A, tptp_fun_B_0(A)))) | (~g_true_only(A!4, tptp_fun_B_0(A!4)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(143,plain,
% 0.47/0.64 (~g_true_only(A!4, tptp_fun_B_0(A!4))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[142, 10])).
% 0.47/0.64 tff(144,assumption,(![B: $i] : g_true_only(A!4, B)), introduced(assumption)).
% 0.47/0.64 tff(145,plain,
% 0.47/0.64 ((~![B: $i] : g_true_only(A!4, B)) | g_true_only(A!4, tptp_fun_B_0(A!4))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(146,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[145, 144, 143])).
% 0.47/0.64 tff(147,plain,(~![B: $i] : g_true_only(A!4, B)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(148,assumption,(~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))), introduced(assumption)).
% 0.47/0.64 tff(149,plain,
% 0.47/0.64 (((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3))) | g_false_only(a, A!2)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(150,plain,
% 0.47/0.64 (g_false_only(a, A!2)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.47/0.64 tff(151,plain,
% 0.47/0.64 (((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, A!2)) | ![B: $i] : (~g_false_only(A!2, B)))) <=> ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, A!2)) | ![B: $i] : (~g_false_only(A!2, B)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(152,plain,
% 0.47/0.64 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | ((~g_false_only(a, A!2)) | ![B: $i] : (~g_false_only(A!2, B)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(153,plain,
% 0.47/0.64 ((~![A: $i] : ((~g_false_only(a, A)) | ![B: $i] : (~g_false_only(A, B)))) | (~g_false_only(a, A!2)) | ![B: $i] : (~g_false_only(A!2, B))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.47/0.64 tff(154,plain,
% 0.47/0.64 (![B: $i] : (~g_false_only(A!2, B))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[153, 68, 150])).
% 0.47/0.64 tff(155,plain,
% 0.47/0.64 (((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3))) | g_false_only(A!2, B!3)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(156,plain,
% 0.47/0.64 (g_false_only(A!2, B!3)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[155, 148])).
% 0.47/0.64 tff(157,plain,
% 0.47/0.64 ((~![B: $i] : (~g_false_only(A!2, B))) | (~g_false_only(A!2, B!3))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(158,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[157, 156, 154])).
% 0.47/0.64 tff(159,plain,((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(160,plain,
% 0.47/0.64 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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)))))))) <=> ((~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![B: $i] : g_true_only(A!4, 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))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(161,plain,
% 0.47/0.64 (^[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)))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(162,plain,
% 0.47/0.64 (![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)))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[161])).
% 0.47/0.64 tff(163,plain,
% 0.47/0.64 ((~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) <=> (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(164,plain,
% 0.47/0.64 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[163, 162])).
% 0.47/0.64 tff(165,plain,
% 0.47/0.64 ((![A: $i, B: $i] : ((~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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)))))))) <=> ((~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![B: $i] : g_true_only(A!4, 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))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[164, 160])).
% 0.47/0.64 tff(166,plain,
% 0.47/0.64 ((![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(167,plain,
% 0.47/0.64 (((~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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)))))))) <=> (![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(168,plain,
% 0.47/0.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(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_both(a, A)) & (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))), 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))))))), (((~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)))))))), ((![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) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))))))))), rewrite((![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) | (~(![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)) & (![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) | (~(![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A)))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(169,plain,
% 0.47/0.64 (![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_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)))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[168])).
% 0.47/0.64 tff(170,plain,
% 0.47/0.64 ((g_false_only(a, A!2) & g_false_only(A!2, B!3)) <=> (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(171,plain,
% 0.47/0.64 (((g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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)))))) <=> ((~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[170, 169])).
% 0.47/0.64 tff(172,plain,
% 0.47/0.64 (((g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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)))))) <=> (![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B) | (~((~g_false_only(a, A!2)) | (~g_false_only(A!2, B!3)))) | ![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))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[171, 167])).
% 0.47/0.64 tff(173,plain,
% 0.47/0.64 ((![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))))) | (g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B)) <=> ((g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(174,plain,
% 0.47/0.64 (^[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))))), ((((~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)))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(175,plain,
% 0.47/0.64 (![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)))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[174])).
% 0.47/0.64 tff(176,plain,
% 0.47/0.64 ((![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)) | (g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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))))) | (g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[175])).
% 0.47/0.64 tff(177,plain,
% 0.47/0.64 ((![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)) | (g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, B)) <=> ((g_false_only(a, A!2) & g_false_only(A!2, B!3)) | ![A: $i] : (![B: $i] : (~g_both(A, B)) | g_false_only(A, tptp_fun_B_1(A))) | ![B: $i] : g_true_only(A!4, 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))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[176, 173])).
% 0.47/0.64 tff(178,plain,
% 0.47/0.64 ((?[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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(179,plain,
% 0.47/0.64 ((~(?[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))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[178])).
% 0.47/0.64 tff(180,plain,
% 0.47/0.64 ((~(?[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))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(181,plain,
% 0.47/0.64 ((~(((?[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))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(182,plain,
% 0.47/0.64 (~(((?[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)))),
% 0.47/0.64 inference(or_elim,[status(thm)],[2])).
% 0.47/0.64 tff(183,plain,
% 0.47/0.65 (~(?[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)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.47/0.65 tff(184,plain,
% 0.47/0.65 (~(?[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)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.47/0.65 tff(185,plain,
% 0.47/0.65 (~(?[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)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.47/0.65 tff(186,plain,
% 0.47/0.65 (~(?[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)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[185, 179])).
% 0.47/0.65 unexpected number of arguments: (let ((a!1 (lambda ((A $i))
% 0.47/0.65 (let ((a!1 (refl (~ (not (g_both a A)) (not (g_both a A)))))
% 0.47/0.65 (a!2 (lambda ((B $i))
% 0.47/0.65 (refl (~ (not (g_both A B)) (not (g_both A B))))))
% 0.47/0.65 (a!3 (exists ((B $i)) (g_both A B)))
% 0.47/0.65 (a!4 (forall ((B $i)) (not (g_both A B))))
% 0.47/0.65 (a!5 (exists ((B $i)) (g_false_only A B)))
% 0.47/0.65 (a!12 (lambda ((B $i))
% 0.47/0.65 (refl (~ (g_true_only A B) (g_true_only A B)))))
% 0.47/0.65 (a!13 (forall ((B $i)) (g_true_only A B))))
% 0.47/0.65 (let ((a!6 (sk (~ a!5 (g_false_only A (B!1 A)))))
% 0.47/0.65 (a!8 (~ (not (and a!3 (not a!5)))
% 0.47/0.65 (or a!4 (g_false_only A (B!1 A)))))
% 0.47/0.65 (a!10 (not (or (g_both a A) (and a!3 (not a!5)))))
% 0.47/0.65 (a!11 (and (not (g_both a A))
% 0.47/0.65 (or a!4 (g_false_only A (B!1 A)))))
% 0.47/0.65 (a!14 (nnf-neg (nnf-pos (proof-bind a!12) (~ a!13 a!13))
% 0.47/0.65 (~ (not (not a!13)) a!13)))
% 0.47/0.65 (a!15 (and (or (g_both a A) (and a!3 (not a!5)))
% 0.47/0.65 (not (g_true_only a A))
% 0.47/0.65 (not a!13))))
% 0.47/0.65 (let ((a!7 (nnf-neg a!6
% 0.47/0.65 (~ (not (not a!5)) (g_false_only A (B!1 A))))))
% 0.47/0.65 (let ((a!9 (nnf-neg (nnf-neg (proof-bind a!2) (~ (not a!3) a!4))
% 0.47/0.65 a!7
% 0.47/0.65 a!8)))
% 0.47/0.65 (nnf-neg (nnf-neg a!1 a!9 (~ a!10 a!11))
% 0.47/0.65 (refl (~ (g_true_only a A) (g_true_only a A)))
% 0.47/0.65 a!14
% 0.47/0.65 (~ (not a!15) (or a!11 (g_true_only a A) a!13)))))))))
% 0.47/0.65 (a!2 (exists ((A $i))
% 0.47/0.65 (let ((a!1 (exists ((B $i)) (g_both A B)))
% 0.47/0.65 (a!2 (exists ((B $i)) (g_false_only A B)))
% 0.47/0.65 (a!3 (forall ((B $i)) (g_true_only A B))))
% 0.47/0.65 (and (or (g_both a A) (and a!1 (not a!2)))
% 0.47/0.65 (not (g_true_only a A))
% 0.47/0.65 (not a!3)))))
% 0.47/0.65 (a!3 (forall ((A $i))
% 0.47/0.65 (let ((a!1 (forall ((B $i)) (not (g_both A B))))
% 0.47/0.65 (a!3 (forall ((B $i)) (g_true_only A B))))
% 0.47/0.65 (let ((a!2 (and (not (g_both a A))
% 0.47/0.65 (or a!1 (g_false_only A (B!1 A))))))
% 0.47/0.65 (or a!2 (g_true_only a A) a!3)))))
% 0.47/0.65 (a!4 (exists ((A $i))
% 0.47/0.65 (let ((a!1 (exists ((B $i)) (g_false_only A B))))
% 0.47/0.65 (and (g_false_only a A) a!1))))
% 0.47/0.65 (a!5 (exists ((B $i)) (g_false_only A!2 B)))
% 0.47/0.65 (a!10 (lambda ((A $i))
% 0.47/0.65 (let ((a!1 (lambda ((B $i))
% 0.47/0.65 (refl (~ (not (g_both A B)) (not (g_both A B))))))
% 0.47/0.65 (a!2 (exists ((B $i)) (g_both A B)))
% 0.47/0.65 (a!3 (forall ((B $i)) (not (g_both A B))))
% 0.47/0.65 (a!4 (exists ((B $i)) (g_false_only A B))))
% 0.47/0.65 (let ((a!5 (sk (~ a!4 (g_false_only A (B!1 A)))))
% 0.47/0.65 (a!7 (~ (not (and a!2 (not a!4)))
% 0.47/0.65 (or a!3 (g_false_only A (B!1 A))))))
% 0.47/0.65 (let ((a!6 (nnf-neg a!5
% 0.47/0.65 (~ (not (not a!4)) (g_false_only A (B!1 A))))))
% 0.47/0.65 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3)) a!6 a!7))))))
% 0.47/0.65 (a!11 (exists ((A $i))
% 0.47/0.65 (let ((a!1 (exists ((B $i)) (g_both A B)))
% 0.47/0.65 (a!2 (exists ((B $i)) (g_false_only A B))))
% 0.47/0.65 (and a!1 (not a!2)))))
% 0.47/0.65 (a!12 (forall ((A $i))
% 0.47/0.65 (let ((a!1 (forall ((B $i)) (not (g_both A B)))))
% 0.47/0.65 (or a!1 (g_false_only A (B!1 A))))))
% 0.47/0.65 (a!13 (exists ((A $i)) (forall ((B $i)) (g_true_only A B))))
% 0.47/0.65 (a!14 (forall ((B $i)) (g_true_only A!4 B)))
% 0.47/0.65 (a!15 (lambda ((B $i)) (refl (~ (g_true_only A!4 B) (g_true_only A!4 B))))))
% 0.47/0.65 (let ((a!6 (sk (~ a!4 (and (g_false_only a A!2) a!5))))
% 0.47/0.65 (a!7 (monotonicity (refl (~ (g_false_only a A!2) (g_false_only a A!2)))
% 0.47/0.65 (sk (~ a!5 (g_false_only A!2 B!3)))
% 0.47/0.65 (~ (and (g_false_only a A!2) a!5)
% 0.47/0.65 (and (g_false_only a A!2) (g_false_only A!2 B!3)))))
% 0.47/0.65 (a!16 (nnf-neg (trans (sk (~ a!13 a!14))
% 0.47/0.65 (nnf-pos (proof-bind a!15) (~ a!14 a!14))
% 0.47/0.65 (~ a!13 a!14))
% 0.47/0.65 (~ (not (not a!13)) a!14)))
% 0.47/0.65 (a!17 (~ (not (and a!2 (not a!4) a!11 (not a!13)))
% 0.47/0.65 (or a!3
% 0.47/0.65 (and (g_false_only a A!2) (g_false_only A!2 B!3))
% 0.47/0.65 a!12
% 0.47/0.65 a!14))))
% 0.47/0.65 (let ((a!8 (trans a!6
% 0.47/0.65 a!7
% 0.47/0.65 (~ a!4 (and (g_false_only a A!2) (g_false_only A!2 B!3))))))
% 0.47/0.65 (let ((a!9 (nnf-neg a!8
% 0.47/0.65 (~ (not (not a!4))
% 0.47/0.65 (and (g_false_only a A!2) (g_false_only A!2 B!3))))))
% 0.47/0.65 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3))
% 0.47/0.65 a!9
% 0.47/0.65 (nnf-neg (proof-bind a!10) (~ (not a!11) a!12))
% 0.47/0.65 a!16
% 0.47/0.65 a!17)))))
% 0.47/0.65 Proof display could not be completed: unexpected number of arguments
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------