TSTP Solution File: NLP267_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NLP267_1 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Mon May 22 15:40:05 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NLP267_1 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 22 12:11:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(class_type, type, (
% 0.21/0.41 class: ( '$ki_world' * $i ) > $o)).
% 0.21/0.41 tff(second_type, type, (
% 0.21/0.41 second: $i)).
% 0.21/0.41 tff(tptp_fun_W_0_type, type, (
% 0.21/0.41 tptp_fun_W_0: '$ki_world')).
% 0.21/0.41 tff(tptp_fun___ki_accessible__type, type, (
% 0.21/0.41 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.21/0.41 tff(tptp_fun___ki_local_world__type, type, (
% 0.21/0.41 tptp_fun___ki_local_world_: '$ki_world')).
% 0.21/0.41 tff(price_type, type, (
% 0.21/0.41 price: ( '$ki_world' * $i ) > $o)).
% 0.21/0.41 tff(seventy_type, type, (
% 0.21/0.41 seventy: $i)).
% 0.21/0.41 tff(dest_type, type, (
% 0.21/0.41 dest: ( '$ki_world' * $i ) > $o)).
% 0.21/0.41 tff(paris_type, type, (
% 0.21/0.41 paris: $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => price(W, seventy))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => price(W, seventy))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.41 tff(11,plain,(
% 0.21/0.41 ~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy))),
% 0.21/0.41 inference(skolemize,[status(sab)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.21/0.41 inference(or_elim,[status(thm)],[11])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (^[W: '$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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (^[W: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second)) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.41 tff(18,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => class(W, second))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','belief2')).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.41 tff(21,plain,(
% 0.21/0.41 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.41 inference(skolemize,[status(sab)],[20])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (((~![W: '$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_(|'$ki_local_world'|, W!0)) | class(W!0, second))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 ((~![W: '$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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | class(W, second))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | class(W!0, second)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (class(W!0, second)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (^[W: '$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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (^[W: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris)) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris)) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.41 tff(32,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => dest(W, paris))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','belief1')).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.41 tff(35,plain,(
% 0.21/0.41 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.41 inference(skolemize,[status(sab)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~![W: '$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_(|'$ki_local_world'|, W!0)) | dest(W!0, paris))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~![W: '$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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | dest(W, paris))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | dest(W!0, paris)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (dest(W!0, paris)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 36, 12])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (~price(W!0, seventy)),
% 0.21/0.41 inference(or_elim,[status(thm)],[11])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (^[W: '$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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (^[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_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![W: '$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_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![W: '$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_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (^[W: '$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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.42 tff(49,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','law2')).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.42 tff(52,plain,(
% 0.21/0.42 ![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[51])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (((~![W: '$ki_world'] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: '$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) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((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) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (((~![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) | (~dest(W!0, paris)) | (~class(W!0, second))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (((~![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) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~![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_(|'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 ((~![W: '$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) | (~dest(W!0, paris)) | (~class(W!0, second))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 ((~dest(W!0, paris)) | (~class(W!0, second))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[60, 54, 12, 41])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[61, 40, 26])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------