%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC006-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:17:30 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : MSC006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 : Thu Jun 19 23:33:11 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(q_type, type, (
% 0.19/0.39 q: ( $i * $i ) > $o)).
% 0.19/0.39 tff(d_type, type, (
% 0.19/0.39 d: $i)).
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $i)).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: ( $i * $i ) > $o)).
% 0.19/0.39 tff(b_type, type, (
% 0.19/0.39 b: $i)).
% 0.19/0.39 tff(c_type, type, (
% 0.19/0.39 c: $i)).
% 0.19/0.39 tff(1,assumption,(~p(c, b)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : refl((p(X, Y) | q(X, Y)) <=> (p(X, Y) | q(X, Y)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (p(X, Y) | q(X, Y)) <=> ![Y: $i, X: $i] : (p(X, Y) | q(X, Y))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (p(X, Y) | q(X, Y)) <=> ![Y: $i, X: $i] : (p(X, Y) | q(X, Y))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![Y: $i, X: $i] : (p(X, Y) | q(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','all_related')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (p(X, Y) | q(X, Y))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : (p(X, Y) | q(X, Y))),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (p(X, Y) | q(X, Y))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(c, b) | q(c, b))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(c, b) | q(c, b))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(c, b) | q(c, b))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(c, b) | q(c, b)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (q(c, b)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~q(c, d)) <=> (~q(c, d))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,axiom,(~q(c, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_q_is_total')).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~q(c, d)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(c, d) | q(c, d))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(c, d) | q(c, d))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(c, d) | q(c, d))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(c, d) | q(c, d)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (p(c, d)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 8, 15])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[Z: $i, Y: $i, X: $i] : rewrite((((~p(X, Y)) | (~p(Y, Z))) | p(X, Z)) <=> (p(X, Z) | (~p(Y, Z)) | (~p(X, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (((~p(X, Y)) | (~p(Y, Z))) | p(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,axiom,(![Z: $i, Y: $i, X: $i] : (((~p(X, Y)) | (~p(Y, Z))) | p(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p_transitivity')).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | ((~p(c, d)) | p(c, b) | (~p(d, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(c, d)) | p(c, b) | (~p(d, b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((p(c, b) | (~p(d, b)) | (~p(c, d))) <=> ((~p(c, d)) | p(c, b) | (~p(d, b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(c, b) | (~p(d, b)) | (~p(c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | ((~p(c, d)) | p(c, b) | (~p(d, b))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(c, b) | (~p(d, b)) | (~p(c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(c, d)) | p(c, b) | (~p(d, b)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(c, b) | (~p(d, b)) | (~p(c, d)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(c, d)) | p(c, b) | (~p(d, b))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (p(c, b) | (~p(d, b))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 28, 19])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~p(d, b)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 1])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(d, b) | q(d, b))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(d, b) | q(d, b))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(d, b) | q(d, b))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(d, b) | q(d, b)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (q(d, b)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 8, 36])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : refl(((~q(X, Y)) | q(Y, X)) <=> ((~q(X, Y)) | q(Y, X)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,axiom,(![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','q_symmetry')).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.19/0.39 inference(skolemize,[status(sab)],[45])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(d, c)) | q(c, d))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(d, c)) | q(c, d))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(d, c)) | q(c, d))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(d, c)) | q(c, d)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~q(d, c)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 47, 15])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (^[Z: $i, Y: $i, X: $i] : rewrite((((~q(X, Y)) | (~q(Y, Z))) | q(X, Z)) <=> (q(X, Z) | (~q(Y, Z)) | (~q(X, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (((~q(X, Y)) | (~q(Y, Z))) | q(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,axiom,(![Z: $i, Y: $i, X: $i] : (((~q(X, Y)) | (~q(Y, Z))) | q(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','q_transitivity')).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.40 tff(59,plain,(
% 0.19/0.40 ![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(d, c) | (~q(d, b)) | (~q(b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(d, c) | (~q(d, b)) | (~q(b, c)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((q(d, c) | (~q(b, c)) | (~q(d, b))) <=> (q(d, c) | (~q(d, b)) | (~q(b, c)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(d, c) | (~q(b, c)) | (~q(d, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(d, c) | (~q(d, b)) | (~q(b, c))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(d, c) | (~q(b, c)) | (~q(d, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(d, c) | (~q(d, b)) | (~q(b, c)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(d, c) | (~q(b, c)) | (~q(d, b)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(d, c) | (~q(d, b)) | (~q(b, c))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~q(d, b)) | (~q(b, c))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 60, 51])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~q(b, c)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 40])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(c, b)) | q(b, c))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(c, b)) | q(b, c))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(c, b)) | q(b, c))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(c, b)) | q(b, c)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 47, 68, 12])).
% 0.19/0.40 tff(73,plain,(p(c, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(d, c) | q(d, c))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(d, c) | q(d, c))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(d, c) | q(d, c))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(d, c) | q(d, c)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (p(d, c)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 8, 51])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | ((~p(d, c)) | (~p(c, b)) | p(d, b))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(d, c)) | (~p(c, b)) | p(d, b))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((p(d, b) | (~p(c, b)) | (~p(d, c))) <=> ((~p(d, c)) | (~p(c, b)) | p(d, b))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(d, b) | (~p(c, b)) | (~p(d, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | ((~p(d, c)) | (~p(c, b)) | p(d, b)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(d, b) | (~p(c, b)) | (~p(d, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(d, c)) | (~p(c, b)) | p(d, b))),
% 0.19/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(d, b) | (~p(c, b)) | (~p(d, c)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (~p(d, c)) | (~p(c, b)) | p(d, b)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (p(d, b)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 28, 77, 73])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((~p(a, b)) <=> (~p(a, b))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,axiom,(~p(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p_is_not_total')).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (~p(a, b)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(a, d)) | (~p(d, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, d)) | (~p(d, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((p(a, b) | (~p(d, b)) | (~p(a, d))) <=> (p(a, b) | (~p(a, d)) | (~p(d, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(d, b)) | (~p(a, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(a, d)) | (~p(d, b))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(d, b)) | (~p(a, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, d)) | (~p(d, b)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(d, b)) | (~p(a, d)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, d)) | (~p(d, b))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~p(a, d)) | (~p(d, b))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 28, 87])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (~p(a, d)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 84])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(a, d) | q(a, d))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(a, d) | q(a, d))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(a, d) | q(a, d))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(a, d) | q(a, d)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (q(a, d)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 8, 95])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(a, c)) | (~p(c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, c)) | (~p(c, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((p(a, b) | (~p(c, b)) | (~p(a, c))) <=> (p(a, b) | (~p(a, c)) | (~p(c, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(c, b)) | (~p(a, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(a, c)) | (~p(c, b))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(c, b)) | (~p(a, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, c)) | (~p(c, b)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | (p(a, b) | (~p(c, b)) | (~p(a, c)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : (p(X, Z) | (~p(Y, Z)) | (~p(X, Y)))) | p(a, b) | (~p(a, c)) | (~p(c, b))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~p(a, c)) | (~p(c, b))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 28, 87])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (~p(a, c)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 73])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(a, c) | q(a, c))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(a, c) | q(a, c))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | (p(a, c) | q(a, c))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (p(X, Y) | q(X, Y))) | p(a, c) | q(a, c)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (q(a, c)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 8, 107])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(a, c)) | q(c, a))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(a, c)) | q(c, a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(a, c)) | q(c, a))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(a, c)) | q(c, a)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (q(c, a)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[114, 47, 111])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(c, d) | (~q(a, d)) | (~q(c, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(c, d) | (~q(a, d)) | (~q(c, a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(c, d) | (~q(a, d)) | (~q(c, a)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(c, d) | (~q(a, d)) | (~q(c, a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~q(a, d)) | (~q(c, a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[118, 60, 15])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 115, 99])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------