%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ007-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:23:08 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ007-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:38:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(male_type, type, (
% 0.13/0.39 male: $i > $o)).
% 0.13/0.39 tff(a_type, type, (
% 0.13/0.39 a: $i)).
% 0.13/0.39 tff(female_type, type, (
% 0.13/0.39 female: $i > $o)).
% 0.13/0.39 tff(b_type, type, (
% 0.13/0.39 b: $i)).
% 0.13/0.39 tff(truthteller_type, type, (
% 0.13/0.39 truthteller: $i > $o)).
% 0.13/0.39 tff(a_truth_type, type, (
% 0.13/0.39 a_truth: $i > $o)).
% 0.13/0.39 tff(a_has_lied_type, type, (
% 0.13/0.39 a_has_lied: $i)).
% 0.13/0.39 tff(liar_type, type, (
% 0.13/0.39 liar: $i > $o)).
% 0.13/0.39 tff(statement_by_type, type, (
% 0.13/0.39 statement_by: $i > $i)).
% 0.13/0.39 tff(a_from_mars_type, type, (
% 0.13/0.39 a_from_mars: $i)).
% 0.13/0.39 tff(from_mars_type, type, (
% 0.13/0.39 from_mars: $i > $o)).
% 0.13/0.39 tff(from_venus_type, type, (
% 0.13/0.39 from_venus: $i > $o)).
% 0.13/0.39 tff(says_type, type, (
% 0.13/0.39 says: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(from_venus(a)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[X: $i] : refl(((~from_mars(X)) | (~from_venus(X))) <=> ((~from_mars(X)) | (~from_venus(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | (~from_venus(X))) <=> ![X: $i] : ((~from_mars(X)) | (~from_venus(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | (~from_venus(X))) <=> ![X: $i] : ((~from_mars(X)) | (~from_venus(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(![X: $i] : ((~from_mars(X)) | (~from_venus(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','not_from_mars_and_venus')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | (~from_venus(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![X: $i] : ((~from_mars(X)) | (~from_venus(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | (~from_venus(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (((~![X: $i] : ((~from_mars(X)) | (~from_venus(X)))) | ((~from_mars(a)) | (~from_venus(a)))) <=> ((~![X: $i] : ((~from_mars(X)) | (~from_venus(X)))) | (~from_mars(a)) | (~from_venus(a)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~![X: $i] : ((~from_mars(X)) | (~from_venus(X)))) | ((~from_mars(a)) | (~from_venus(a)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![X: $i] : ((~from_mars(X)) | (~from_venus(X)))) | (~from_mars(a)) | (~from_venus(a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~from_mars(a)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((from_mars(a) | (~a_truth(a_from_mars))) <=> (from_mars(a) | (~a_truth(a_from_mars)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,axiom,(from_mars(a) | (~a_truth(a_from_mars))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_from_mars2')).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (from_mars(a) | (~a_truth(a_from_mars))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~a_truth(a_from_mars)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((a_truth(a_from_mars) | a_truth(statement_by(b))) <=> (a_truth(a_from_mars) | a_truth(statement_by(b)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,axiom,(a_truth(a_from_mars) | a_truth(statement_by(b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truth_of_bs_statement')).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (a_truth(a_from_mars) | a_truth(statement_by(b))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (a_truth(statement_by(b))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[X: $i] : refl((truthteller(X) | (~a_truth(statement_by(X)))) <=> (truthteller(X) | (~a_truth(statement_by(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X: $i] : (truthteller(X) | (~a_truth(statement_by(X)))) <=> ![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i] : (truthteller(X) | (~a_truth(statement_by(X)))) <=> ![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[X: $i] : rewrite(((~a_truth(statement_by(X))) | truthteller(X)) <=> (truthteller(X) | (~a_truth(statement_by(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![X: $i] : ((~a_truth(statement_by(X))) | truthteller(X)) <=> ![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,axiom,(![X: $i] : ((~a_truth(statement_by(X))) | truthteller(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','true_statements_made_by_truthtellers')).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.39 tff(29,plain,(
% 0.13/0.39 ![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))) | (truthteller(b) | (~a_truth(statement_by(b))))) <=> ((~![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))) | truthteller(b) | (~a_truth(statement_by(b))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((~![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))) | (truthteller(b) | (~a_truth(statement_by(b))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![X: $i] : (truthteller(X) | (~a_truth(statement_by(X))))) | truthteller(b) | (~a_truth(statement_by(b)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (truthteller(b) | (~a_truth(statement_by(b)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (truthteller(b)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (says(b, a_has_lied) <=> says(b, a_has_lied)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,axiom,(says(b, a_has_lied)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_says_a_lies')).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (says(b, a_has_lied)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : refl(((~truthteller(X)) | a_truth(Y) | (~says(X, Y))) <=> ((~truthteller(X)) | a_truth(Y) | (~says(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y))) <=> ![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y))) <=> ![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : rewrite((((~truthteller(X)) | (~says(X, Y))) | a_truth(Y)) <=> ((~truthteller(X)) | a_truth(Y) | (~says(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (((~truthteller(X)) | (~says(X, Y))) | a_truth(Y)) <=> ![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.39 tff(44,axiom,(![Y: $i, X: $i] : (((~truthteller(X)) | (~says(X, Y))) | a_truth(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','truthtellers_make_true_statements')).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.39 tff(47,plain,(
% 0.13/0.39 ![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[46])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | (a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (((~truthteller(b)) | a_truth(a_has_lied) | (~says(b, a_has_lied))) <=> (a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(b)) | a_truth(a_has_lied) | (~says(b, a_has_lied)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | (a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(b)) | a_truth(a_has_lied) | (~says(b, a_has_lied)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(b)) | a_truth(a_has_lied) | (~says(b, a_has_lied)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_has_lied) | (~says(b, a_has_lied)) | (~truthteller(b))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (a_truth(a_has_lied) | (~truthteller(b))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 48, 38])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (a_truth(a_has_lied)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[55, 35])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : refl(((~liar(X)) | (~a_truth(Y)) | (~says(X, Y))) <=> ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y))) <=> ![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y))) <=> ![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : rewrite((((~liar(X)) | (~says(X, Y))) | (~a_truth(Y))) <=> ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (((~liar(X)) | (~says(X, Y))) | (~a_truth(Y))) <=> ![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.39 tff(62,axiom,(![Y: $i, X: $i] : (((~liar(X)) | (~says(X, Y))) | (~a_truth(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','liars_make_false_statements')).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.13/0.39 tff(65,plain,(
% 0.13/0.39 ![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[64])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~liar(b)) | (~a_truth(a_has_lied)) | (~says(b, a_has_lied)))) <=> ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | (~liar(b)) | (~a_truth(a_has_lied)) | (~says(b, a_has_lied)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~liar(b)) | (~a_truth(a_has_lied)) | (~says(b, a_has_lied)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | (~liar(b)) | (~a_truth(a_has_lied)) | (~says(b, a_has_lied))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 ((~liar(b)) | (~a_truth(a_has_lied))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[69, 66, 38])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 (~liar(b)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ((from_mars(a) | from_mars(b)) <=> (from_mars(a) | from_mars(b))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 ((from_mars(b) | from_mars(a)) <=> (from_mars(a) | from_mars(b))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(74,axiom,(from_mars(b) | from_mars(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_from_mars')).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (from_mars(a) | from_mars(b)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (from_mars(a) | from_mars(b)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (from_mars(b)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[76, 12])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (^[X: $i] : refl(((~from_mars(X)) | liar(X) | (~female(X))) <=> ((~from_mars(X)) | liar(X) | (~female(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X))) <=> ![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X))) <=> ![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~from_mars(X)) | (~female(X))) <=> ((~from_mars(X)) | (~female(X)))), ((((~from_mars(X)) | (~female(X))) | liar(X)) <=> (((~from_mars(X)) | (~female(X))) | liar(X)))), rewrite((((~from_mars(X)) | (~female(X))) | liar(X)) <=> ((~from_mars(X)) | liar(X) | (~female(X)))), ((((~from_mars(X)) | (~female(X))) | liar(X)) <=> ((~from_mars(X)) | liar(X) | (~female(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 (![X: $i] : (((~from_mars(X)) | (~female(X))) | liar(X)) <=> ![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.13/0.39 tff(83,axiom,(![X: $i] : (((~from_mars(X)) | (~female(X))) | liar(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','marsian_females_are_liars')).
% 0.13/0.39 tff(84,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.39 tff(85,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.13/0.39 tff(86,plain,(
% 0.13/0.39 ![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[85])).
% 0.13/0.39 tff(87,plain,
% 0.13/0.39 (![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.13/0.39 tff(88,plain,
% 0.13/0.39 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | (liar(b) | (~from_mars(b)) | (~female(b)))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | liar(b) | (~from_mars(b)) | (~female(b)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(89,plain,
% 0.13/0.39 (((~from_mars(b)) | liar(b) | (~female(b))) <=> (liar(b) | (~from_mars(b)) | (~female(b)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(90,plain,
% 0.13/0.39 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(b)) | liar(b) | (~female(b)))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | (liar(b) | (~from_mars(b)) | (~female(b))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.13/0.39 tff(91,plain,
% 0.13/0.39 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(b)) | liar(b) | (~female(b)))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | liar(b) | (~from_mars(b)) | (~female(b)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[90, 88])).
% 0.13/0.39 tff(92,plain,
% 0.13/0.39 ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(b)) | liar(b) | (~female(b)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(93,plain,
% 0.13/0.39 ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | liar(b) | (~from_mars(b)) | (~female(b))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.13/0.39 tff(94,plain,
% 0.13/0.39 (~female(b)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[93, 87, 77, 71])).
% 0.13/0.39 tff(95,plain,
% 0.21/0.39 (says(a, a_from_mars) <=> says(a, a_from_mars)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(96,axiom,(says(a, a_from_mars)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_says_hes_from_mars')).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 (says(a, a_from_mars)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.39 tff(98,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | (a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(99,plain,
% 0.21/0.39 (((~truthteller(a)) | a_truth(a_from_mars) | (~says(a, a_from_mars))) <=> (a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(100,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(a)) | a_truth(a_from_mars) | (~says(a, a_from_mars)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | (a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[99])).
% 0.21/0.39 tff(101,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(a)) | a_truth(a_from_mars) | (~says(a, a_from_mars)))) <=> ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[100, 98])).
% 0.21/0.39 tff(102,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | ((~truthteller(a)) | a_truth(a_from_mars) | (~says(a, a_from_mars)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(103,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~truthteller(X)) | a_truth(Y) | (~says(X, Y)))) | a_truth(a_from_mars) | (~says(a, a_from_mars)) | (~truthteller(a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.39 tff(104,plain,
% 0.21/0.39 (a_truth(a_from_mars) | (~truthteller(a))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[103, 48, 97])).
% 0.21/0.39 tff(105,plain,
% 0.21/0.39 (~truthteller(a)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[104, 16])).
% 0.21/0.39 tff(106,plain,
% 0.21/0.39 (^[X: $i] : refl(((~from_venus(X)) | truthteller(X) | (~female(X))) <=> ((~from_venus(X)) | truthteller(X) | (~female(X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(107,plain,
% 0.21/0.39 (![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X))) <=> ![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.39 tff(108,plain,
% 0.21/0.39 (![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X))) <=> ![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(109,plain,
% 0.21/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~from_venus(X)) | (~female(X))) <=> ((~from_venus(X)) | (~female(X)))), ((((~from_venus(X)) | (~female(X))) | truthteller(X)) <=> (((~from_venus(X)) | (~female(X))) | truthteller(X)))), rewrite((((~from_venus(X)) | (~female(X))) | truthteller(X)) <=> ((~from_venus(X)) | truthteller(X) | (~female(X)))), ((((~from_venus(X)) | (~female(X))) | truthteller(X)) <=> ((~from_venus(X)) | truthteller(X) | (~female(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(110,plain,
% 0.21/0.39 (![X: $i] : (((~from_venus(X)) | (~female(X))) | truthteller(X)) <=> ![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.39 tff(111,axiom,(![X: $i] : (((~from_venus(X)) | (~female(X))) | truthteller(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','venusian_female_are_truthtellers')).
% 0.21/0.39 tff(112,plain,
% 0.21/0.39 (![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.39 tff(113,plain,
% 0.21/0.39 (![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.39 tff(114,plain,(
% 0.21/0.39 ![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[113])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 (![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~female(a)) | truthteller(a) | (~from_venus(a)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | (~female(a)) | truthteller(a) | (~from_venus(a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 (((~from_venus(a)) | truthteller(a) | (~female(a))) <=> ((~female(a)) | truthteller(a) | (~from_venus(a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(a)) | truthteller(a) | (~female(a)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~female(a)) | truthteller(a) | (~from_venus(a))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(a)) | truthteller(a) | (~female(a)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | (~female(a)) | truthteller(a) | (~from_venus(a)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(a)) | truthteller(a) | (~female(a)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | (~female(a)) | truthteller(a) | (~from_venus(a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 ((~female(a)) | truthteller(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[121, 115, 1])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (~female(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[122, 105])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 (^[X: $i] : refl((female(X) | male(X)) <=> (female(X) | male(X)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (![X: $i] : (female(X) | male(X)) <=> ![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (![X: $i] : (female(X) | male(X)) <=> ![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (^[X: $i] : rewrite((male(X) | female(X)) <=> (female(X) | male(X)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (![X: $i] : (male(X) | female(X)) <=> ![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.40 tff(129,axiom,(![X: $i] : (male(X) | female(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','male_or_female')).
% 0.21/0.40 tff(130,plain,
% 0.21/0.40 (![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.40 tff(131,plain,
% 0.21/0.40 (![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.21/0.40 tff(132,plain,(
% 0.21/0.40 ![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(skolemize,[status(sab)],[131])).
% 0.21/0.40 tff(133,plain,
% 0.21/0.40 (![X: $i] : (female(X) | male(X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.21/0.40 tff(134,plain,
% 0.21/0.40 (((~![X: $i] : (female(X) | male(X))) | (female(a) | male(a))) <=> ((~![X: $i] : (female(X) | male(X))) | female(a) | male(a))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(135,plain,
% 0.21/0.40 ((~![X: $i] : (female(X) | male(X))) | (female(a) | male(a))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(136,plain,
% 0.21/0.40 ((~![X: $i] : (female(X) | male(X))) | female(a) | male(a)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.40 tff(137,plain,
% 0.21/0.40 (male(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 0.21/0.40 tff(138,plain,
% 0.21/0.40 (((~male(a)) | female(b)) <=> ((~male(a)) | female(b))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(139,axiom,((~male(a)) | female(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','different_sex2')).
% 0.21/0.40 tff(140,plain,
% 0.21/0.40 ((~male(a)) | female(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.40 tff(141,plain,
% 0.21/0.40 ((~male(a)) | female(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[140, 138])).
% 0.21/0.40 tff(142,plain,
% 0.21/0.40 ((~male(a)) | female(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.21/0.40 tff(143,plain,
% 0.21/0.40 ((~male(a)) | female(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.21/0.40 tff(144,plain,
% 0.21/0.40 ((~male(a)) | female(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[143, 138])).
% 0.21/0.40 tff(145,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[144, 137, 94])).
% 0.21/0.40 tff(146,plain,(~from_venus(a)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(147,plain,
% 0.21/0.40 (^[X: $i] : refl((from_mars(X) | from_venus(X)) <=> (from_mars(X) | from_venus(X)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(148,plain,
% 0.21/0.40 (![X: $i] : (from_mars(X) | from_venus(X)) <=> ![X: $i] : (from_mars(X) | from_venus(X))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.40 tff(149,plain,
% 0.21/0.40 (![X: $i] : (from_mars(X) | from_venus(X)) <=> ![X: $i] : (from_mars(X) | from_venus(X))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(150,axiom,(![X: $i] : (from_mars(X) | from_venus(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','from_mars_or_venus')).
% 0.21/0.40 tff(151,plain,
% 0.21/0.40 (![X: $i] : (from_mars(X) | from_venus(X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.40 tff(152,plain,(
% 0.21/0.40 ![X: $i] : (from_mars(X) | from_venus(X))),
% 0.21/0.40 inference(skolemize,[status(sab)],[151])).
% 0.21/0.40 tff(153,plain,
% 0.21/0.40 (![X: $i] : (from_mars(X) | from_venus(X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.21/0.40 tff(154,plain,
% 0.21/0.40 (((~![X: $i] : (from_mars(X) | from_venus(X))) | (from_mars(a) | from_venus(a))) <=> ((~![X: $i] : (from_mars(X) | from_venus(X))) | from_mars(a) | from_venus(a))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(155,plain,
% 0.21/0.40 ((~![X: $i] : (from_mars(X) | from_venus(X))) | (from_mars(a) | from_venus(a))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(156,plain,
% 0.21/0.40 ((~![X: $i] : (from_mars(X) | from_venus(X))) | from_mars(a) | from_venus(a)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.40 tff(157,plain,
% 0.21/0.40 (from_mars(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[156, 153, 146])).
% 0.21/0.40 tff(158,plain,
% 0.21/0.40 ((a_truth(a_from_mars) | (~from_mars(a))) <=> (a_truth(a_from_mars) | (~from_mars(a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(159,plain,
% 0.21/0.40 (((~from_mars(a)) | a_truth(a_from_mars)) <=> (a_truth(a_from_mars) | (~from_mars(a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(160,axiom,((~from_mars(a)) | a_truth(a_from_mars)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_from_mars1')).
% 0.21/0.40 tff(161,plain,
% 0.21/0.40 (a_truth(a_from_mars) | (~from_mars(a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.40 tff(162,plain,
% 0.21/0.40 (a_truth(a_from_mars) | (~from_mars(a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.21/0.40 tff(163,plain,
% 0.21/0.40 (a_truth(a_from_mars)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[162, 157])).
% 0.21/0.40 tff(164,plain,
% 0.21/0.40 (((~a_truth(a_from_mars)) | (~a_truth(statement_by(b)))) <=> ((~a_truth(a_from_mars)) | (~a_truth(statement_by(b))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(165,axiom,((~a_truth(a_from_mars)) | (~a_truth(statement_by(b)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_from_mars3')).
% 0.21/0.40 tff(166,plain,
% 0.21/0.40 ((~a_truth(a_from_mars)) | (~a_truth(statement_by(b)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.40 tff(167,plain,
% 0.21/0.40 (~a_truth(statement_by(b))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.21/0.40 tff(168,plain,
% 0.21/0.40 (^[X: $i] : refl((liar(X) | a_truth(statement_by(X))) <=> (liar(X) | a_truth(statement_by(X))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(169,plain,
% 0.21/0.40 (![X: $i] : (liar(X) | a_truth(statement_by(X))) <=> ![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[168])).
% 0.21/0.40 tff(170,plain,
% 0.21/0.40 (![X: $i] : (liar(X) | a_truth(statement_by(X))) <=> ![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(171,plain,
% 0.21/0.40 (^[X: $i] : rewrite((a_truth(statement_by(X)) | liar(X)) <=> (liar(X) | a_truth(statement_by(X))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(172,plain,
% 0.21/0.40 (![X: $i] : (a_truth(statement_by(X)) | liar(X)) <=> ![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[171])).
% 0.21/0.40 tff(173,axiom,(![X: $i] : (a_truth(statement_by(X)) | liar(X))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ001-0.ax','false_statements_made_by_liars')).
% 0.21/0.40 tff(174,plain,
% 0.21/0.40 (![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.40 tff(175,plain,
% 0.21/0.40 (![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.21/0.40 tff(176,plain,(
% 0.21/0.40 ![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[175])).
% 0.21/0.40 tff(177,plain,
% 0.21/0.40 (![X: $i] : (liar(X) | a_truth(statement_by(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.21/0.40 tff(178,plain,
% 0.21/0.40 (((~![X: $i] : (liar(X) | a_truth(statement_by(X)))) | (liar(b) | a_truth(statement_by(b)))) <=> ((~![X: $i] : (liar(X) | a_truth(statement_by(X)))) | liar(b) | a_truth(statement_by(b)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(179,plain,
% 0.21/0.40 ((~![X: $i] : (liar(X) | a_truth(statement_by(X)))) | (liar(b) | a_truth(statement_by(b)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(180,plain,
% 0.21/0.40 ((~![X: $i] : (liar(X) | a_truth(statement_by(X)))) | liar(b) | a_truth(statement_by(b))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.40 tff(181,plain,
% 0.21/0.40 (liar(b) | a_truth(statement_by(b))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[180, 177])).
% 0.21/0.40 tff(182,plain,
% 0.21/0.40 (liar(b)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[181, 167])).
% 0.21/0.40 tff(183,plain,
% 0.21/0.40 (~a_truth(a_has_lied)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[70, 182])).
% 0.21/0.40 tff(184,plain,
% 0.21/0.40 (~truthteller(b)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 183])).
% 0.21/0.40 tff(185,plain,
% 0.21/0.40 ((from_venus(a) | from_venus(b)) <=> (from_venus(a) | from_venus(b))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(186,axiom,(from_venus(a) | from_venus(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_from_venus')).
% 0.21/0.40 tff(187,plain,
% 0.21/0.40 (from_venus(a) | from_venus(b)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.40 tff(188,plain,
% 0.21/0.40 (from_venus(b)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[187, 146])).
% 0.21/0.40 tff(189,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | (truthteller(b) | (~female(b)) | (~from_venus(b)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | truthteller(b) | (~female(b)) | (~from_venus(b)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(190,plain,
% 0.21/0.40 (((~from_venus(b)) | truthteller(b) | (~female(b))) <=> (truthteller(b) | (~female(b)) | (~from_venus(b)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(191,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(b)) | truthteller(b) | (~female(b)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | (truthteller(b) | (~female(b)) | (~from_venus(b))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[190])).
% 0.21/0.40 tff(192,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(b)) | truthteller(b) | (~female(b)))) <=> ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | truthteller(b) | (~female(b)) | (~from_venus(b)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[191, 189])).
% 0.21/0.40 tff(193,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | ((~from_venus(b)) | truthteller(b) | (~female(b)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(194,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_venus(X)) | truthteller(X) | (~female(X)))) | truthteller(b) | (~female(b)) | (~from_venus(b))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.40 tff(195,plain,
% 0.21/0.40 (truthteller(b) | (~female(b))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[194, 115, 188])).
% 0.21/0.40 tff(196,plain,
% 0.21/0.40 (~female(b)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[195, 184])).
% 0.21/0.40 tff(197,plain,
% 0.21/0.40 (~male(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[144, 196])).
% 0.21/0.40 tff(198,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars)))) <=> ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | (~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(199,plain,
% 0.21/0.40 (((~liar(a)) | (~a_truth(a_from_mars)) | (~says(a, a_from_mars))) <=> ((~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(200,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~liar(a)) | (~a_truth(a_from_mars)) | (~says(a, a_from_mars)))) <=> ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.40 tff(201,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~liar(a)) | (~a_truth(a_from_mars)) | (~says(a, a_from_mars)))) <=> ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | (~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[200, 198])).
% 0.21/0.40 tff(202,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | ((~liar(a)) | (~a_truth(a_from_mars)) | (~says(a, a_from_mars)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(203,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : ((~liar(X)) | (~a_truth(Y)) | (~says(X, Y)))) | (~a_truth(a_from_mars)) | (~liar(a)) | (~says(a, a_from_mars))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.40 tff(204,plain,
% 0.21/0.40 ((~a_truth(a_from_mars)) | (~liar(a))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[203, 66, 97])).
% 0.21/0.40 tff(205,plain,
% 0.21/0.40 (~liar(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[204, 163])).
% 0.21/0.40 tff(206,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(a)) | (~female(a)) | liar(a))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | (~from_mars(a)) | (~female(a)) | liar(a))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(207,plain,
% 0.21/0.40 (((~from_mars(a)) | liar(a) | (~female(a))) <=> ((~from_mars(a)) | (~female(a)) | liar(a))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(208,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(a)) | liar(a) | (~female(a)))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(a)) | (~female(a)) | liar(a)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[207])).
% 0.21/0.40 tff(209,plain,
% 0.21/0.40 (((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(a)) | liar(a) | (~female(a)))) <=> ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | (~from_mars(a)) | (~female(a)) | liar(a))),
% 0.21/0.40 inference(transitivity,[status(thm)],[208, 206])).
% 0.21/0.40 tff(210,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | ((~from_mars(a)) | liar(a) | (~female(a)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(211,plain,
% 0.21/0.40 ((~![X: $i] : ((~from_mars(X)) | liar(X) | (~female(X)))) | (~from_mars(a)) | (~female(a)) | liar(a)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.21/0.40 tff(212,plain,
% 0.21/0.40 (~female(a)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[211, 87, 157, 205])).
% 0.21/0.40 tff(213,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[136, 133, 212, 197])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------