%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL954_19 : TPTP v9.3.1. Released v8.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:01:14 PM UTC 2026
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL954_19 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.33 % Computer : n006.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 5 14:51:03 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.22/0.54 % SZS status Theorem
% 0.22/0.54 % SZS output start Proof
% 0.22/0.54 tff(true_type, type, (
% 0.22/0.54 true: |'$ki_world'| > $o)).
% 0.22/0.54 tff(tptp_fun___ki_accessible__type, type, (
% 0.22/0.54 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.22/0.54 tff(tptp_fun___ki_local_world__type, type, (
% 0.22/0.54 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.22/0.54 tff(1,plain,
% 0.22/0.54 ((~$true) <=> $false),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(2,plain,
% 0.22/0.54 (![W: |'$ki_world'|] : $true <=> $true),
% 0.22/0.54 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.54 tff(3,plain,
% 0.22/0.54 (^[W: |'$ki_world'|] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W, W0) => true(W0)) <=> (true(W0) | (~tptp_fun___ki_accessible_(W, W0))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) <=> ![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0))))), quant_intro(proof_bind(^[W0: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W, W0) => true(W0)) <=> (true(W0) | (~tptp_fun___ki_accessible_(W, W0))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) <=> ![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0))))), ((![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0))) <=> (![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0))) => ![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0)))))), rewrite((![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0))) => ![W0: |'$ki_world'|] : (true(W0) | (~tptp_fun___ki_accessible_(W, W0)))) <=> $true), ((![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0))) <=> $true)), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => $true))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => $true) <=> $true), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)))) <=> $true))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(4,plain,
% 0.22/0.54 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)))) <=> ![W: |'$ki_world'|] : $true),
% 0.22/0.54 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.54 tff(5,plain,
% 0.22/0.54 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)))) <=> $true),
% 0.22/0.54 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.54 tff(6,plain,
% 0.22/0.54 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0))))) <=> (~$true)),
% 0.22/0.54 inference(monotonicity,[status(thm)],[5])).
% 0.22/0.54 tff(7,plain,
% 0.22/0.54 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0))))) <=> $false),
% 0.22/0.54 inference(transitivity,[status(thm)],[6, 1])).
% 0.22/0.54 tff(8,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => true(W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.22/0.54 tff(9,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.54 % SZS output end Proof
% 0.22/0.54 % E exiting
%------------------------------------------------------------------------------