%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NLP267_17 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NLP267_17 : TPTP v9.0.0. Released v8.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Thu Jun 19 23:58:09 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(dest_type, type, (
% 0.21/0.38 dest: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.38 tff(paris_type, type, (
% 0.21/0.38 paris: $i)).
% 0.21/0.38 tff(tptp_fun_W_0_type, type, (
% 0.21/0.38 tptp_fun_W_0: |'$ki_world'|)).
% 0.21/0.38 tff(class_type, type, (
% 0.21/0.38 class: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.38 tff(second_type, type, (
% 0.21/0.38 second: $i)).
% 0.21/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.21/0.38 tptp_fun___ki_accessible_: ( |'$ki_index'| * |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.21/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.21/0.38 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.21/0.38 tff(tptp_fun___idx_b_s___type, type, (
% 0.21/0.38 tptp_fun___idx_b_s__: |'$ki_index'|)).
% 0.21/0.38 tff(price_type, type, (
% 0.21/0.38 price: ( |'$ki_world'| * $i ) > $o)).
% 0.21/0.38 tff(seventy_type, type, (
% 0.21/0.38 seventy: $i)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => price(W, seventy))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(3,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => price(W, seventy))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | price(W, seventy))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.38 tff(8,plain,(
% 0.21/0.38 ~((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy))),
% 0.21/0.38 inference(skolemize,[status(sab)],[7])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)),
% 0.21/0.38 inference(or_elim,[status(thm)],[8])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second))))) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second))) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (^[W: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => (dest(W, paris) & class(W, second))) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => (dest(W, paris) & class(W, second))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.39 tff(17,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => (dest(W, paris) & class(W, second)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,(
% 0.21/0.39 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (dest(W, paris) & class(W, second)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))) | ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~((~dest(W!0, paris)) | (~class(W!0, second)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~((~dest(W!0, paris)) | (~class(W!0, second)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))) | ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~((~dest(W!0, paris)) | (~class(W!0, second)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~((~dest(W, paris)) | (~class(W, second)))))) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~((~dest(W!0, paris)) | (~class(W!0, second))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~((~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (((~dest(W!0, paris)) | (~class(W!0, second))) | dest(W!0, paris)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (dest(W!0, paris)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (((~dest(W!0, paris)) | (~class(W!0, second))) | class(W!0, second)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (class(W!0, second)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (~price(W!0, seventy)),
% 0.21/0.39 inference(or_elim,[status(thm)],[8])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (^[W: |'$ki_world'|] : refl((price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (^[W: |'$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_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | ((~dest(W, paris)) | (~class(W, second)))))), rewrite((price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | ((~dest(W, paris)) | (~class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))), ((price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second)))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite(((dest(W, paris) & class(W, second)) => price(W, seventy)) <=> ((~(dest(W, paris) & class(W, second))) | price(W, seventy))), ((tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((~(dest(W, paris) & class(W, second))) | price(W, seventy))))), rewrite((tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((~(dest(W, paris) & class(W, second))) | price(W, seventy))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))), ((tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy))) <=> ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.39 tff(39,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W) => ((dest(W, paris) & class(W, second)) => price(W, seventy)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.39 tff(42,plain,(
% 0.21/0.39 ![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~(dest(W, paris) & class(W, second))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 ((price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second))) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | ((~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))) <=> ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (price(W!0, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | (~dest(W!0, paris)) | (~class(W!0, second)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.40 ((~![W: |'$ki_world'|] : (price(W, seventy) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W)) | (~dest(W, paris)) | (~class(W, second)))) | (~tptp_fun___ki_accessible_(|'#idx(b_s)'|, |'$ki_local_world'|, W!0)) | price(W!0, seventy) | (~dest(W!0, paris)) | (~class(W!0, second))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ((~dest(W!0, paris)) | (~class(W!0, second))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[50, 44, 9, 31])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 30, 28])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------