%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN726-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:55 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN726-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:41:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(q_type, type, (
% 0.12/0.38 q: ( $i * $i ) > $o)).
% 0.12/0.38 tff(sk2_type, type, (
% 0.12/0.38 sk2: $i)).
% 0.12/0.38 tff(sk4_type, type, (
% 0.12/0.38 sk4: $i)).
% 0.12/0.38 tff(sk3_type, type, (
% 0.12/0.38 sk3: $i)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: ( $i * $i ) > $o)).
% 0.12/0.38 tff(sk1_type, type, (
% 0.12/0.38 sk1: $i)).
% 0.12/0.38 tff(1,assumption,(~p(sk1, sk3)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl((p(A, B) | q(A, B)) <=> (p(A, B) | q(A, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![B: $i, A: $i] : (p(A, B) | q(A, B)) <=> ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![B: $i, A: $i] : (p(A, B) | q(A, B)) <=> ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(![B: $i, A: $i] : (p(A, B) | q(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_4')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk3) | q(sk1, sk3))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk3) | q(sk1, sk3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk3) | q(sk1, sk3))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk3) | q(sk1, sk3)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (q(sk1, sk3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl(((~q(A, B)) | q(B, A)) <=> ((~q(A, B)) | q(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A)) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A)) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[B: $i, A: $i] : rewrite((q(B, A) | (~q(A, B))) <=> ((~q(A, B)) | q(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![B: $i, A: $i] : (q(B, A) | (~q(A, B))) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,axiom,(![B: $i, A: $i] : (q(B, A) | (~q(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_3')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38 tff(21,plain,(
% 0.12/0.38 ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk3)) | q(sk3, sk1))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk3)) | q(sk3, sk1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk3)) | q(sk3, sk1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk3)) | q(sk3, sk1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (q(sk3, sk1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((~q(sk3, sk4)) <=> (~q(sk3, sk4))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,axiom,(~q(sk3, sk4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_6')).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~q(sk3, sk4)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((q(A, C) | (~q(A, B))) <=> ((~q(A, B)) | q(A, C))), (((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> (((~q(A, B)) | q(A, C)) | (~q(B, C))))), rewrite((((~q(A, B)) | q(A, C)) | (~q(B, C))) <=> ((~q(B, C)) | (~q(A, B)) | q(A, C))), (((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> ((~q(B, C)) | (~q(A, B)) | q(A, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.39 tff(34,axiom,(![B: $i, A: $i, C: $i] : ((q(A, C) | (~q(A, B))) | (~q(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_2')).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.39 tff(37,plain,(
% 0.12/0.39 ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(skolemize,[status(sab)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk4)) | (~q(sk3, sk1)) | q(sk3, sk4))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk4)) | (~q(sk3, sk1)) | q(sk3, sk4))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk4)) | (~q(sk3, sk1)) | q(sk3, sk4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk4)) | (~q(sk3, sk1)) | q(sk3, sk4)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ((~q(sk1, sk4)) | (~q(sk3, sk1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 38, 29])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (~q(sk1, sk4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[42, 26])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk4) | q(sk1, sk4))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk4) | q(sk1, sk4))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk4) | q(sk1, sk4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk4) | q(sk1, sk4)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (p(sk1, sk4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 8, 43])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk4, sk3)) | q(sk3, sk4))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk4, sk3)) | q(sk3, sk4))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk4, sk3)) | q(sk3, sk4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk4, sk3)) | q(sk3, sk4)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (~q(sk4, sk3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[50, 22, 29])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk3) | q(sk4, sk3))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk3) | q(sk4, sk3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk3) | q(sk4, sk3))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk3) | q(sk4, sk3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (p(sk4, sk3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[54, 8, 51])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((p(A, C) | (~p(A, B))) <=> ((~p(A, B)) | p(A, C))), (((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> (((~p(A, B)) | p(A, C)) | (~p(B, C))))), rewrite((((~p(A, B)) | p(A, C)) | (~p(B, C))) <=> ((~p(B, C)) | (~p(A, B)) | p(A, C))), (((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> ((~p(B, C)) | (~p(A, B)) | p(A, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.39 tff(60,axiom,(![B: $i, A: $i, C: $i] : ((p(A, C) | (~p(A, B))) | (~p(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_1')).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.39 tff(63,plain,(
% 0.12/0.39 ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(skolemize,[status(sab)],[62])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[67, 64, 55, 1, 47])).
% 0.12/0.39 tff(69,plain,(p(sk1, sk3)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~p(sk1, sk2)) <=> (~p(sk1, sk2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(71,axiom,(~p(sk1, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400_5')).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (~p(sk1, sk2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2)) <=> (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[75, 73])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 ((~p(sk3, sk2)) | (~p(sk1, sk3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[78, 64, 72])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (~p(sk3, sk2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[79, 69])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk2) | q(sk3, sk2))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk2) | q(sk3, sk2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk2) | q(sk3, sk2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk2) | q(sk3, sk2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (q(sk3, sk2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[83, 8, 80])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk3, sk2)) | q(sk2, sk3))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk3, sk2)) | q(sk2, sk3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk3, sk2)) | q(sk2, sk3))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk3, sk2)) | q(sk2, sk3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (q(sk2, sk3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 22, 84])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk3)) | (~q(sk4, sk2)) | q(sk4, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk2, sk3)) | (~q(sk4, sk2)) | q(sk4, sk3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk3)) | (~q(sk4, sk2)) | q(sk4, sk3))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk2, sk3)) | (~q(sk4, sk2)) | q(sk4, sk3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (~q(sk4, sk2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[91, 38, 51, 88])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk4) | q(sk3, sk4))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk4) | q(sk3, sk4))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk4) | q(sk3, sk4))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk4) | q(sk3, sk4)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (p(sk3, sk4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[95, 8, 29])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (((~p(sk3, sk4)) | (~p(sk1, sk3)) | p(sk1, sk4)) <=> ((~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | (~p(sk1, sk3)) | p(sk1, sk4))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | (~p(sk1, sk3)) | p(sk1, sk4))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | (~p(sk1, sk3)) | p(sk1, sk4))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk1, sk4) | (~p(sk1, sk3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (p(sk1, sk4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[102, 64, 96, 69])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (((~p(sk4, sk2)) | (~p(sk1, sk4)) | p(sk1, sk2)) <=> (p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk1, sk4)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[105])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk1, sk4)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[106, 104])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk1, sk4)) | p(sk1, sk2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk1, sk4)) | (~p(sk4, sk2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 (~p(sk4, sk2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[109, 64, 72, 103])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk2) | q(sk4, sk2))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk2) | q(sk4, sk2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk2) | q(sk4, sk2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk2) | q(sk4, sk2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[113, 8, 110, 92])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------