%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ028-6 : TPTP v9.0.0. Released v2.0.0.
% 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 05:23:12 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : PUZ028-6 : TPTP v9.0.0. Released v2.0.0.
% 0.02/0.11 % 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 02:42:26 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(familiar_type, type, (
% 0.18/0.38 familiar: ( $i * $i ) > $o)).
% 0.18/0.38 tff(n2_type, type, (
% 0.18/0.38 n2: $i)).
% 0.18/0.38 tff(n4_type, type, (
% 0.18/0.38 n4: $i)).
% 0.18/0.38 tff(not_familiar_type, type, (
% 0.18/0.38 not_familiar: ( $i * $i ) > $o)).
% 0.18/0.38 tff(n1_type, type, (
% 0.18/0.38 n1: $i)).
% 0.18/0.38 tff(n5_type, type, (
% 0.18/0.38 n5: $i)).
% 0.18/0.38 tff(n3_type, type, (
% 0.18/0.38 n3: $i)).
% 0.18/0.38 tff(n6_type, type, (
% 0.18/0.38 n6: $i)).
% 0.18/0.38 tff(person_type, type, (
% 0.18/0.38 person: $i > $o)).
% 0.18/0.38 tff(not_equal_type, type, (
% 0.18/0.38 not_equal: ( $i * $i ) > $o)).
% 0.18/0.38 tff(1,assumption,(familiar(n4, n1)), introduced(assumption)).
% 0.18/0.38 tff(2,assumption,(familiar(n1, n3)), introduced(assumption)).
% 0.18/0.38 tff(3,assumption,(familiar(n6, n1)), introduced(assumption)).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (^[X2: $i, X1: $i] : refl(((~familiar(X1, X2)) | familiar(X2, X1)) <=> ((~familiar(X1, X2)) | familiar(X2, X1)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1)) <=> ![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1)) <=> ![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(7,axiom,(![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_familiar')).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.38 tff(9,plain,(
% 0.18/0.38 ![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))),
% 0.18/0.38 inference(skolemize,[status(sab)],[8])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n6, n1)) | familiar(n1, n6))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n6, n1)) | familiar(n1, n6))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n6, n1)) | familiar(n1, n6))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n6, n1)) | familiar(n1, n6)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (familiar(n1, n6)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (^[X3: $i, X2: $i, X1: $i] : refl(((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3))) <=> ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (^[X3: $i, X2: $i, X1: $i] : rewrite((((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X3, X1))) <=> ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : (((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X3, X1))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.38 tff(20,axiom,(![X3: $i, X2: $i, X1: $i] : (((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X3, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','three_familiar')).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.38 tff(23,plain,(
% 0.18/0.38 ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[22])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n6, n1)) | (~familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n6, n1)) | (~familiar(n3, n6)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n6, n1)) | (~familiar(n3, n6)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n6, n1)) | (~familiar(n3, n6))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (~familiar(n3, n6)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[27, 24, 2, 3])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (^[Y: $i, X: $i] : refl(((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) <=> ((~person(X)) | not_familiar(X, Y) | familiar(X, Y))), ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) <=> (((~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~person(Y))))), rewrite((((~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~person(Y))) <=> ((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))), ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) <=> ((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)))), (((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~not_equal(X, Y))) <=> (((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~not_equal(X, Y))))), rewrite((((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~not_equal(X, Y))) <=> ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))), (((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~not_equal(X, Y))) <=> ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~not_equal(X, Y))) <=> ![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.38 tff(34,axiom,(![Y: $i, X: $i] : ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~not_equal(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','familiar_or_not')).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.38 tff(37,plain,(
% 0.18/0.38 ![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(skolemize,[status(sab)],[36])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (not_equal(n3, n6) <=> not_equal(n3, n6)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(40,axiom,(not_equal(n3, n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_3_6')).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (not_equal(n3, n6)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (person(n6) <=> person(n6)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(43,axiom,(person(n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_6')).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (person(n6)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (person(n3) <=> person(n3)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(46,axiom,(person(n3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_3')).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (person(n3)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~not_equal(n3, n6)) | (~person(n6)) | (~person(n3)) | not_familiar(n3, n6) | familiar(n3, n6)) <=> ((~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n6)) | (~person(n6)) | (~person(n3)) | not_familiar(n3, n6) | familiar(n3, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n6)) | (~person(n6)) | (~person(n3)) | not_familiar(n3, n6) | familiar(n3, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6))),
% 0.18/0.38 inference(transitivity,[status(thm)],[50, 48])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n6)) | (~person(n6)) | (~person(n3)) | not_familiar(n3, n6) | familiar(n3, n6))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n6)) | (~not_equal(n3, n6)) | not_familiar(n3, n6) | familiar(n3, n6)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (not_familiar(n3, n6) | familiar(n3, n6)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[53, 47, 44, 41, 38])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (not_familiar(n3, n6)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[54, 28])).
% 0.18/0.38 tff(56,assumption,(familiar(n1, n6)), introduced(assumption)).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n6)) | (~familiar(n4, n1)) | (~familiar(n6, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n6)) | (~familiar(n4, n1)) | (~familiar(n6, n4)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n6)) | (~familiar(n4, n1)) | (~familiar(n6, n4)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n6)) | (~familiar(n4, n1)) | (~familiar(n6, n4))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (~familiar(n6, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 24, 56, 1])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (not_equal(n6, n4) <=> not_equal(n6, n4)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(62,axiom,(not_equal(n6, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_6_4')).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (not_equal(n6, n4)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (person(n4) <=> person(n4)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(65,axiom,(person(n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_4')).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (person(n4)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~not_equal(n6, n4)) | (~person(n4)) | (~person(n6)) | not_familiar(n6, n4) | familiar(n6, n4)) <=> ((~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n4)) | (~person(n4)) | (~person(n6)) | not_familiar(n6, n4) | familiar(n6, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n4)) | (~person(n4)) | (~person(n6)) | not_familiar(n6, n4) | familiar(n6, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4))),
% 0.18/0.39 inference(transitivity,[status(thm)],[69, 67])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n4)) | (~person(n4)) | (~person(n6)) | not_familiar(n6, n4) | familiar(n6, n4))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n6, n4)) | not_familiar(n6, n4) | familiar(n6, n4)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (not_familiar(n6, n4) | familiar(n6, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[72, 66, 44, 63, 38])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (not_familiar(n6, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[73, 60])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n4, n1)) | (~familiar(n3, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n4, n1)) | (~familiar(n3, n4)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n4, n1)) | (~familiar(n3, n4)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n4, n1)) | (~familiar(n3, n4))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (~familiar(n3, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[77, 24, 2, 1])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (not_equal(n3, n4) <=> not_equal(n3, n4)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(80,axiom,(not_equal(n3, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_3_4')).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (not_equal(n3, n4)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (((~not_equal(n3, n4)) | (~person(n4)) | (~person(n3)) | not_familiar(n3, n4) | familiar(n3, n4)) <=> ((~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n4)) | (~person(n4)) | (~person(n3)) | not_familiar(n3, n4) | familiar(n3, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[83])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n4)) | (~person(n4)) | (~person(n3)) | not_familiar(n3, n4) | familiar(n3, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4))),
% 0.18/0.39 inference(transitivity,[status(thm)],[84, 82])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n4)) | (~person(n4)) | (~person(n3)) | not_familiar(n3, n4) | familiar(n3, n4))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n4)) | (~not_equal(n3, n4)) | not_familiar(n3, n4) | familiar(n3, n4)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (not_familiar(n3, n4) | familiar(n3, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[87, 47, 66, 81, 38])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (not_familiar(n3, n4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[88, 78])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (^[X2: $i, X1: $i] : refl(((~not_familiar(X1, X2)) | not_familiar(X2, X1)) <=> ((~not_familiar(X1, X2)) | not_familiar(X2, X1)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1)) <=> ![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1)) <=> ![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(93,axiom,(![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_not_familiar')).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.39 tff(95,plain,(
% 0.18/0.39 ![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))),
% 0.18/0.39 inference(skolemize,[status(sab)],[94])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n4)) | not_familiar(n4, n3))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n4)) | not_familiar(n4, n3))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n4)) | not_familiar(n4, n3))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n4)) | not_familiar(n4, n3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 (not_familiar(n4, n3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[99, 96, 89])).
% 0.18/0.39 tff(101,assumption,(not_familiar(n3, n6)), introduced(assumption)).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (^[X3: $i, X2: $i, X1: $i] : refl(((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3))) <=> ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 (^[X3: $i, X2: $i, X1: $i] : rewrite((((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X3, X1))) <=> ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : (((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X3, X1))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.39 tff(107,axiom,(![X3: $i, X2: $i, X1: $i] : (((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X3, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','three_not_familiar')).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.39 tff(109,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.39 tff(110,plain,(
% 0.18/0.39 ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[109])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 (((~not_familiar(n6, n4)) | (~not_familiar(n3, n6)) | (~not_familiar(n4, n3))) <=> ((~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n3, n6)) | (~not_familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[113])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n3, n6)) | (~not_familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[114, 112])).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n3, n6)) | (~not_familiar(n4, n3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n3)) | (~not_familiar(n3, n6))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[117, 111, 101, 100, 74])).
% 0.18/0.39 tff(119,plain,((~familiar(n4, n1)) | (~not_familiar(n3, n6)) | (~familiar(n1, n6)) | (~familiar(n1, n3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (~familiar(n4, n1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[119, 55, 14, 2])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (not_equal(n4, n1) <=> not_equal(n4, n1)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(122,axiom,(not_equal(n4, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_4_1')).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (not_equal(n4, n1)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (person(n1) <=> person(n1)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(125,axiom,(person(n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_1')).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (person(n1)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (((~not_equal(n4, n1)) | (~person(n1)) | (~person(n4)) | not_familiar(n4, n1) | familiar(n4, n1)) <=> ((~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n1)) | (~person(n1)) | (~person(n4)) | not_familiar(n4, n1) | familiar(n4, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[128])).
% 0.18/0.40 tff(130,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n1)) | (~person(n1)) | (~person(n4)) | not_familiar(n4, n1) | familiar(n4, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1))),
% 0.18/0.40 inference(transitivity,[status(thm)],[129, 127])).
% 0.18/0.40 tff(131,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n1)) | (~person(n1)) | (~person(n4)) | not_familiar(n4, n1) | familiar(n4, n1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(132,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n4)) | (~not_equal(n4, n1)) | not_familiar(n4, n1) | familiar(n4, n1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.40 tff(133,plain,
% 0.18/0.40 (not_familiar(n4, n1) | familiar(n4, n1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[132, 126, 66, 123, 38])).
% 0.18/0.40 tff(134,plain,
% 0.18/0.40 (not_familiar(n4, n1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[133, 120])).
% 0.18/0.40 tff(135,plain,
% 0.18/0.40 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n3)) | familiar(n3, n1))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n3)) | familiar(n3, n1))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(136,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n3)) | familiar(n3, n1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(137,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n3)) | familiar(n3, n1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 (familiar(n3, n1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[137, 10, 2])).
% 0.18/0.40 tff(139,plain,
% 0.18/0.40 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n6)) | not_familiar(n6, n3))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n6)) | not_familiar(n6, n3))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n6)) | not_familiar(n6, n3))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n6)) | not_familiar(n6, n3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 (not_familiar(n6, n3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[141, 96, 55])).
% 0.18/0.40 tff(143,assumption,(not_familiar(n6, n3)), introduced(assumption)).
% 0.18/0.40 tff(144,assumption,(familiar(n1, n5)), introduced(assumption)).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (~familiar(n5, n6)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[147, 24, 144, 3])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 (not_equal(n5, n6) <=> not_equal(n5, n6)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(150,axiom,(not_equal(n5, n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_5_6')).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (not_equal(n5, n6)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.18/0.40 tff(152,plain,
% 0.18/0.40 (person(n5) <=> person(n5)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(153,axiom,(person(n5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_5')).
% 0.18/0.40 tff(154,plain,
% 0.18/0.40 (person(n5)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.18/0.40 tff(155,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(156,plain,
% 0.18/0.40 (((~not_equal(n5, n6)) | (~person(n6)) | (~person(n5)) | not_familiar(n5, n6) | familiar(n5, n6)) <=> ((~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(157,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n6)) | (~person(n6)) | (~person(n5)) | not_familiar(n5, n6) | familiar(n5, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[156])).
% 0.18/0.40 tff(158,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n6)) | (~person(n6)) | (~person(n5)) | not_familiar(n5, n6) | familiar(n5, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6))),
% 0.18/0.40 inference(transitivity,[status(thm)],[157, 155])).
% 0.18/0.40 tff(159,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n6)) | (~person(n6)) | (~person(n5)) | not_familiar(n5, n6) | familiar(n5, n6))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(160,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n5)) | (~person(n6)) | (~not_equal(n5, n6)) | not_familiar(n5, n6) | familiar(n5, n6)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.40 tff(161,plain,
% 0.18/0.40 (not_familiar(n5, n6) | familiar(n5, n6)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[160, 154, 44, 151, 38])).
% 0.18/0.40 tff(162,plain,
% 0.18/0.40 (not_familiar(n5, n6)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[161, 148])).
% 0.18/0.40 tff(163,assumption,(familiar(n3, n1)), introduced(assumption)).
% 0.18/0.40 tff(164,plain,
% 0.18/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n3, n1)) | (~familiar(n5, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n3, n1)) | (~familiar(n5, n3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(165,plain,
% 0.18/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n3, n1)) | (~familiar(n5, n3)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(166,plain,
% 0.18/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n3, n1)) | (~familiar(n5, n3))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.40 tff(167,plain,
% 0.18/0.40 (~familiar(n5, n3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[166, 24, 144, 163])).
% 0.18/0.40 tff(168,plain,
% 0.18/0.40 (not_equal(n5, n3) <=> not_equal(n5, n3)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(169,axiom,(not_equal(n5, n3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_5_3')).
% 0.18/0.40 tff(170,plain,
% 0.18/0.40 (not_equal(n5, n3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.40 tff(171,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(172,plain,
% 0.18/0.40 (((~not_equal(n5, n3)) | (~person(n3)) | (~person(n5)) | not_familiar(n5, n3) | familiar(n5, n3)) <=> ((~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(173,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n3)) | (~person(n3)) | (~person(n5)) | not_familiar(n5, n3) | familiar(n5, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[172])).
% 0.18/0.40 tff(174,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n3)) | (~person(n3)) | (~person(n5)) | not_familiar(n5, n3) | familiar(n5, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3))),
% 0.18/0.40 inference(transitivity,[status(thm)],[173, 171])).
% 0.18/0.40 tff(175,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n3)) | (~person(n3)) | (~person(n5)) | not_familiar(n5, n3) | familiar(n5, n3))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(176,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n5, n3)) | not_familiar(n5, n3) | familiar(n5, n3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.18/0.40 tff(177,plain,
% 0.18/0.40 (not_familiar(n5, n3) | familiar(n5, n3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[176, 47, 154, 170, 38])).
% 0.18/0.40 tff(178,plain,
% 0.18/0.40 (not_familiar(n5, n3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[177, 167])).
% 0.18/0.40 tff(179,plain,
% 0.18/0.40 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n3)) | not_familiar(n3, n5))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n3)) | not_familiar(n3, n5))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(180,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n3)) | not_familiar(n3, n5))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(181,plain,
% 0.18/0.40 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n3)) | not_familiar(n3, n5)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.18/0.40 tff(182,plain,
% 0.18/0.40 (not_familiar(n3, n5)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[181, 96, 178])).
% 0.18/0.40 tff(183,plain,
% 0.18/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(184,plain,
% 0.18/0.41 (((~not_familiar(n6, n3)) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5))) <=> ((~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(185,plain,
% 0.18/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n3)) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[184])).
% 0.18/0.41 tff(186,plain,
% 0.18/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n3)) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[185, 183])).
% 0.18/0.41 tff(187,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n3)) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(188,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n3, n5)) | (~not_familiar(n6, n3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.18/0.41 tff(189,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[188, 111, 182, 162, 143])).
% 0.18/0.41 tff(190,plain,((~familiar(n1, n5)) | (~not_familiar(n6, n3)) | (~familiar(n6, n1)) | (~familiar(n3, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(191,plain,
% 0.18/0.41 (~familiar(n1, n5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[190, 142, 3, 138])).
% 0.18/0.41 tff(192,plain,
% 0.18/0.41 (not_equal(n1, n5) <=> not_equal(n1, n5)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(193,axiom,(not_equal(n1, n5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_1_5')).
% 0.18/0.41 tff(194,plain,
% 0.18/0.41 (not_equal(n1, n5)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.18/0.41 tff(195,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(196,plain,
% 0.18/0.41 (((~not_equal(n1, n5)) | (~person(n5)) | (~person(n1)) | not_familiar(n1, n5) | familiar(n1, n5)) <=> ((~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(197,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n5)) | (~person(n5)) | (~person(n1)) | not_familiar(n1, n5) | familiar(n1, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[196])).
% 0.18/0.41 tff(198,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n5)) | (~person(n5)) | (~person(n1)) | not_familiar(n1, n5) | familiar(n1, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5))),
% 0.18/0.41 inference(transitivity,[status(thm)],[197, 195])).
% 0.18/0.41 tff(199,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n5)) | (~person(n5)) | (~person(n1)) | not_familiar(n1, n5) | familiar(n1, n5))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(200,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n5)) | (~person(n5)) | not_familiar(n1, n5) | familiar(n1, n5)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.18/0.41 tff(201,plain,
% 0.18/0.41 (not_familiar(n1, n5) | familiar(n1, n5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[200, 126, 154, 194, 38])).
% 0.18/0.41 tff(202,plain,
% 0.18/0.41 (not_familiar(n1, n5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[201, 191])).
% 0.18/0.41 tff(203,plain,
% 0.18/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n4, n1)) | (~not_familiar(n5, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1)) | (~not_familiar(n5, n4)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(204,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n4, n1)) | (~not_familiar(n5, n4)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(205,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1)) | (~not_familiar(n5, n4))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.18/0.41 tff(206,plain,
% 0.18/0.41 (~not_familiar(n5, n4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[205, 111, 202, 134])).
% 0.18/0.41 tff(207,plain,
% 0.18/0.41 (not_equal(n5, n4) <=> not_equal(n5, n4)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(208,axiom,(not_equal(n5, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_5_4')).
% 0.18/0.41 tff(209,plain,
% 0.18/0.41 (not_equal(n5, n4)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.18/0.41 tff(210,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(211,plain,
% 0.18/0.41 (((~not_equal(n5, n4)) | (~person(n4)) | (~person(n5)) | not_familiar(n5, n4) | familiar(n5, n4)) <=> ((~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(212,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n4)) | (~person(n4)) | (~person(n5)) | not_familiar(n5, n4) | familiar(n5, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[211])).
% 0.18/0.41 tff(213,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n4)) | (~person(n4)) | (~person(n5)) | not_familiar(n5, n4) | familiar(n5, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4))),
% 0.18/0.41 inference(transitivity,[status(thm)],[212, 210])).
% 0.18/0.41 tff(214,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n4)) | (~person(n4)) | (~person(n5)) | not_familiar(n5, n4) | familiar(n5, n4))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(215,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n5, n4)) | not_familiar(n5, n4) | familiar(n5, n4)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.18/0.41 tff(216,plain,
% 0.18/0.41 (not_familiar(n5, n4) | familiar(n5, n4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[215, 66, 154, 209, 38])).
% 0.18/0.41 tff(217,plain,
% 0.18/0.41 (familiar(n5, n4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[216, 206])).
% 0.18/0.41 tff(218,assumption,(familiar(n1, n2)), introduced(assumption)).
% 0.18/0.41 tff(219,plain,
% 0.18/0.41 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n2)) | familiar(n2, n1))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n2)) | familiar(n2, n1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(220,plain,
% 0.18/0.41 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n2)) | familiar(n2, n1))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(221,plain,
% 0.18/0.41 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n2)) | familiar(n2, n1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.18/0.41 tff(222,plain,
% 0.18/0.41 (familiar(n2, n1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[221, 10, 218])).
% 0.18/0.41 tff(223,assumption,(not_familiar(n6, n1)), introduced(assumption)).
% 0.18/0.41 tff(224,plain,
% 0.18/0.41 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n5)) | familiar(n5, n1))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n5)) | familiar(n5, n1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(225,plain,
% 0.18/0.41 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n5)) | familiar(n5, n1))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(226,plain,
% 0.18/0.41 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n5)) | familiar(n5, n1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.18/0.41 tff(227,plain,
% 0.18/0.41 (familiar(n5, n1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[226, 10, 144])).
% 0.18/0.41 tff(228,plain,
% 0.18/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n2, n1)) | (~familiar(n5, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n2, n1)) | (~familiar(n5, n2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(229,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n2, n1)) | (~familiar(n5, n2)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(230,plain,
% 0.18/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n2, n1)) | (~familiar(n5, n2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.18/0.41 tff(231,plain,
% 0.18/0.41 (~familiar(n5, n2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[230, 24, 144, 222])).
% 0.18/0.41 tff(232,plain,
% 0.18/0.41 (not_equal(n5, n2) <=> not_equal(n5, n2)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(233,axiom,(not_equal(n5, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_5_2')).
% 0.18/0.41 tff(234,plain,
% 0.18/0.41 (not_equal(n5, n2)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.18/0.41 tff(235,plain,
% 0.18/0.41 (person(n2) <=> person(n2)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(236,axiom,(person(n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','person_2')).
% 0.18/0.41 tff(237,plain,
% 0.18/0.41 (person(n2)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.18/0.41 tff(238,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(239,plain,
% 0.18/0.42 (((~not_equal(n5, n2)) | (~person(n2)) | (~person(n5)) | not_familiar(n5, n2) | familiar(n5, n2)) <=> ((~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(240,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n2)) | (~person(n2)) | (~person(n5)) | not_familiar(n5, n2) | familiar(n5, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[239])).
% 0.18/0.42 tff(241,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n2)) | (~person(n2)) | (~person(n5)) | not_familiar(n5, n2) | familiar(n5, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2))),
% 0.18/0.42 inference(transitivity,[status(thm)],[240, 238])).
% 0.18/0.42 tff(242,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n5, n2)) | (~person(n2)) | (~person(n5)) | not_familiar(n5, n2) | familiar(n5, n2))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(243,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n5)) | (~not_equal(n5, n2)) | not_familiar(n5, n2) | familiar(n5, n2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.18/0.42 tff(244,plain,
% 0.18/0.42 (not_familiar(n5, n2) | familiar(n5, n2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[243, 237, 154, 234, 38])).
% 0.18/0.42 tff(245,plain,
% 0.18/0.42 (not_familiar(n5, n2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[244, 231])).
% 0.18/0.42 tff(246,assumption,(not_familiar(n5, n2)), introduced(assumption)).
% 0.18/0.42 tff(247,assumption,(familiar(n5, n1)), introduced(assumption)).
% 0.18/0.42 tff(248,plain,
% 0.18/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(249,plain,
% 0.18/0.42 (((~familiar(n1, n3)) | (~familiar(n5, n1)) | (~familiar(n3, n5))) <=> ((~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(250,plain,
% 0.18/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n5, n1)) | (~familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[249])).
% 0.18/0.42 tff(251,plain,
% 0.18/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n5, n1)) | (~familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[250, 248])).
% 0.18/0.42 tff(252,plain,
% 0.18/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n5, n1)) | (~familiar(n3, n5)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(253,plain,
% 0.18/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n3, n5)) | (~familiar(n5, n1))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.18/0.42 tff(254,plain,
% 0.18/0.42 (~familiar(n3, n5)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[253, 24, 2, 247])).
% 0.18/0.42 tff(255,plain,
% 0.18/0.42 (not_equal(n3, n5) <=> not_equal(n3, n5)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(256,axiom,(not_equal(n3, n5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_3_5')).
% 0.18/0.42 tff(257,plain,
% 0.18/0.42 (not_equal(n3, n5)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.18/0.42 tff(258,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(259,plain,
% 0.18/0.42 (((~not_equal(n3, n5)) | (~person(n5)) | (~person(n3)) | not_familiar(n3, n5) | familiar(n3, n5)) <=> ((~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(260,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n5)) | (~person(n5)) | (~person(n3)) | not_familiar(n3, n5) | familiar(n3, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[259])).
% 0.18/0.42 tff(261,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n5)) | (~person(n5)) | (~person(n3)) | not_familiar(n3, n5) | familiar(n3, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5))),
% 0.18/0.42 inference(transitivity,[status(thm)],[260, 258])).
% 0.18/0.42 tff(262,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n5)) | (~person(n5)) | (~person(n3)) | not_familiar(n3, n5) | familiar(n3, n5))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(263,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n3)) | (~person(n5)) | (~not_equal(n3, n5)) | not_familiar(n3, n5) | familiar(n3, n5)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.18/0.42 tff(264,plain,
% 0.18/0.42 (not_familiar(n3, n5) | familiar(n3, n5)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[263, 47, 154, 257, 38])).
% 0.18/0.42 tff(265,plain,
% 0.18/0.42 (not_familiar(n3, n5)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[264, 254])).
% 0.18/0.42 tff(266,assumption,(familiar(n2, n1)), introduced(assumption)).
% 0.18/0.42 tff(267,plain,
% 0.18/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n2, n1)) | (~familiar(n3, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n2, n1)) | (~familiar(n3, n2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(268,plain,
% 0.18/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n3)) | (~familiar(n2, n1)) | (~familiar(n3, n2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(269,plain,
% 0.18/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n3)) | (~familiar(n2, n1)) | (~familiar(n3, n2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.18/0.42 tff(270,plain,
% 0.18/0.42 (~familiar(n3, n2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[269, 24, 2, 266])).
% 0.18/0.42 tff(271,plain,
% 0.18/0.42 (not_equal(n3, n2) <=> not_equal(n3, n2)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(272,axiom,(not_equal(n3, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_3_2')).
% 0.18/0.42 tff(273,plain,
% 0.18/0.42 (not_equal(n3, n2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.18/0.42 tff(274,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(275,plain,
% 0.18/0.42 (((~not_equal(n3, n2)) | (~person(n2)) | (~person(n3)) | not_familiar(n3, n2) | familiar(n3, n2)) <=> ((~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(276,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n2)) | (~person(n2)) | (~person(n3)) | not_familiar(n3, n2) | familiar(n3, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[275])).
% 0.18/0.42 tff(277,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n2)) | (~person(n2)) | (~person(n3)) | not_familiar(n3, n2) | familiar(n3, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2))),
% 0.18/0.42 inference(transitivity,[status(thm)],[276, 274])).
% 0.18/0.42 tff(278,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n3, n2)) | (~person(n2)) | (~person(n3)) | not_familiar(n3, n2) | familiar(n3, n2))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(279,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n3)) | (~not_equal(n3, n2)) | not_familiar(n3, n2) | familiar(n3, n2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.18/0.42 tff(280,plain,
% 0.18/0.42 (not_familiar(n3, n2) | familiar(n3, n2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[279, 237, 47, 273, 38])).
% 0.18/0.42 tff(281,plain,
% 0.18/0.42 (not_familiar(n3, n2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[280, 270])).
% 0.18/0.42 tff(282,plain,
% 0.18/0.42 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n2)) | not_familiar(n2, n3))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n2)) | not_familiar(n2, n3))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(283,plain,
% 0.18/0.42 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n3, n2)) | not_familiar(n2, n3))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(284,plain,
% 0.18/0.42 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n3, n2)) | not_familiar(n2, n3)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.18/0.42 tff(285,plain,
% 0.18/0.42 (not_familiar(n2, n3)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[284, 96, 281])).
% 0.18/0.42 tff(286,plain,
% 0.18/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n3, n5)) | (~not_familiar(n2, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n2)) | (~not_familiar(n3, n5)) | (~not_familiar(n2, n3)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(287,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n3, n5)) | (~not_familiar(n2, n3)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(288,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n2)) | (~not_familiar(n3, n5)) | (~not_familiar(n2, n3))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.18/0.43 tff(289,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[288, 111, 285, 265, 246])).
% 0.18/0.43 tff(290,plain,((~familiar(n1, n3)) | (~not_familiar(n5, n2)) | (~familiar(n5, n1)) | (~familiar(n2, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(291,plain,
% 0.18/0.43 (~familiar(n1, n3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[290, 245, 227, 222])).
% 0.18/0.43 tff(292,plain,
% 0.18/0.43 (not_equal(n1, n3) <=> not_equal(n1, n3)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(293,axiom,(not_equal(n1, n3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_1_3')).
% 0.18/0.43 tff(294,plain,
% 0.18/0.43 (not_equal(n1, n3)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.18/0.43 tff(295,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(296,plain,
% 0.18/0.43 (((~not_equal(n1, n3)) | (~person(n3)) | (~person(n1)) | not_familiar(n1, n3) | familiar(n1, n3)) <=> ((~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(297,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n3)) | (~person(n3)) | (~person(n1)) | not_familiar(n1, n3) | familiar(n1, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[296])).
% 0.18/0.43 tff(298,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n3)) | (~person(n3)) | (~person(n1)) | not_familiar(n1, n3) | familiar(n1, n3))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3))),
% 0.18/0.43 inference(transitivity,[status(thm)],[297, 295])).
% 0.18/0.43 tff(299,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n3)) | (~person(n3)) | (~person(n1)) | not_familiar(n1, n3) | familiar(n1, n3))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(300,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n3)) | (~person(n3)) | not_familiar(n1, n3) | familiar(n1, n3)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.18/0.43 tff(301,plain,
% 0.18/0.43 (not_familiar(n1, n3) | familiar(n1, n3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[300, 126, 47, 294, 38])).
% 0.18/0.43 tff(302,plain,
% 0.18/0.43 (not_familiar(n1, n3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[301, 291])).
% 0.18/0.43 tff(303,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n4, n1)) | (~familiar(n5, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n4, n1)) | (~familiar(n5, n4)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(304,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n4, n1)) | (~familiar(n5, n4)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(305,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n4, n1)) | (~familiar(n5, n4))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.18/0.43 tff(306,plain,
% 0.18/0.43 (~familiar(n5, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[305, 24, 144, 1])).
% 0.18/0.43 tff(307,plain,
% 0.18/0.43 (not_familiar(n5, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[216, 306])).
% 0.18/0.43 tff(308,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(309,plain,
% 0.18/0.43 (((~familiar(n1, n2)) | (~familiar(n4, n1)) | (~familiar(n2, n4))) <=> ((~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(310,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n4, n1)) | (~familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[309])).
% 0.18/0.43 tff(311,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n4, n1)) | (~familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[310, 308])).
% 0.18/0.43 tff(312,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n4, n1)) | (~familiar(n2, n4)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(313,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n4)) | (~familiar(n4, n1))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.18/0.43 tff(314,plain,
% 0.18/0.43 (~familiar(n2, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[313, 24, 218, 1])).
% 0.18/0.43 tff(315,plain,
% 0.18/0.43 (not_equal(n2, n4) <=> not_equal(n2, n4)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(316,axiom,(not_equal(n2, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_2_4')).
% 0.18/0.43 tff(317,plain,
% 0.18/0.43 (not_equal(n2, n4)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.18/0.43 tff(318,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(319,plain,
% 0.18/0.43 (((~not_equal(n2, n4)) | (~person(n4)) | (~person(n2)) | not_familiar(n2, n4) | familiar(n2, n4)) <=> ((~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(320,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n4)) | (~person(n4)) | (~person(n2)) | not_familiar(n2, n4) | familiar(n2, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[319])).
% 0.18/0.43 tff(321,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n4)) | (~person(n4)) | (~person(n2)) | not_familiar(n2, n4) | familiar(n2, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4))),
% 0.18/0.43 inference(transitivity,[status(thm)],[320, 318])).
% 0.18/0.43 tff(322,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n4)) | (~person(n4)) | (~person(n2)) | not_familiar(n2, n4) | familiar(n2, n4))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(323,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n4)) | (~not_equal(n2, n4)) | not_familiar(n2, n4) | familiar(n2, n4)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.18/0.43 tff(324,plain,
% 0.18/0.43 (not_familiar(n2, n4) | familiar(n2, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[323, 237, 66, 317, 38])).
% 0.18/0.43 tff(325,plain,
% 0.18/0.43 (not_familiar(n2, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[324, 314])).
% 0.18/0.43 tff(326,plain,
% 0.18/0.43 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n2, n4)) | not_familiar(n4, n2))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n2, n4)) | not_familiar(n4, n2))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(327,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n2, n4)) | not_familiar(n4, n2))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(328,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n2, n4)) | not_familiar(n4, n2)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.18/0.43 tff(329,plain,
% 0.18/0.43 (not_familiar(n4, n2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[328, 96, 325])).
% 0.18/0.43 tff(330,plain,
% 0.18/0.43 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n2)) | not_familiar(n2, n5))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n2)) | not_familiar(n2, n5))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(331,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n2)) | not_familiar(n2, n5))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(332,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n2)) | not_familiar(n2, n5)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.18/0.43 tff(333,plain,
% 0.18/0.43 (not_familiar(n2, n5)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[332, 96, 245])).
% 0.18/0.43 tff(334,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(335,plain,
% 0.18/0.43 (((~not_familiar(n5, n4)) | (~not_familiar(n2, n5)) | (~not_familiar(n4, n2))) <=> ((~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(336,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n2, n5)) | (~not_familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[335])).
% 0.18/0.43 tff(337,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n2, n5)) | (~not_familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[336, 334])).
% 0.18/0.43 tff(338,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n2, n5)) | (~not_familiar(n4, n2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(339,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n2)) | (~not_familiar(n2, n5))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.18/0.43 tff(340,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[339, 111, 333, 329, 307])).
% 0.18/0.43 tff(341,plain,((~familiar(n4, n1)) | (~familiar(n1, n5)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(342,plain,
% 0.18/0.43 (~familiar(n4, n1)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[341, 144, 218])).
% 0.18/0.43 tff(343,plain,
% 0.18/0.43 (not_familiar(n4, n1)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[133, 342])).
% 0.18/0.43 tff(344,assumption,(familiar(n6, n4)), introduced(assumption)).
% 0.18/0.43 tff(345,assumption,(not_familiar(n4, n1)), introduced(assumption)).
% 0.18/0.43 tff(346,assumption,(not_familiar(n1, n3)), introduced(assumption)).
% 0.18/0.43 tff(347,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n4, n1)) | (~not_familiar(n3, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n4, n1)) | (~not_familiar(n3, n4)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(348,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n4, n1)) | (~not_familiar(n3, n4)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(349,plain,
% 0.18/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n4, n1)) | (~not_familiar(n3, n4))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.18/0.43 tff(350,plain,
% 0.18/0.43 (~not_familiar(n3, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[349, 111, 346, 345])).
% 0.18/0.43 tff(351,plain,
% 0.18/0.43 (familiar(n3, n4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[88, 350])).
% 0.18/0.43 tff(352,plain,
% 0.18/0.43 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n4)) | familiar(n4, n3))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n4)) | familiar(n4, n3))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(353,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n4)) | familiar(n4, n3))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(354,plain,
% 0.18/0.43 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n4)) | familiar(n4, n3)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.18/0.43 tff(355,plain,
% 0.18/0.43 (familiar(n4, n3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[354, 10, 351])).
% 0.18/0.43 tff(356,plain,
% 0.18/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n6, n1)) | (~not_familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n6, n1)) | (~not_familiar(n3, n6)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(357,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n6, n1)) | (~not_familiar(n3, n6)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(358,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n6, n1)) | (~not_familiar(n3, n6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.18/0.44 tff(359,plain,
% 0.18/0.44 (~not_familiar(n3, n6)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[358, 111, 346, 223])).
% 0.18/0.44 tff(360,plain,
% 0.18/0.44 (familiar(n3, n6)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[54, 359])).
% 0.18/0.44 tff(361,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(362,plain,
% 0.18/0.44 (((~familiar(n6, n4)) | (~familiar(n3, n6)) | (~familiar(n4, n3))) <=> ((~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(363,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n3, n6)) | (~familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[362])).
% 0.18/0.44 tff(364,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n3, n6)) | (~familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[363, 361])).
% 0.18/0.44 tff(365,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n3, n6)) | (~familiar(n4, n3)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(366,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n4)) | (~familiar(n4, n3)) | (~familiar(n3, n6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.18/0.44 tff(367,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[366, 24, 360, 355, 344])).
% 0.18/0.44 tff(368,plain,((~not_familiar(n1, n3)) | (~familiar(n6, n4)) | (~not_familiar(n6, n1)) | (~not_familiar(n4, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(369,plain,
% 0.18/0.44 (~familiar(n6, n4)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[368, 343, 223, 302])).
% 0.18/0.44 tff(370,plain,
% 0.18/0.44 (not_familiar(n6, n4)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[73, 369])).
% 0.18/0.44 tff(371,plain,
% 0.18/0.44 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n6, n1)) | not_familiar(n1, n6))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n6, n1)) | not_familiar(n1, n6))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(372,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n6, n1)) | not_familiar(n1, n6))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(373,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n6, n1)) | not_familiar(n1, n6)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.18/0.44 tff(374,plain,
% 0.18/0.44 (not_familiar(n1, n6)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[373, 96, 223])).
% 0.18/0.44 tff(375,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n6)) | (~not_familiar(n4, n1)) | (~not_familiar(n6, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n6)) | (~not_familiar(n4, n1)) | (~not_familiar(n6, n4)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(376,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n6)) | (~not_familiar(n4, n1)) | (~not_familiar(n6, n4)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(377,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n6)) | (~not_familiar(n4, n1)) | (~not_familiar(n6, n4))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.18/0.44 tff(378,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[377, 111, 374, 343, 370])).
% 0.18/0.44 tff(379,plain,((~familiar(n1, n5)) | (~not_familiar(n6, n1)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(380,plain,
% 0.18/0.44 (~familiar(n1, n5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[379, 223, 218])).
% 0.18/0.44 tff(381,plain,
% 0.18/0.44 (not_familiar(n1, n5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[201, 380])).
% 0.18/0.44 tff(382,plain,
% 0.18/0.44 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n5)) | not_familiar(n5, n1))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n5)) | not_familiar(n5, n1))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(383,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n5)) | not_familiar(n5, n1))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(384,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n5)) | not_familiar(n5, n1)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.18/0.44 tff(385,plain,
% 0.18/0.44 (not_familiar(n5, n1)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[384, 96, 381])).
% 0.18/0.44 tff(386,assumption,(not_familiar(n5, n6)), introduced(assumption)).
% 0.18/0.44 tff(387,assumption,(not_familiar(n5, n4)), introduced(assumption)).
% 0.18/0.44 tff(388,plain,
% 0.18/0.44 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n4)) | not_familiar(n4, n5))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n4)) | not_familiar(n4, n5))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(389,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n4)) | not_familiar(n4, n5))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(390,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n4)) | not_familiar(n4, n5)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.18/0.44 tff(391,plain,
% 0.18/0.44 (not_familiar(n4, n5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[390, 96, 387])).
% 0.18/0.44 tff(392,plain,
% 0.18/0.44 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n6)) | not_familiar(n6, n5))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n6)) | not_familiar(n6, n5))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(393,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n5, n6)) | not_familiar(n6, n5))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(394,plain,
% 0.18/0.44 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n5, n6)) | not_familiar(n6, n5)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.18/0.44 tff(395,plain,
% 0.18/0.44 (not_familiar(n6, n5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[394, 96, 386])).
% 0.18/0.44 tff(396,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(397,plain,
% 0.18/0.44 (((~not_familiar(n5, n4)) | (~not_familiar(n6, n5)) | (~not_familiar(n4, n6))) <=> ((~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(398,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n6, n5)) | (~not_familiar(n4, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[397])).
% 0.18/0.44 tff(399,plain,
% 0.18/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n6, n5)) | (~not_familiar(n4, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[398, 396])).
% 0.18/0.44 tff(400,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n6, n5)) | (~not_familiar(n4, n6)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(401,plain,
% 0.18/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n4)) | (~not_familiar(n4, n6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.18/0.44 tff(402,plain,
% 0.18/0.44 (~not_familiar(n4, n6)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[401, 111, 387, 395])).
% 0.18/0.44 tff(403,plain,
% 0.18/0.44 (not_equal(n4, n6) <=> not_equal(n4, n6)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(404,axiom,(not_equal(n4, n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_4_6')).
% 0.18/0.44 tff(405,plain,
% 0.18/0.44 (not_equal(n4, n6)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.18/0.44 tff(406,plain,
% 0.18/0.44 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(407,plain,
% 0.18/0.44 (((~not_equal(n4, n6)) | (~person(n6)) | (~person(n4)) | not_familiar(n4, n6) | familiar(n4, n6)) <=> ((~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(408,plain,
% 0.18/0.44 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n6)) | (~person(n6)) | (~person(n4)) | not_familiar(n4, n6) | familiar(n4, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6)))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[407])).
% 0.18/0.44 tff(409,plain,
% 0.18/0.44 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n6)) | (~person(n6)) | (~person(n4)) | not_familiar(n4, n6) | familiar(n4, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6))),
% 0.18/0.45 inference(transitivity,[status(thm)],[408, 406])).
% 0.18/0.45 tff(410,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n6)) | (~person(n6)) | (~person(n4)) | not_familiar(n4, n6) | familiar(n4, n6))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(411,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n6)) | (~not_equal(n4, n6)) | not_familiar(n4, n6) | familiar(n4, n6)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.18/0.45 tff(412,plain,
% 0.18/0.45 (not_familiar(n4, n6) | familiar(n4, n6)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[411, 66, 44, 405, 38])).
% 0.18/0.45 tff(413,plain,
% 0.18/0.45 (familiar(n4, n6)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[412, 402])).
% 0.18/0.45 tff(414,plain,
% 0.18/0.45 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n6)) | familiar(n6, n4))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n6)) | familiar(n6, n4))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(415,plain,
% 0.18/0.45 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n6)) | familiar(n6, n4))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(416,plain,
% 0.18/0.45 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n6)) | familiar(n6, n4)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.18/0.45 tff(417,plain,
% 0.18/0.45 (familiar(n6, n4)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[416, 10, 413])).
% 0.18/0.45 tff(418,assumption,(not_familiar(n4, n5)), introduced(assumption)).
% 0.18/0.45 tff(419,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(420,plain,
% 0.18/0.45 (((~not_familiar(n5, n2)) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4))) <=> ((~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(421,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[420])).
% 0.18/0.45 tff(422,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[421, 419])).
% 0.18/0.45 tff(423,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(424,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n5)) | (~not_familiar(n2, n4)) | (~not_familiar(n5, n2))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.18/0.45 tff(425,plain,
% 0.18/0.45 (~not_familiar(n2, n4)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[424, 111, 418, 246])).
% 0.18/0.45 tff(426,plain,
% 0.18/0.45 (familiar(n2, n4)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[324, 425])).
% 0.18/0.45 tff(427,plain,
% 0.18/0.45 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n2, n4)) | familiar(n4, n2))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n2, n4)) | familiar(n4, n2))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(428,plain,
% 0.18/0.45 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n2, n4)) | familiar(n4, n2))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(429,plain,
% 0.18/0.45 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n2, n4)) | familiar(n4, n2)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.18/0.45 tff(430,plain,
% 0.18/0.45 (familiar(n4, n2)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[429, 10, 426])).
% 0.18/0.45 tff(431,assumption,(not_familiar(n6, n5)), introduced(assumption)).
% 0.18/0.45 tff(432,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(433,plain,
% 0.18/0.45 (((~not_familiar(n5, n2)) | (~not_familiar(n6, n5)) | (~not_familiar(n2, n6))) <=> ((~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(434,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n6, n5)) | (~not_familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[433])).
% 0.18/0.45 tff(435,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n6, n5)) | (~not_familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[434, 432])).
% 0.18/0.45 tff(436,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n2)) | (~not_familiar(n6, n5)) | (~not_familiar(n2, n6)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(437,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n5)) | (~not_familiar(n5, n2)) | (~not_familiar(n2, n6))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.18/0.45 tff(438,plain,
% 0.18/0.45 (~not_familiar(n2, n6)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[437, 111, 246, 431])).
% 0.18/0.45 tff(439,plain,
% 0.18/0.45 (not_equal(n2, n6) <=> not_equal(n2, n6)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(440,axiom,(not_equal(n2, n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_2_6')).
% 0.18/0.45 tff(441,plain,
% 0.18/0.45 (not_equal(n2, n6)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.18/0.45 tff(442,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(443,plain,
% 0.18/0.45 (((~not_equal(n2, n6)) | (~person(n6)) | (~person(n2)) | not_familiar(n2, n6) | familiar(n2, n6)) <=> ((~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(444,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n6)) | (~person(n6)) | (~person(n2)) | not_familiar(n2, n6) | familiar(n2, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[443])).
% 0.18/0.45 tff(445,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n6)) | (~person(n6)) | (~person(n2)) | not_familiar(n2, n6) | familiar(n2, n6))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6))),
% 0.18/0.45 inference(transitivity,[status(thm)],[444, 442])).
% 0.18/0.45 tff(446,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n2, n6)) | (~person(n6)) | (~person(n2)) | not_familiar(n2, n6) | familiar(n2, n6))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(447,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n2, n6)) | not_familiar(n2, n6) | familiar(n2, n6)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.18/0.45 tff(448,plain,
% 0.18/0.45 (not_familiar(n2, n6) | familiar(n2, n6)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[447, 237, 44, 441, 38])).
% 0.18/0.45 tff(449,plain,
% 0.18/0.45 (familiar(n2, n6)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[448, 438])).
% 0.18/0.45 tff(450,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n2, n6)) | (~familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n4)) | (~familiar(n2, n6)) | (~familiar(n4, n2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(451,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n2, n6)) | (~familiar(n4, n2)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(452,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n4)) | (~familiar(n2, n6)) | (~familiar(n4, n2))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.18/0.45 tff(453,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[452, 24, 449, 430, 344])).
% 0.18/0.45 tff(454,plain,((~not_familiar(n5, n2)) | (~familiar(n6, n4)) | (~not_familiar(n6, n5)) | (~not_familiar(n4, n5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(455,plain,
% 0.18/0.45 (~not_familiar(n5, n2)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[454, 417, 395, 391])).
% 0.18/0.45 tff(456,plain,
% 0.18/0.45 (familiar(n5, n2)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[244, 455])).
% 0.18/0.45 tff(457,plain,
% 0.18/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n1)) | (~familiar(n5, n2)) | (~familiar(n1, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n1)) | (~familiar(n5, n2)) | (~familiar(n1, n5)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(458,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n1)) | (~familiar(n5, n2)) | (~familiar(n1, n5)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(459,plain,
% 0.18/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n1)) | (~familiar(n5, n2)) | (~familiar(n1, n5))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.18/0.45 tff(460,plain,
% 0.18/0.45 (~familiar(n1, n5)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[459, 24, 266, 456])).
% 0.18/0.45 tff(461,plain,
% 0.18/0.45 (not_familiar(n1, n5)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[201, 460])).
% 0.18/0.46 tff(462,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(463,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(464,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.18/0.46 tff(465,plain,
% 0.18/0.46 (~not_familiar(n6, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[464, 111, 461, 386])).
% 0.18/0.46 tff(466,plain,
% 0.18/0.46 (not_equal(n6, n1) <=> not_equal(n6, n1)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(467,axiom,(not_equal(n6, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_6_1')).
% 0.18/0.46 tff(468,plain,
% 0.18/0.46 (not_equal(n6, n1)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.18/0.46 tff(469,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(470,plain,
% 0.18/0.46 (((~not_equal(n6, n1)) | (~person(n1)) | (~person(n6)) | not_familiar(n6, n1) | familiar(n6, n1)) <=> ((~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(471,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n1)) | (~person(n1)) | (~person(n6)) | not_familiar(n6, n1) | familiar(n6, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1)))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[470])).
% 0.18/0.46 tff(472,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n1)) | (~person(n1)) | (~person(n6)) | not_familiar(n6, n1) | familiar(n6, n1))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1))),
% 0.18/0.46 inference(transitivity,[status(thm)],[471, 469])).
% 0.18/0.46 tff(473,plain,
% 0.18/0.46 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n1)) | (~person(n1)) | (~person(n6)) | not_familiar(n6, n1) | familiar(n6, n1))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(474,plain,
% 0.18/0.46 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~person(n6)) | (~not_equal(n6, n1)) | not_familiar(n6, n1) | familiar(n6, n1)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.18/0.46 tff(475,plain,
% 0.18/0.46 (not_familiar(n6, n1) | familiar(n6, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[474, 126, 44, 468, 38])).
% 0.18/0.46 tff(476,plain,
% 0.18/0.46 (familiar(n6, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[475, 465])).
% 0.18/0.46 tff(477,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(478,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(479,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n1, n5)) | (~not_familiar(n4, n1))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.18/0.46 tff(480,plain,
% 0.18/0.46 (~not_familiar(n4, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[479, 111, 461, 387])).
% 0.18/0.46 tff(481,plain,
% 0.18/0.46 (familiar(n4, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[133, 480])).
% 0.18/0.46 tff(482,plain,
% 0.18/0.46 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n1)) | familiar(n1, n4))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n1)) | familiar(n1, n4))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(483,plain,
% 0.18/0.46 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n1)) | familiar(n1, n4))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(484,plain,
% 0.18/0.46 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n1)) | familiar(n1, n4)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.18/0.46 tff(485,plain,
% 0.18/0.46 (familiar(n1, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[484, 10, 481])).
% 0.18/0.46 tff(486,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(487,plain,
% 0.18/0.46 (((~familiar(n6, n1)) | (~familiar(n4, n6)) | (~familiar(n1, n4))) <=> ((~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(488,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n4, n6)) | (~familiar(n1, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[487])).
% 0.18/0.46 tff(489,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n4, n6)) | (~familiar(n1, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[488, 486])).
% 0.18/0.46 tff(490,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n4, n6)) | (~familiar(n1, n4)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(491,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.18/0.46 tff(492,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[491, 24, 485, 413, 476])).
% 0.18/0.46 tff(493,plain,((~not_familiar(n5, n4)) | (~not_familiar(n5, n6)) | (~familiar(n2, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(494,plain,
% 0.18/0.46 (~not_familiar(n5, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[493, 386, 222])).
% 0.18/0.46 tff(495,plain,
% 0.18/0.46 (familiar(n5, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[216, 494])).
% 0.18/0.46 tff(496,assumption,(not_familiar(n1, n5)), introduced(assumption)).
% 0.18/0.46 tff(497,plain,
% 0.18/0.46 (~not_familiar(n6, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[464, 111, 496, 386])).
% 0.18/0.46 tff(498,plain,
% 0.18/0.46 (familiar(n6, n1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[475, 497])).
% 0.18/0.46 tff(499,assumption,(not_familiar(n4, n6)), introduced(assumption)).
% 0.18/0.46 tff(500,assumption,(familiar(n5, n2)), introduced(assumption)).
% 0.18/0.46 tff(501,plain,
% 0.18/0.46 (~not_familiar(n5, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[493, 386, 266])).
% 0.18/0.46 tff(502,plain,
% 0.18/0.46 (familiar(n5, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[216, 501])).
% 0.18/0.46 tff(503,plain,
% 0.18/0.46 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n4)) | familiar(n4, n5))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n4)) | familiar(n4, n5))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(504,plain,
% 0.18/0.46 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n4)) | familiar(n4, n5))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(505,plain,
% 0.18/0.46 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n4)) | familiar(n4, n5)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.18/0.46 tff(506,plain,
% 0.18/0.46 (familiar(n4, n5)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[505, 10, 502])).
% 0.18/0.46 tff(507,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(508,plain,
% 0.18/0.46 (((~familiar(n5, n2)) | (~familiar(n4, n5)) | (~familiar(n2, n4))) <=> ((~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(509,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n2)) | (~familiar(n4, n5)) | (~familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[508])).
% 0.18/0.46 tff(510,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n2)) | (~familiar(n4, n5)) | (~familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[509, 507])).
% 0.18/0.46 tff(511,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n2)) | (~familiar(n4, n5)) | (~familiar(n2, n4)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(512,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n5, n2)) | (~familiar(n2, n4))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.18/0.46 tff(513,plain,
% 0.18/0.46 (~familiar(n2, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[512, 24, 506, 500])).
% 0.18/0.46 tff(514,plain,
% 0.18/0.46 (not_familiar(n2, n4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[324, 513])).
% 0.18/0.46 tff(515,plain,
% 0.18/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n6)) | (~not_familiar(n2, n4)) | (~not_familiar(n6, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n6)) | (~not_familiar(n2, n4)) | (~not_familiar(n6, n2)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(516,plain,
% 0.18/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n6)) | (~not_familiar(n2, n4)) | (~not_familiar(n6, n2)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(517,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n6)) | (~not_familiar(n2, n4)) | (~not_familiar(n6, n2))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.18/0.47 tff(518,plain,
% 0.18/0.47 (~not_familiar(n6, n2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[517, 111, 514, 499])).
% 0.18/0.47 tff(519,plain,
% 0.18/0.47 (not_equal(n6, n2) <=> not_equal(n6, n2)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(520,axiom,(not_equal(n6, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_6_2')).
% 0.18/0.47 tff(521,plain,
% 0.18/0.47 (not_equal(n6, n2)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.18/0.47 tff(522,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(523,plain,
% 0.18/0.47 (((~not_equal(n6, n2)) | (~person(n2)) | (~person(n6)) | not_familiar(n6, n2) | familiar(n6, n2)) <=> ((~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(524,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n2)) | (~person(n2)) | (~person(n6)) | not_familiar(n6, n2) | familiar(n6, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[523])).
% 0.18/0.47 tff(525,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n2)) | (~person(n2)) | (~person(n6)) | not_familiar(n6, n2) | familiar(n6, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2))),
% 0.18/0.47 inference(transitivity,[status(thm)],[524, 522])).
% 0.18/0.47 tff(526,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n6, n2)) | (~person(n2)) | (~person(n6)) | not_familiar(n6, n2) | familiar(n6, n2))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(527,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n2)) | (~person(n6)) | (~not_equal(n6, n2)) | not_familiar(n6, n2) | familiar(n6, n2)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.18/0.47 tff(528,plain,
% 0.18/0.47 (not_familiar(n6, n2) | familiar(n6, n2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[527, 237, 44, 521, 38])).
% 0.18/0.47 tff(529,plain,
% 0.18/0.47 (familiar(n6, n2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[528, 518])).
% 0.18/0.47 tff(530,plain,
% 0.18/0.47 (~familiar(n1, n5)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[459, 24, 266, 500])).
% 0.18/0.47 tff(531,plain,
% 0.18/0.47 (not_familiar(n1, n5)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[201, 530])).
% 0.18/0.47 tff(532,plain,
% 0.18/0.47 (~not_familiar(n6, n1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[464, 111, 531, 386])).
% 0.18/0.47 tff(533,plain,
% 0.18/0.47 (familiar(n6, n1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[475, 532])).
% 0.18/0.47 tff(534,plain,
% 0.18/0.47 (familiar(n1, n6)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[13, 10, 533])).
% 0.18/0.47 tff(535,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n1)) | (~familiar(n6, n2)) | (~familiar(n1, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n1)) | (~familiar(n6, n2)) | (~familiar(n1, n6)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(536,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n1)) | (~familiar(n6, n2)) | (~familiar(n1, n6)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(537,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n1)) | (~familiar(n6, n2)) | (~familiar(n1, n6))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.18/0.47 tff(538,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[537, 24, 534, 266, 529])).
% 0.18/0.47 tff(539,plain,((~familiar(n5, n2)) | (~familiar(n2, n1)) | (~not_familiar(n4, n6)) | (~not_familiar(n5, n6))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(540,plain,
% 0.18/0.47 (~familiar(n5, n2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[539, 499, 222, 386])).
% 0.18/0.47 tff(541,plain,
% 0.18/0.47 (not_familiar(n5, n2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[244, 540])).
% 0.18/0.47 tff(542,plain,
% 0.18/0.47 (~not_familiar(n2, n6)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[437, 111, 541, 395])).
% 0.18/0.47 tff(543,plain,
% 0.18/0.47 (familiar(n2, n6)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[448, 542])).
% 0.18/0.47 tff(544,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(545,plain,
% 0.18/0.47 (((~familiar(n2, n6)) | (~familiar(n1, n2)) | (~familiar(n6, n1))) <=> ((~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(546,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n6)) | (~familiar(n1, n2)) | (~familiar(n6, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[545])).
% 0.18/0.47 tff(547,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n6)) | (~familiar(n1, n2)) | (~familiar(n6, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[546, 544])).
% 0.18/0.47 tff(548,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n6)) | (~familiar(n1, n2)) | (~familiar(n6, n1)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(549,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.18/0.47 tff(550,plain,
% 0.18/0.47 (~familiar(n6, n1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[549, 24, 218, 543])).
% 0.18/0.47 tff(551,plain,
% 0.18/0.47 (not_familiar(n6, n1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[475, 550])).
% 0.18/0.47 tff(552,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(553,plain,
% 0.18/0.47 (((~not_familiar(n6, n1)) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4))) <=> ((~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(554,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[553])).
% 0.18/0.47 tff(555,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[554, 552])).
% 0.18/0.47 tff(556,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(557,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n6)) | (~not_familiar(n1, n4)) | (~not_familiar(n6, n1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.18/0.47 tff(558,plain,
% 0.18/0.47 (~not_familiar(n1, n4)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[557, 111, 499, 551])).
% 0.18/0.47 tff(559,plain,
% 0.18/0.47 (not_equal(n1, n4) <=> not_equal(n1, n4)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(560,axiom,(not_equal(n1, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_1_4')).
% 0.18/0.47 tff(561,plain,
% 0.18/0.47 (not_equal(n1, n4)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.18/0.47 tff(562,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(563,plain,
% 0.18/0.47 (((~not_equal(n1, n4)) | (~person(n4)) | (~person(n1)) | not_familiar(n1, n4) | familiar(n1, n4)) <=> ((~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(564,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n4)) | (~person(n4)) | (~person(n1)) | not_familiar(n1, n4) | familiar(n1, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[563])).
% 0.18/0.47 tff(565,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n4)) | (~person(n4)) | (~person(n1)) | not_familiar(n1, n4) | familiar(n1, n4))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4))),
% 0.18/0.47 inference(transitivity,[status(thm)],[564, 562])).
% 0.18/0.47 tff(566,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n4)) | (~person(n4)) | (~person(n1)) | not_familiar(n1, n4) | familiar(n1, n4))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(567,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n1)) | (~not_equal(n1, n4)) | (~person(n4)) | not_familiar(n1, n4) | familiar(n1, n4)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.18/0.47 tff(568,plain,
% 0.18/0.47 (not_familiar(n1, n4) | familiar(n1, n4)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[567, 126, 66, 561, 38])).
% 0.18/0.47 tff(569,plain,
% 0.18/0.47 (familiar(n1, n4)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[568, 558])).
% 0.18/0.47 tff(570,plain,
% 0.18/0.47 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n4)) | familiar(n4, n1))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n4)) | familiar(n4, n1))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(571,plain,
% 0.18/0.47 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n1, n4)) | familiar(n4, n1))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(572,plain,
% 0.18/0.47 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n1, n4)) | familiar(n4, n1)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.18/0.47 tff(573,plain,
% 0.18/0.47 (familiar(n4, n1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[572, 10, 569])).
% 0.18/0.47 tff(574,plain,
% 0.18/0.47 (((~not_familiar(n6, n1)) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5))) <=> ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(575,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[574])).
% 0.18/0.47 tff(576,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[575, 462])).
% 0.18/0.47 tff(577,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(578,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.18/0.47 tff(579,plain,
% 0.18/0.47 (~not_familiar(n1, n5)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[578, 111, 386, 551])).
% 0.18/0.47 tff(580,plain,
% 0.18/0.47 (familiar(n1, n5)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[201, 579])).
% 0.18/0.47 tff(581,plain,
% 0.18/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n1, n5)) | (~familiar(n4, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n1, n5)) | (~familiar(n4, n1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(582,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n1, n5)) | (~familiar(n4, n1)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(583,plain,
% 0.18/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n1, n5)) | (~familiar(n4, n1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.18/0.47 tff(584,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[583, 24, 580, 573, 495])).
% 0.18/0.47 tff(585,plain,((~not_familiar(n4, n6)) | (~not_familiar(n5, n6)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(586,plain,
% 0.18/0.47 (~not_familiar(n4, n6)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[585, 386, 218])).
% 0.18/0.47 tff(587,plain,
% 0.18/0.47 (familiar(n4, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[412, 586])).
% 0.18/0.48 tff(588,plain,
% 0.18/0.48 (~familiar(n1, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[491, 24, 587, 498])).
% 0.18/0.48 tff(589,plain,
% 0.18/0.48 (not_familiar(n1, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[568, 588])).
% 0.18/0.48 tff(590,plain,
% 0.18/0.48 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n4)) | not_familiar(n4, n1))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n4)) | not_familiar(n4, n1))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(591,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n4)) | not_familiar(n4, n1))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(592,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n4)) | not_familiar(n4, n1)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.18/0.48 tff(593,plain,
% 0.18/0.48 (not_familiar(n4, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[592, 96, 589])).
% 0.18/0.48 tff(594,plain,
% 0.18/0.48 (((~familiar(n1, n2)) | (~familiar(n6, n1)) | (~familiar(n2, n6))) <=> ((~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(595,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n6, n1)) | (~familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[594])).
% 0.18/0.48 tff(596,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n6, n1)) | (~familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[595, 544])).
% 0.18/0.48 tff(597,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n2)) | (~familiar(n6, n1)) | (~familiar(n2, n6)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(598,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n2)) | (~familiar(n2, n6)) | (~familiar(n6, n1))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.18/0.48 tff(599,plain,
% 0.18/0.48 (~familiar(n2, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[598, 24, 218, 498])).
% 0.18/0.48 tff(600,plain,
% 0.18/0.48 (not_familiar(n2, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[448, 599])).
% 0.18/0.48 tff(601,plain,
% 0.18/0.48 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n2, n6)) | not_familiar(n6, n2))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n2, n6)) | not_familiar(n6, n2))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(602,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n2, n6)) | not_familiar(n6, n2))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(603,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n2, n6)) | not_familiar(n6, n2)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.18/0.48 tff(604,plain,
% 0.18/0.48 (not_familiar(n6, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[603, 96, 600])).
% 0.18/0.48 tff(605,assumption,(not_familiar(n6, n2)), introduced(assumption)).
% 0.18/0.48 tff(606,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n2)) | (~not_familiar(n3, n6)) | (~not_familiar(n2, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n2)) | (~not_familiar(n3, n6)) | (~not_familiar(n2, n3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(607,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n2)) | (~not_familiar(n3, n6)) | (~not_familiar(n2, n3)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(608,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n2)) | (~not_familiar(n3, n6)) | (~not_familiar(n2, n3))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.18/0.48 tff(609,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[608, 111, 285, 55, 605])).
% 0.18/0.48 tff(610,plain,((~familiar(n1, n3)) | (~not_familiar(n6, n2)) | (~familiar(n6, n1)) | (~familiar(n2, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(611,plain,
% 0.18/0.48 (~familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[610, 604, 498, 222])).
% 0.18/0.48 tff(612,plain,
% 0.18/0.48 (not_familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[301, 611])).
% 0.18/0.48 tff(613,plain,
% 0.18/0.48 (~not_familiar(n3, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[349, 111, 612, 593])).
% 0.18/0.48 tff(614,plain,
% 0.18/0.48 (familiar(n3, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[88, 613])).
% 0.18/0.48 tff(615,plain,
% 0.18/0.48 (familiar(n4, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[354, 10, 614])).
% 0.18/0.48 tff(616,plain,
% 0.18/0.48 (not_familiar(n5, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[384, 96, 496])).
% 0.18/0.48 tff(617,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(618,plain,
% 0.18/0.48 (((~not_familiar(n1, n3)) | (~not_familiar(n5, n1)) | (~not_familiar(n3, n5))) <=> ((~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(619,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n5, n1)) | (~not_familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[618])).
% 0.18/0.48 tff(620,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n5, n1)) | (~not_familiar(n3, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[619, 617])).
% 0.18/0.48 tff(621,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n5, n1)) | (~not_familiar(n3, n5)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(622,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n3, n5)) | (~not_familiar(n5, n1))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.18/0.48 tff(623,plain,
% 0.18/0.48 (~not_familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[622, 111, 612, 616])).
% 0.18/0.48 tff(624,plain,
% 0.18/0.48 (familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[264, 623])).
% 0.18/0.48 tff(625,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n3, n5)) | (~familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n3, n5)) | (~familiar(n4, n3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(626,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n3, n5)) | (~familiar(n4, n3)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(627,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n3, n5)) | (~familiar(n4, n3))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.18/0.48 tff(628,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[627, 24, 624, 615, 495])).
% 0.18/0.48 tff(629,plain,((~not_familiar(n1, n5)) | (~familiar(n1, n2)) | (~not_familiar(n5, n6))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(630,plain,
% 0.18/0.48 (~not_familiar(n1, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[629, 386, 218])).
% 0.18/0.48 tff(631,plain,
% 0.18/0.48 (familiar(n1, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[201, 630])).
% 0.18/0.48 tff(632,plain,
% 0.18/0.48 (~familiar(n5, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[230, 24, 631, 222])).
% 0.18/0.48 tff(633,plain,
% 0.18/0.48 (not_familiar(n5, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[244, 632])).
% 0.18/0.48 tff(634,plain,
% 0.18/0.48 (familiar(n5, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[226, 10, 631])).
% 0.18/0.48 tff(635,plain,
% 0.18/0.48 (~familiar(n4, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[583, 24, 631, 495])).
% 0.18/0.48 tff(636,plain,
% 0.18/0.48 (not_familiar(n4, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[133, 635])).
% 0.18/0.48 tff(637,plain,
% 0.18/0.48 (~not_familiar(n2, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[437, 111, 633, 395])).
% 0.18/0.48 tff(638,plain,
% 0.18/0.48 (familiar(n2, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[448, 637])).
% 0.18/0.48 tff(639,plain,
% 0.18/0.48 (~familiar(n6, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[549, 24, 218, 638])).
% 0.18/0.48 tff(640,plain,
% 0.18/0.48 (not_familiar(n6, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[475, 639])).
% 0.18/0.48 tff(641,plain,
% 0.18/0.48 (familiar(n6, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[416, 10, 587])).
% 0.18/0.48 tff(642,plain,
% 0.18/0.48 (~not_familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[368, 641, 640, 636])).
% 0.18/0.48 tff(643,plain,
% 0.18/0.48 (familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[301, 642])).
% 0.18/0.48 tff(644,plain,
% 0.18/0.48 (~familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[253, 24, 643, 634])).
% 0.18/0.48 tff(645,plain,
% 0.18/0.48 (not_familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[264, 644])).
% 0.18/0.48 tff(646,plain,
% 0.18/0.48 (~familiar(n3, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[269, 24, 643, 222])).
% 0.18/0.48 tff(647,plain,
% 0.18/0.48 (not_familiar(n3, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[280, 646])).
% 0.18/0.48 tff(648,plain,
% 0.18/0.48 (not_familiar(n2, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[284, 96, 647])).
% 0.18/0.48 tff(649,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[288, 111, 648, 645, 633])).
% 0.18/0.48 tff(650,plain,((~not_familiar(n5, n6)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(651,plain,
% 0.18/0.48 (~not_familiar(n5, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[650, 218])).
% 0.18/0.48 tff(652,plain,
% 0.18/0.48 (familiar(n5, n6)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[161, 651])).
% 0.18/0.48 tff(653,plain,
% 0.18/0.48 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n6)) | familiar(n6, n5))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n6)) | familiar(n6, n5))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(654,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n6)) | familiar(n6, n5))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(655,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n6)) | familiar(n6, n5)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.18/0.48 tff(656,plain,
% 0.18/0.48 (familiar(n6, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[655, 10, 652])).
% 0.18/0.48 tff(657,assumption,(familiar(n6, n5)), introduced(assumption)).
% 0.18/0.48 tff(658,assumption,(not_familiar(n5, n1)), introduced(assumption)).
% 0.18/0.48 tff(659,plain,
% 0.18/0.48 (~not_familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[622, 111, 346, 658])).
% 0.18/0.48 tff(660,plain,
% 0.18/0.48 (familiar(n3, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[264, 659])).
% 0.18/0.48 tff(661,plain,
% 0.18/0.48 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n5)) | familiar(n5, n3))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n5)) | familiar(n5, n3))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(662,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n5)) | familiar(n5, n3))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(663,plain,
% 0.18/0.48 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n5)) | familiar(n5, n3)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.18/0.48 tff(664,plain,
% 0.18/0.48 (familiar(n5, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[663, 10, 660])).
% 0.18/0.48 tff(665,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(666,plain,
% 0.18/0.48 (((~familiar(n6, n5)) | (~familiar(n3, n6)) | (~familiar(n5, n3))) <=> ((~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(667,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n5)) | (~familiar(n3, n6)) | (~familiar(n5, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[666])).
% 0.18/0.48 tff(668,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n5)) | (~familiar(n3, n6)) | (~familiar(n5, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[667, 665])).
% 0.18/0.48 tff(669,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n5)) | (~familiar(n3, n6)) | (~familiar(n5, n3)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(670,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n6, n5)) | (~familiar(n5, n3)) | (~familiar(n3, n6))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.18/0.48 tff(671,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[670, 24, 360, 664, 657])).
% 0.18/0.48 tff(672,plain,((~not_familiar(n1, n3)) | (~familiar(n6, n5)) | (~not_familiar(n6, n1)) | (~not_familiar(n5, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(673,plain,
% 0.18/0.48 (~not_familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[672, 223, 656, 385])).
% 0.18/0.48 tff(674,plain,
% 0.18/0.48 (familiar(n1, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[301, 673])).
% 0.18/0.48 tff(675,plain,
% 0.18/0.48 (~familiar(n3, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[269, 24, 2, 222])).
% 0.18/0.48 tff(676,plain,
% 0.18/0.48 (not_familiar(n3, n2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[280, 675])).
% 0.18/0.48 tff(677,plain,
% 0.18/0.48 (not_familiar(n2, n3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[284, 96, 676])).
% 0.18/0.48 tff(678,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(679,plain,
% 0.18/0.48 (((~not_familiar(n3, n4)) | (~not_familiar(n2, n3)) | (~not_familiar(n4, n2))) <=> ((~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(680,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n3, n4)) | (~not_familiar(n2, n3)) | (~not_familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[679])).
% 0.18/0.48 tff(681,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n3, n4)) | (~not_familiar(n2, n3)) | (~not_familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[680, 678])).
% 0.18/0.48 tff(682,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n3, n4)) | (~not_familiar(n2, n3)) | (~not_familiar(n4, n2)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(683,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n4, n2)) | (~not_familiar(n3, n4)) | (~not_familiar(n2, n3))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.18/0.48 tff(684,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[683, 111, 677, 89, 329])).
% 0.18/0.48 tff(685,plain,((~familiar(n4, n1)) | (~familiar(n1, n3)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(686,plain,
% 0.18/0.48 (~familiar(n4, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[685, 674, 218])).
% 0.18/0.48 tff(687,plain,
% 0.18/0.48 (not_familiar(n4, n1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[133, 686])).
% 0.18/0.48 tff(688,plain,
% 0.18/0.48 (~not_familiar(n6, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[377, 111, 374, 687])).
% 0.18/0.48 tff(689,plain,
% 0.18/0.48 (familiar(n6, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[73, 688])).
% 0.18/0.48 tff(690,plain,
% 0.18/0.48 (~not_familiar(n5, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[205, 111, 381, 687])).
% 0.18/0.48 tff(691,plain,
% 0.18/0.48 (familiar(n5, n4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[216, 690])).
% 0.18/0.48 tff(692,plain,
% 0.18/0.48 (familiar(n4, n5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[505, 10, 691])).
% 0.18/0.48 tff(693,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(694,plain,
% 0.18/0.48 (((~familiar(n6, n4)) | (~familiar(n5, n6)) | (~familiar(n4, n5))) <=> ((~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(695,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n5, n6)) | (~familiar(n4, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[694])).
% 0.18/0.48 tff(696,plain,
% 0.18/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n5, n6)) | (~familiar(n4, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[695, 693])).
% 0.18/0.48 tff(697,plain,
% 0.18/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n4)) | (~familiar(n5, n6)) | (~familiar(n4, n5)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(698,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n5)) | (~familiar(n6, n4)) | (~familiar(n5, n6))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.18/0.49 tff(699,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[698, 24, 692, 652, 689])).
% 0.18/0.49 tff(700,plain,((~not_familiar(n6, n1)) | (~familiar(n1, n2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(701,plain,
% 0.18/0.49 (~not_familiar(n6, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[700, 218])).
% 0.18/0.49 tff(702,plain,
% 0.18/0.49 (familiar(n6, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[475, 701])).
% 0.18/0.49 tff(703,plain,
% 0.18/0.49 (~familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[598, 24, 218, 702])).
% 0.18/0.49 tff(704,plain,
% 0.18/0.49 (not_familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[448, 703])).
% 0.18/0.49 tff(705,plain,
% 0.18/0.49 (not_familiar(n6, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[603, 96, 704])).
% 0.18/0.49 tff(706,plain,
% 0.18/0.49 (~familiar(n1, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[610, 705, 702, 222])).
% 0.18/0.49 tff(707,plain,
% 0.18/0.49 (not_familiar(n1, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[301, 706])).
% 0.18/0.49 tff(708,plain,
% 0.18/0.49 (((~familiar(n6, n1)) | (~familiar(n5, n6)) | (~familiar(n1, n5))) <=> ((~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(709,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n5, n6)) | (~familiar(n1, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[708])).
% 0.18/0.49 tff(710,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n5, n6)) | (~familiar(n1, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[709, 145])).
% 0.18/0.49 tff(711,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n1)) | (~familiar(n5, n6)) | (~familiar(n1, n5)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(712,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n1, n5)) | (~familiar(n6, n1)) | (~familiar(n5, n6))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.18/0.49 tff(713,plain,
% 0.18/0.49 (~familiar(n1, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[712, 24, 652, 702])).
% 0.18/0.49 tff(714,plain,
% 0.18/0.49 (not_familiar(n1, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[201, 713])).
% 0.18/0.49 tff(715,plain,
% 0.18/0.49 (~not_familiar(n5, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[205, 111, 496, 345])).
% 0.18/0.49 tff(716,plain,
% 0.18/0.49 (familiar(n5, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[216, 715])).
% 0.18/0.49 tff(717,plain,
% 0.18/0.49 (~not_familiar(n3, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[622, 111, 346, 616])).
% 0.18/0.49 tff(718,plain,
% 0.18/0.49 (familiar(n3, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[264, 717])).
% 0.18/0.49 tff(719,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[627, 24, 718, 355, 716])).
% 0.18/0.49 tff(720,plain,((~not_familiar(n4, n1)) | (~not_familiar(n1, n5)) | (~not_familiar(n1, n3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(721,plain,
% 0.18/0.49 (~not_familiar(n4, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[720, 714, 707])).
% 0.18/0.49 tff(722,plain,
% 0.18/0.49 (familiar(n4, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[133, 721])).
% 0.18/0.49 tff(723,plain,
% 0.18/0.49 (familiar(n1, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[13, 10, 702])).
% 0.18/0.49 tff(724,plain,
% 0.18/0.49 (~familiar(n6, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[59, 24, 723, 722])).
% 0.18/0.49 tff(725,plain,
% 0.18/0.49 (not_familiar(n6, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[73, 724])).
% 0.18/0.49 tff(726,plain,
% 0.18/0.49 (~familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[313, 24, 218, 722])).
% 0.18/0.49 tff(727,plain,
% 0.18/0.49 (not_familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[324, 726])).
% 0.18/0.49 tff(728,plain,
% 0.18/0.49 (not_familiar(n4, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[328, 96, 727])).
% 0.18/0.49 tff(729,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n2, n6)) | (~not_familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n4)) | (~not_familiar(n2, n6)) | (~not_familiar(n4, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(730,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n4)) | (~not_familiar(n2, n6)) | (~not_familiar(n4, n2)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(731,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n4)) | (~not_familiar(n2, n6)) | (~not_familiar(n4, n2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.18/0.49 tff(732,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[731, 111, 704, 728, 725])).
% 0.18/0.49 tff(733,plain,(~familiar(n1, n2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(734,plain,
% 0.18/0.49 (not_equal(n1, n2) <=> not_equal(n1, n2)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(735,axiom,(not_equal(n1, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_1_2')).
% 0.18/0.49 tff(736,plain,
% 0.18/0.49 (not_equal(n1, n2)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.18/0.49 tff(737,plain,
% 0.18/0.49 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n2)) | (~person(n2)) | (~person(n1)) | not_familiar(n1, n2) | familiar(n1, n2))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~not_equal(n1, n2)) | (~person(n2)) | (~person(n1)) | not_familiar(n1, n2) | familiar(n1, n2))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(738,plain,
% 0.18/0.49 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n1, n2)) | (~person(n2)) | (~person(n1)) | not_familiar(n1, n2) | familiar(n1, n2))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(739,plain,
% 0.18/0.49 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~not_equal(n1, n2)) | (~person(n2)) | (~person(n1)) | not_familiar(n1, n2) | familiar(n1, n2)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.18/0.49 tff(740,plain,
% 0.18/0.49 (not_familiar(n1, n2) | familiar(n1, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[739, 126, 237, 736, 38])).
% 0.18/0.49 tff(741,plain,
% 0.18/0.49 (not_familiar(n1, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[740, 733])).
% 0.18/0.49 tff(742,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(743,plain,
% 0.18/0.49 (((~not_familiar(n1, n2)) | (~not_familiar(n4, n1)) | (~not_familiar(n2, n4))) <=> ((~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(744,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n4, n1)) | (~not_familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[743])).
% 0.18/0.49 tff(745,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n4, n1)) | (~not_familiar(n2, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[744, 742])).
% 0.18/0.49 tff(746,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n4, n1)) | (~not_familiar(n2, n4)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(747,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n2, n4)) | (~not_familiar(n4, n1)) | (~not_familiar(n1, n2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.18/0.49 tff(748,plain,
% 0.18/0.49 (~not_familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[747, 111, 741, 134])).
% 0.18/0.49 tff(749,plain,
% 0.18/0.49 (familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[324, 748])).
% 0.18/0.49 tff(750,plain,
% 0.18/0.49 (familiar(n4, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[429, 10, 749])).
% 0.18/0.49 tff(751,plain,
% 0.18/0.49 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n2)) | not_familiar(n2, n1))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n2)) | not_familiar(n2, n1))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(752,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n2)) | not_familiar(n2, n1))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(753,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n2)) | not_familiar(n2, n1)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.18/0.49 tff(754,plain,
% 0.18/0.49 (not_familiar(n2, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[753, 96, 741])).
% 0.18/0.49 tff(755,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n2, n1)) | (~not_familiar(n5, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n2, n1)) | (~not_familiar(n5, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(756,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n2, n1)) | (~not_familiar(n5, n2)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(757,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n2, n1)) | (~not_familiar(n5, n2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.18/0.49 tff(758,plain,
% 0.18/0.49 (~not_familiar(n5, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[757, 111, 202, 754])).
% 0.18/0.49 tff(759,plain,
% 0.18/0.49 (familiar(n5, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[244, 758])).
% 0.18/0.49 tff(760,plain,
% 0.18/0.49 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n2)) | familiar(n2, n5))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n2)) | familiar(n2, n5))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(761,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n5, n2)) | familiar(n2, n5))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(762,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n5, n2)) | familiar(n2, n5)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.18/0.49 tff(763,plain,
% 0.18/0.49 (familiar(n2, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[762, 10, 759])).
% 0.18/0.49 tff(764,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n2, n5)) | (~familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n2, n5)) | (~familiar(n4, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(765,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n5, n4)) | (~familiar(n2, n5)) | (~familiar(n4, n2)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(766,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n5, n4)) | (~familiar(n2, n5)) | (~familiar(n4, n2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.18/0.49 tff(767,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[766, 24, 763, 750, 217])).
% 0.18/0.49 tff(768,plain,((~familiar(n6, n1)) | (~familiar(n1, n3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(769,plain,
% 0.18/0.49 (~familiar(n6, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[768, 2])).
% 0.18/0.49 tff(770,plain,
% 0.18/0.49 (not_familiar(n6, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[475, 769])).
% 0.18/0.49 tff(771,plain,
% 0.18/0.49 (not_familiar(n1, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[373, 96, 770])).
% 0.18/0.49 tff(772,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(773,plain,
% 0.18/0.49 (((~not_familiar(n1, n2)) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6))) <=> ((~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(774,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[773])).
% 0.18/0.49 tff(775,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[774, 772])).
% 0.18/0.49 tff(776,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n2)) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(777,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n6, n1)) | (~not_familiar(n2, n6)) | (~not_familiar(n1, n2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[776, 775])).
% 0.18/0.49 tff(778,plain,
% 0.18/0.49 (~not_familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[777, 111, 741, 770])).
% 0.18/0.49 tff(779,plain,
% 0.18/0.49 (familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[448, 778])).
% 0.18/0.49 tff(780,assumption,(not_familiar(n1, n6)), introduced(assumption)).
% 0.18/0.49 tff(781,plain,
% 0.18/0.49 (~not_familiar(n6, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[377, 111, 780, 345])).
% 0.18/0.49 tff(782,plain,
% 0.18/0.49 (familiar(n6, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[73, 781])).
% 0.18/0.49 tff(783,plain,
% 0.18/0.49 (~not_familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[747, 111, 741, 345])).
% 0.18/0.49 tff(784,plain,
% 0.18/0.49 (familiar(n2, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[324, 783])).
% 0.18/0.49 tff(785,plain,
% 0.18/0.49 (familiar(n4, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[429, 10, 784])).
% 0.18/0.49 tff(786,assumption,(familiar(n2, n6)), introduced(assumption)).
% 0.18/0.49 tff(787,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[452, 24, 786, 785, 782])).
% 0.18/0.49 tff(788,plain,((~not_familiar(n4, n1)) | (~familiar(n2, n6)) | (~not_familiar(n1, n6))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(789,plain,
% 0.18/0.49 (~not_familiar(n4, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[788, 779, 771])).
% 0.18/0.49 tff(790,plain,
% 0.18/0.49 (familiar(n4, n1)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[133, 789])).
% 0.18/0.49 tff(791,plain,
% 0.18/0.49 (~not_familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[777, 111, 741, 223])).
% 0.18/0.49 tff(792,plain,
% 0.18/0.49 (familiar(n2, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[448, 791])).
% 0.18/0.49 tff(793,plain,
% 0.18/0.49 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n2, n6)) | familiar(n6, n2))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n2, n6)) | familiar(n6, n2))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(794,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n2, n6)) | familiar(n6, n2))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(795,plain,
% 0.18/0.49 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n2, n6)) | familiar(n6, n2)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.18/0.49 tff(796,plain,
% 0.18/0.49 (familiar(n6, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[795, 10, 792])).
% 0.18/0.49 tff(797,plain,
% 0.18/0.49 (((~not_familiar(n1, n5)) | (~not_familiar(n6, n1)) | (~not_familiar(n5, n6))) <=> ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(798,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n6, n1)) | (~not_familiar(n5, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[797])).
% 0.18/0.49 tff(799,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n6, n1)) | (~not_familiar(n5, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[798, 462])).
% 0.18/0.49 tff(800,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n6, n1)) | (~not_familiar(n5, n6)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(801,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n1, n5)) | (~not_familiar(n6, n1))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.18/0.49 tff(802,plain,
% 0.18/0.49 (~not_familiar(n5, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[801, 111, 496, 223])).
% 0.18/0.49 tff(803,plain,
% 0.18/0.49 (familiar(n5, n6)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[161, 802])).
% 0.18/0.49 tff(804,plain,
% 0.18/0.49 (~not_familiar(n5, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[757, 111, 496, 754])).
% 0.18/0.49 tff(805,plain,
% 0.18/0.49 (familiar(n5, n2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[244, 804])).
% 0.18/0.49 tff(806,plain,
% 0.18/0.49 (familiar(n2, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[762, 10, 805])).
% 0.18/0.49 tff(807,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(808,plain,
% 0.18/0.49 (((~familiar(n6, n2)) | (~familiar(n5, n6)) | (~familiar(n2, n5))) <=> ((~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(809,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n2)) | (~familiar(n5, n6)) | (~familiar(n2, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[808])).
% 0.18/0.49 tff(810,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n2)) | (~familiar(n5, n6)) | (~familiar(n2, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[809, 807])).
% 0.18/0.49 tff(811,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n6, n2)) | (~familiar(n5, n6)) | (~familiar(n2, n5)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(812,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n5)) | (~familiar(n6, n2)) | (~familiar(n5, n6))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.18/0.49 tff(813,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[812, 24, 806, 803, 796])).
% 0.18/0.49 tff(814,plain,((~not_familiar(n1, n5)) | (~not_familiar(n6, n1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(815,plain,
% 0.18/0.49 (~not_familiar(n1, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[814, 770])).
% 0.18/0.49 tff(816,plain,
% 0.18/0.49 (familiar(n1, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[201, 815])).
% 0.18/0.49 tff(817,plain,
% 0.18/0.49 (~familiar(n5, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[305, 24, 816, 790])).
% 0.18/0.49 tff(818,plain,
% 0.18/0.49 (not_familiar(n5, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[216, 817])).
% 0.18/0.49 tff(819,plain,
% 0.18/0.49 (~familiar(n3, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[77, 24, 2, 790])).
% 0.18/0.49 tff(820,plain,
% 0.18/0.49 (not_familiar(n3, n4)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[88, 819])).
% 0.18/0.49 tff(821,plain,
% 0.18/0.49 (not_familiar(n4, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[99, 96, 820])).
% 0.18/0.49 tff(822,plain,
% 0.18/0.49 (~familiar(n5, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[166, 24, 816, 138])).
% 0.18/0.49 tff(823,plain,
% 0.18/0.49 (not_familiar(n5, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[177, 822])).
% 0.18/0.49 tff(824,plain,
% 0.18/0.49 (not_familiar(n3, n5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[181, 96, 823])).
% 0.18/0.49 tff(825,plain,
% 0.18/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n3, n5)) | (~not_familiar(n4, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n3, n5)) | (~not_familiar(n4, n3)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(826,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n4)) | (~not_familiar(n3, n5)) | (~not_familiar(n4, n3)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(827,plain,
% 0.18/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n4)) | (~not_familiar(n3, n5)) | (~not_familiar(n4, n3))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.18/0.49 tff(828,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[827, 111, 824, 821, 818])).
% 0.18/0.49 tff(829,plain,(~familiar(n1, n3)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(830,plain,
% 0.18/0.49 (not_familiar(n1, n3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[301, 829])).
% 0.18/0.49 tff(831,plain,
% 0.18/0.49 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n3)) | not_familiar(n3, n1))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n3)) | not_familiar(n3, n1))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(832,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n1, n3)) | not_familiar(n3, n1))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(833,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n1, n3)) | not_familiar(n3, n1)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.18/0.50 tff(834,plain,
% 0.18/0.50 (not_familiar(n3, n1)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[833, 96, 830])).
% 0.18/0.50 tff(835,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n3, n1)) | (~not_familiar(n5, n3)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n3, n1)) | (~not_familiar(n5, n3)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(836,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n5)) | (~not_familiar(n3, n1)) | (~not_familiar(n5, n3)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(837,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n5)) | (~not_familiar(n3, n1)) | (~not_familiar(n5, n3))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.18/0.50 tff(838,plain,
% 0.18/0.50 (~not_familiar(n5, n3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[837, 111, 496, 834])).
% 0.18/0.50 tff(839,plain,
% 0.18/0.50 (familiar(n5, n3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[177, 838])).
% 0.18/0.50 tff(840,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n2, n1)) | (~not_familiar(n3, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n2, n1)) | (~not_familiar(n3, n2)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(841,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n1, n3)) | (~not_familiar(n2, n1)) | (~not_familiar(n3, n2)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(842,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n1, n3)) | (~not_familiar(n2, n1)) | (~not_familiar(n3, n2))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.18/0.50 tff(843,plain,
% 0.18/0.50 (~not_familiar(n3, n2)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[842, 111, 830, 754])).
% 0.18/0.50 tff(844,plain,
% 0.18/0.50 (familiar(n3, n2)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[280, 843])).
% 0.18/0.50 tff(845,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n2)) | (~familiar(n5, n3)) | (~familiar(n2, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n3, n2)) | (~familiar(n5, n3)) | (~familiar(n2, n5)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(846,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n2)) | (~familiar(n5, n3)) | (~familiar(n2, n5)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(847,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n3, n2)) | (~familiar(n5, n3)) | (~familiar(n2, n5))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.18/0.50 tff(848,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[847, 24, 806, 844, 839])).
% 0.18/0.50 tff(849,plain,(~not_familiar(n1, n5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(850,plain,
% 0.18/0.50 (familiar(n1, n5)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[201, 849])).
% 0.18/0.50 tff(851,plain,
% 0.18/0.50 (~familiar(n5, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[305, 24, 850, 1])).
% 0.18/0.50 tff(852,plain,
% 0.18/0.50 (~not_familiar(n3, n6)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[358, 111, 830, 223])).
% 0.18/0.50 tff(853,plain,
% 0.18/0.50 (familiar(n3, n6)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[54, 852])).
% 0.18/0.50 tff(854,plain,
% 0.18/0.50 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n2)) | familiar(n2, n3))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n2)) | familiar(n2, n3))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(855,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n3, n2)) | familiar(n2, n3))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(856,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n3, n2)) | familiar(n2, n3)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.18/0.50 tff(857,plain,
% 0.18/0.50 (familiar(n2, n3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[856, 10, 844])).
% 0.18/0.50 tff(858,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(859,plain,
% 0.18/0.50 (((~familiar(n3, n6)) | (~familiar(n2, n3)) | (~familiar(n6, n2))) <=> ((~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(860,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n6)) | (~familiar(n2, n3)) | (~familiar(n6, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[859])).
% 0.18/0.50 tff(861,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n6)) | (~familiar(n2, n3)) | (~familiar(n6, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[860, 858])).
% 0.18/0.50 tff(862,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n6)) | (~familiar(n2, n3)) | (~familiar(n6, n2)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(863,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n6, n2)) | (~familiar(n3, n6))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.18/0.50 tff(864,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[863, 24, 857, 853, 796])).
% 0.18/0.50 tff(865,plain,(~not_familiar(n6, n1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(866,plain,
% 0.18/0.50 (familiar(n6, n1)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[475, 865])).
% 0.18/0.50 tff(867,plain,
% 0.18/0.50 (familiar(n1, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[484, 10, 1])).
% 0.18/0.50 tff(868,assumption,(familiar(n1, n4)), introduced(assumption)).
% 0.18/0.50 tff(869,plain,
% 0.18/0.50 (((~familiar(n1, n4)) | (~familiar(n6, n1)) | (~familiar(n4, n6))) <=> ((~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(870,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n4)) | (~familiar(n6, n1)) | (~familiar(n4, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[869])).
% 0.18/0.50 tff(871,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n4)) | (~familiar(n6, n1)) | (~familiar(n4, n6)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[870, 486])).
% 0.18/0.50 tff(872,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n1, n4)) | (~familiar(n6, n1)) | (~familiar(n4, n6)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(873,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n4, n6)) | (~familiar(n6, n1)) | (~familiar(n1, n4))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.18/0.50 tff(874,plain,
% 0.18/0.50 (~familiar(n4, n6)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[873, 24, 868, 3])).
% 0.18/0.50 tff(875,plain,
% 0.18/0.50 (not_familiar(n4, n6)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[412, 874])).
% 0.18/0.50 tff(876,plain,
% 0.18/0.50 (((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n4, n6)) | not_familiar(n6, n4))) <=> ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n4, n6)) | not_familiar(n6, n4))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(877,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | ((~not_familiar(n4, n6)) | not_familiar(n6, n4))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(878,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | not_familiar(X2, X1))) | (~not_familiar(n4, n6)) | not_familiar(n6, n4)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.18/0.50 tff(879,plain,
% 0.18/0.50 (not_familiar(n6, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[878, 96, 875])).
% 0.18/0.50 tff(880,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(881,plain,
% 0.18/0.50 (((~not_familiar(n5, n6)) | (~not_familiar(n4, n5)) | (~not_familiar(n6, n4))) <=> ((~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(882,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n4, n5)) | (~not_familiar(n6, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[881])).
% 0.18/0.50 tff(883,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n4, n5)) | (~not_familiar(n6, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[882, 880])).
% 0.18/0.50 tff(884,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | ((~not_familiar(n5, n6)) | (~not_familiar(n4, n5)) | (~not_familiar(n6, n4)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(885,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X2)) | (~not_familiar(X3, X1)) | (~not_familiar(X2, X3)))) | (~not_familiar(n5, n6)) | (~not_familiar(n6, n4)) | (~not_familiar(n4, n5))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.18/0.50 tff(886,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[885, 111, 418, 162, 879])).
% 0.18/0.50 tff(887,plain,((~familiar(n6, n1)) | (~not_familiar(n4, n5)) | (~familiar(n1, n5)) | (~familiar(n1, n4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(888,plain,
% 0.18/0.50 (~not_familiar(n4, n5)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[887, 867, 866, 850])).
% 0.18/0.50 tff(889,plain,
% 0.18/0.50 (not_equal(n4, n5) <=> not_equal(n4, n5)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(890,axiom,(not_equal(n4, n5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_4_5')).
% 0.18/0.50 tff(891,plain,
% 0.18/0.50 (not_equal(n4, n5)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.18/0.50 tff(892,plain,
% 0.18/0.50 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(893,plain,
% 0.18/0.50 (((~not_equal(n4, n5)) | (~person(n5)) | (~person(n4)) | not_familiar(n4, n5) | familiar(n4, n5)) <=> ((~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(894,plain,
% 0.18/0.50 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n5)) | (~person(n5)) | (~person(n4)) | not_familiar(n4, n5) | familiar(n4, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[893])).
% 0.18/0.50 tff(895,plain,
% 0.18/0.50 (((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n5)) | (~person(n5)) | (~person(n4)) | not_familiar(n4, n5) | familiar(n4, n5))) <=> ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5))),
% 0.18/0.50 inference(transitivity,[status(thm)],[894, 892])).
% 0.18/0.50 tff(896,plain,
% 0.18/0.50 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~not_equal(n4, n5)) | (~person(n5)) | (~person(n4)) | not_familiar(n4, n5) | familiar(n4, n5))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(897,plain,
% 0.18/0.50 ((~![Y: $i, X: $i] : ((~not_equal(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(n4)) | (~person(n5)) | (~not_equal(n4, n5)) | not_familiar(n4, n5) | familiar(n4, n5)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.18/0.50 tff(898,plain,
% 0.18/0.50 (not_familiar(n4, n5) | familiar(n4, n5)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[897, 66, 154, 891, 38])).
% 0.18/0.50 tff(899,plain,
% 0.18/0.50 (familiar(n4, n5)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[898, 888])).
% 0.18/0.50 tff(900,plain,
% 0.18/0.50 (((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n5)) | familiar(n5, n4))) <=> ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n5)) | familiar(n5, n4))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(901,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | ((~familiar(n4, n5)) | familiar(n5, n4))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(902,plain,
% 0.18/0.50 ((~![X2: $i, X1: $i] : ((~familiar(X1, X2)) | familiar(X2, X1))) | (~familiar(n4, n5)) | familiar(n5, n4)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.18/0.50 tff(903,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[902, 10, 899, 851])).
% 0.18/0.50 tff(904,plain,(~familiar(n4, n1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(905,plain,
% 0.18/0.50 (not_familiar(n4, n1)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[133, 904])).
% 0.18/0.50 tff(906,plain,
% 0.18/0.50 (~not_familiar(n2, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[747, 111, 741, 905])).
% 0.18/0.50 tff(907,plain,
% 0.18/0.50 (familiar(n2, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[324, 906])).
% 0.18/0.50 tff(908,plain,
% 0.18/0.50 (familiar(n4, n2)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[429, 10, 907])).
% 0.18/0.50 tff(909,plain,
% 0.18/0.50 (~not_familiar(n3, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[349, 111, 830, 905])).
% 0.18/0.50 tff(910,plain,
% 0.18/0.50 (familiar(n3, n4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[88, 909])).
% 0.18/0.50 tff(911,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(912,plain,
% 0.18/0.50 (((~familiar(n3, n4)) | (~familiar(n2, n3)) | (~familiar(n4, n2))) <=> ((~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(913,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n4)) | (~familiar(n2, n3)) | (~familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[912])).
% 0.18/0.50 tff(914,plain,
% 0.18/0.50 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n4)) | (~familiar(n2, n3)) | (~familiar(n4, n2)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[913, 911])).
% 0.18/0.50 tff(915,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | ((~familiar(n3, n4)) | (~familiar(n2, n3)) | (~familiar(n4, n2)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(916,plain,
% 0.18/0.50 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X2)) | (~familiar(X3, X1)) | (~familiar(X2, X3)))) | (~familiar(n2, n3)) | (~familiar(n4, n2)) | (~familiar(n3, n4))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.18/0.50 tff(917,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[916, 24, 857, 910, 908])).
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50 % E exiting
%------------------------------------------------------------------------------