%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL231-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 : Fri Sep 25 02:06:06 PM UTC 2026
% Result : Unsatisfiable 112.86s 22.60s
% Output : CNFRefutation 112.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 83 unt; 11 def)
% Number of atoms : 198 ( 82 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f4,plain,
! [X0,X1] : true = axiom(implies(X0,or(X1,X0))),
inference(reorient_equations,[],[f3]) ).
fof(f7,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f8,plain,
! [X2,X0,X1] : true = axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f10,plain,
! [X2,X0,X1] : true = axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f12,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f13,plain,
! [X0] : true = ifeq(axiom(X0),true,theorem(X0),true),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] : ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f15,plain,
! [X0,X1] : true = ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
theorem(implies(implies(implies(p,q),implies(p,r)),implies(p,implies(q,r)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f17,plain,
true != theorem(implies(implies(implies(p,q),implies(p,r)),implies(p,implies(q,r)))),
inference(reorient_equations,[],[f16]) ).
fof(f19,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f4,f11]) ).
fof(f21,plain,
! [X2,X0,X1] : true = axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f8,f11]) ).
fof(f22,plain,
! [X2,X0,X1] : true = axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f10,f11,f11,f11]) ).
fof(f23,plain,
! [X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(definition_unfolding,[],[f15,f11]) ).
fof(f24,plain,
true != theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r)))),
inference(definition_unfolding,[],[f17,f11,f11,f11,f11,f11,f11]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : axiom(or(not(X0),or(X1,X0))) = true,
inference(cnf_transformation,[],[f19]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) = true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) = true,
inference(cnf_transformation,[],[f22]) ).
tcf(c_65,plain,
! [X0: $i] : ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : ifeq(theorem(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_67,negated_conjecture,
theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r)))) != true,
inference(cnf_transformation,[],[f24]) ).
tcf(c_101,definition,
iPr_def_10 = not(p),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_102,definition,
iPr_def_11 = or(iPr_def_10,q),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_103,definition,
iPr_def_12 = not(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_104,definition,
iPr_def_13 = or(iPr_def_10,r),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_105,definition,
iPr_def_14 = or(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_106,definition,
iPr_def_15 = not(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_107,definition,
iPr_def_16 = not(q),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_108,definition,
iPr_def_17 = or(iPr_def_16,r),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_109,definition,
iPr_def_18 = or(iPr_def_10,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_110,definition,
iPr_def_19 = or(iPr_def_15,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_111,definition,
iPr_def_20 = theorem(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_112,negated_conjecture,
iPr_def_20 != true,
inference(demodulation,[status(thm)],[c_67,c_107,c_108,c_109,c_104,c_101,c_102,c_103,c_105,c_106,c_110,c_111]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : ifeq(theorem(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) = true,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) = true,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] : axiom(or(not(X0),or(X1,X0))) = true,
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_119,plain,
! [X0: $i] : ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_215,plain,
! [X0: $i] : ifeq(theorem(or(not(X0),iPr_def_19)),true,ifeq(theorem(X0),true,iPr_def_20,true),true) = true,
inference(superposition,[status(thm)],[c_111,c_113]) ).
tcf(c_229,plain,
! [X0: $i] : axiom(or(not(or(not(X0),r)),or(not(or(iPr_def_16,X0)),iPr_def_17))) = true,
inference(superposition,[status(thm)],[c_108,c_114]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : ifeq(true,true,theorem(or(not(X0),or(X1,X0))),true) = true,
inference(superposition,[status(thm)],[c_117,c_119]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),true) = true,
inference(superposition,[status(thm)],[c_115,c_119]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),true) = true,
inference(superposition,[status(thm)],[c_114,c_119]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] : theorem(or(not(X0),or(X1,X0))) = true,
inference(demodulation,[status(thm)],[c_267,c_120]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) = true,
inference(demodulation,[status(thm)],[c_269,c_120]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i,X2: $i] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) = true,
inference(demodulation,[status(thm)],[c_270,c_120]) ).
tcf(c_405,plain,
axiom(or(not(or(iPr_def_12,r)),or(not(or(iPr_def_16,iPr_def_11)),iPr_def_17))) = true,
inference(superposition,[status(thm)],[c_103,c_229]) ).
tcf(c_485,plain,
theorem(or(not(q),iPr_def_11)) = true,
inference(superposition,[status(thm)],[c_102,c_275]) ).
tcf(c_548,plain,
! [X0: $i] : theorem(or(not(or(X0,iPr_def_13)),or(iPr_def_10,or(X0,r)))) = true,
inference(superposition,[status(thm)],[c_104,c_280]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),true) = true,
inference(superposition,[status(thm)],[c_280,c_113]) ).
tcf(c_584,plain,
! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_17)),or(not(or(iPr_def_10,X0)),iPr_def_18))) = true,
inference(superposition,[status(thm)],[c_109,c_281]) ).
tcf(c_585,plain,
! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_18)),or(not(or(iPr_def_15,X0)),iPr_def_19))) = true,
inference(superposition,[status(thm)],[c_110,c_281]) ).
tcf(c_596,plain,
theorem(or(iPr_def_16,iPr_def_11)) = true,
inference(light_normalisation,[status(thm)],[c_485,c_107]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true) = true,
inference(demodulation,[status(thm)],[c_568,c_120]) ).
tcf(c_705,plain,
ifeq(true,true,theorem(or(not(or(iPr_def_12,r)),or(not(or(iPr_def_16,iPr_def_11)),iPr_def_17))),true) = true,
inference(superposition,[status(thm)],[c_405,c_119]) ).
tcf(c_1258,plain,
theorem(or(not(iPr_def_14),or(iPr_def_10,or(iPr_def_12,r)))) = true,
inference(superposition,[status(thm)],[c_105,c_548]) ).
tcf(c_1391,plain,
theorem(or(iPr_def_15,or(iPr_def_10,or(iPr_def_12,r)))) = true,
inference(light_normalisation,[status(thm)],[c_1258,c_106]) ).
tcf(c_1492,plain,
theorem(or(not(or(iPr_def_12,r)),or(not(or(iPr_def_16,iPr_def_11)),iPr_def_17))) = true,
inference(demodulation,[status(thm)],[c_705,c_120]) ).
tcf(c_1818,plain,
ifeq(theorem(or(not(or(iPr_def_15,or(iPr_def_10,or(iPr_def_12,r)))),iPr_def_19)),true,ifeq(true,true,iPr_def_20,true),true) = true,
inference(superposition,[status(thm)],[c_1391,c_215]) ).
tcf(c_2451,plain,
ifeq(theorem(or(not(or(iPr_def_15,or(iPr_def_10,or(iPr_def_12,r)))),iPr_def_19)),true,iPr_def_20,true) = true,
inference(demodulation,[status(thm)],[c_1818,c_120]) ).
tcf(c_3051,plain,
! [X0: $i] : ifeq(true,true,ifeq(theorem(or(not(X0),iPr_def_17)),true,theorem(or(not(or(iPr_def_10,X0)),iPr_def_18)),true),true) = true,
inference(superposition,[status(thm)],[c_584,c_113]) ).
tcf(c_3071,plain,
! [X0: $i] : ifeq(true,true,ifeq(theorem(or(not(X0),iPr_def_18)),true,theorem(or(not(or(iPr_def_15,X0)),iPr_def_19)),true),true) = true,
inference(superposition,[status(thm)],[c_585,c_113]) ).
tcf(c_3299,plain,
! [X0: $i] : ifeq(theorem(or(not(X0),iPr_def_18)),true,theorem(or(not(or(iPr_def_15,X0)),iPr_def_19)),true) = true,
inference(demodulation,[status(thm)],[c_3071,c_120]) ).
tcf(c_3300,plain,
! [X0: $i] : ifeq(theorem(or(not(X0),iPr_def_17)),true,theorem(or(not(or(iPr_def_10,X0)),iPr_def_18)),true) = true,
inference(demodulation,[status(thm)],[c_3051,c_120]) ).
tcf(c_3982,plain,
ifeq(true,true,theorem(or(not(or(iPr_def_16,iPr_def_11)),or(not(or(iPr_def_12,r)),iPr_def_17))),true) = true,
inference(superposition,[status(thm)],[c_1492,c_684]) ).
tcf(c_4259,plain,
theorem(or(not(or(iPr_def_16,iPr_def_11)),or(not(or(iPr_def_12,r)),iPr_def_17))) = true,
inference(demodulation,[status(thm)],[c_3982,c_120]) ).
tcf(c_7092,plain,
ifeq(true,true,ifeq(theorem(or(iPr_def_16,iPr_def_11)),true,theorem(or(not(or(iPr_def_12,r)),iPr_def_17)),true),true) = true,
inference(superposition,[status(thm)],[c_4259,c_113]) ).
tcf(c_7165,plain,
ifeq(theorem(or(iPr_def_16,iPr_def_11)),true,theorem(or(not(or(iPr_def_12,r)),iPr_def_17)),true) = true,
inference(demodulation,[status(thm)],[c_7092,c_120]) ).
tcf(c_7166,plain,
ifeq(true,true,theorem(or(not(or(iPr_def_12,r)),iPr_def_17)),true) = true,
inference(light_normalisation,[status(thm)],[c_7165,c_596]) ).
tcf(c_7167,plain,
theorem(or(not(or(iPr_def_12,r)),iPr_def_17)) = true,
inference(demodulation,[status(thm)],[c_7166,c_120]) ).
tcf(c_45039,plain,
ifeq(true,true,theorem(or(not(or(iPr_def_10,or(iPr_def_12,r))),iPr_def_18)),true) = true,
inference(superposition,[status(thm)],[c_7167,c_3300]) ).
tcf(c_45671,plain,
theorem(or(not(or(iPr_def_10,or(iPr_def_12,r))),iPr_def_18)) = true,
inference(demodulation,[status(thm)],[c_45039,c_120]) ).
tcf(c_46458,plain,
ifeq(true,true,theorem(or(not(or(iPr_def_15,or(iPr_def_10,or(iPr_def_12,r)))),iPr_def_19)),true) = true,
inference(superposition,[status(thm)],[c_45671,c_3299]) ).
tcf(c_46696,plain,
theorem(or(not(or(iPr_def_15,or(iPr_def_10,or(iPr_def_12,r)))),iPr_def_19)) = true,
inference(demodulation,[status(thm)],[c_46458,c_120]) ).
tcf(c_49354,plain,
ifeq(true,true,iPr_def_20,true) = true,
inference(superposition,[status(thm)],[c_46696,c_2451]) ).
tcf(c_49463,plain,
true = iPr_def_20,
inference(demodulation,[status(thm)],[c_49354,c_120]) ).
tcf(c_56937,plain,
$false,
inference(superposition,[status(thm)],[c_49463,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL231-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 22:29:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running UEQ theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 112.86/22.60 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 112.86/22.60 % SZS status Started for theBenchmark.p
% 112.86/22.60 % SZS status Unsatisfiable for theBenchmark.p
% 112.86/22.60
% 112.86/22.60 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 112.86/22.60
% 112.86/22.60 % ------ iProver source info
% 112.86/22.60
% 112.86/22.60 % git: date: 2026-07-19 20:42:38 +0200
% 112.86/22.60 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 112.86/22.60 % git: non_committed_changes: false
% 112.86/22.60
% 112.86/22.60 % ------ Parsing...% successful
% 112.86/22.60
% 112.86/22.60
% 112.86/22.60 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 112.86/22.60
% 112.86/22.60 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 112.86/22.60
% 112.86/22.60 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 112.86/22.60
% 112.86/22.60 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 112.86/22.60 % ------ Proving...
% 112.86/22.60 % ------ Problem Properties
% 112.86/22.60
% 112.86/22.60 %
% 112.86/22.60 % clauses 20
% 112.86/22.60 % conjectures 1
% 112.86/22.60 % EPR 1
% 112.86/22.60 % Horn 20
% 112.86/22.60 % unary 20
% 112.86/22.60 % binary 0
% 112.86/22.60 % lits 20
% 112.86/22.60 % lits eq 20
% 112.86/22.60 % fd_pure 0
% 112.86/22.60 % fd_pseudo 0
% 112.86/22.60 % fd_cond 0
% 112.86/22.60 % fd_pseudo_cond 0
% 112.86/22.60 % AC symbols 0
% 112.86/22.60
% 112.86/22.60 % ------ Input Options Time Limit: Unbounded
% 112.86/22.60
% 112.86/22.60
% 112.86/22.60 % ------
% 112.86/22.60 % Current options:
% 112.86/22.60 % ------
% 112.86/22.60
% 112.86/22.60
% 112.86/22.60 %
% 112.86/22.60
% 112.86/22.60 % ------ Proving...
% 112.86/22.60 %
% 112.86/22.60
% 112.86/22.60 % SZS status Unsatisfiable for theBenchmark.p
% 112.86/22.60
% 112.86/22.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 112.86/22.60
% 112.86/22.60
%------------------------------------------------------------------------------