%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NLP267_2 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:18:39 AM UTC 2025
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NLP267_2 : TPTP v9.0.0. Released v8.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 23:58:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(dest_type, type, (
% 0.21/0.37 dest: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.37 tff(paris_type, type, (
% 0.21/0.37 paris: $i)).
% 0.21/0.37 tff(tptp_fun_W_0_type, type, (
% 0.21/0.37 tptp_fun_W_0: |'$ki_world'|)).
% 0.21/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.21/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.21/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.21/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.21/0.37 tff(price_type, type, (
% 0.21/0.37 price: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.37 tff(seventy_type, type, (
% 0.21/0.37 seventy: $i)).
% 0.21/0.37 tff(class_type, type, (
% 0.21/0.37 class: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.37 tff(second_type, type, (
% 0.21/0.37 second: $i)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(2,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => price(W, seventy))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(3,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => price(W, seventy))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.21/0.37 tff(4,plain,
% 0.21/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.37 tff(5,plain,
% 0.21/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.37 tff(6,plain,
% 0.21/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.37 tff(7,plain,
% 0.21/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.37 tff(8,plain,(
% 0.21/0.37 ~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy))),
% 0.21/0.37 inference(skolemize,[status(sab)],[7])).
% 0.21/0.37 tff(9,plain,
% 0.21/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.21/0.37 inference(or_elim,[status(thm)],[8])).
% 0.21/0.37 tff(10,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(11,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.37 tff(12,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(13,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(14,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.37 tff(15,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','belief1')).
% 0.21/0.37 tff(16,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.37 tff(17,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.37 tff(18,plain,(
% 0.21/0.37 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(skolemize,[status(sab)],[17])).
% 0.21/0.37 tff(19,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.37 tff(20,plain,
% 0.21/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | dest(W!0, paris))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | dest(W!0, paris))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(21,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | dest(W!0, paris))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(22,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | dest(W!0, paris)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.37 tff(23,plain,
% 0.21/0.37 (dest(W!0, paris)),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.21/0.37 tff(24,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(25,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.37 tff(26,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(27,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(28,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.37 tff(29,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','belief2')).
% 0.21/0.37 tff(30,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.37 tff(31,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.37 tff(32,plain,(
% 0.21/0.37 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(skolemize,[status(sab)],[31])).
% 0.21/0.37 tff(33,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.37 tff(34,plain,
% 0.21/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | class(W!0, second))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | class(W!0, second))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(35,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | class(W!0, second))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(36,plain,
% 0.21/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | class(W!0, second)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.37 tff(37,plain,
% 0.21/0.37 (class(W!0, second)),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[36, 33, 9])).
% 0.21/0.37 tff(38,plain,
% 0.21/0.37 (~price(W!0, seventy)),
% 0.21/0.37 inference(or_elim,[status(thm)],[8])).
% 0.21/0.37 tff(39,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : refl((price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(40,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.37 tff(41,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : trans(monotonicity(trans(monotonicity(rewrite((dest(W, paris) & class(W, second)) <=> (~((~dest(W, paris)) | (~class(W, second))))), ((~(dest(W, paris) & class(W, second))) <=> (~(~((~dest(W, paris)) | (~class(W, second))))))), rewrite((~(~((~dest(W, paris)) | (~class(W, second))))) <=> ((~dest(W, paris)) | (~class(W, second)))), ((~(dest(W, paris) & class(W, second))) <=> ((~dest(W, paris)) | (~class(W, second))))), ((price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ((~dest(W, paris)) | (~class(W, second)))))), rewrite((price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ((~dest(W, paris)) | (~class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))), ((price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(42,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.37 tff(43,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(44,plain,
% 0.21/0.37 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite(((dest(W, paris) & class(W, second)) => price(W, seventy)) <=> ((~(dest(W, paris) & class(W, second))) | price(W, seventy))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((~(dest(W, paris) & class(W, second))) | price(W, seventy))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((~(dest(W, paris) & class(W, second))) | price(W, seventy))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(45,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.38 tff(46,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','law2')).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.38 tff(49,plain,(
% 0.21/0.38 ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[48])).
% 0.21/0.38 tff(50,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.38 tff(51,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.21/0.38 tff(52,plain,
% 0.21/0.38 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(53,plain,
% 0.21/0.38 ((price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(54,plain,
% 0.21/0.38 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.38 tff(55,plain,
% 0.21/0.38 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris)))),
% 0.21/0.38 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.38 tff(56,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(57,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~class(W!0, second)) | (~dest(W!0, paris))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.38 tff(58,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[57, 51, 9, 38, 37, 23])).
% 0.21/0.38 % SZS output end Proof
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------