%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 02:06:02 PM UTC 2026
% Result : Unsatisfiable 140.75s 28.95s
% Output : CNFRefutation 140.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 85 ( 85 unt; 8 def)
% Number of atoms : 167 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : axiom(or(not(or(X0,X0)),X0)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f3,axiom,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f4,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f6,plain,
! [X0,X1] : true = axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : axiom(or(not(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(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(reorient_equations,[],[f7]) ).
fof(f11,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f12,plain,
! [X0] : true = ifeq(axiom(X0),true,theorem(X0),true),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] : ifeq(theorem(X0),true,ifeq(axiom(or(not(X0),X1)),true,theorem(X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f14,plain,
! [X0,X1] : true = ifeq(theorem(X0),true,ifeq(axiom(or(not(X0),X1)),true,theorem(X1),true),true),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X2,X0,X1] : ifeq(theorem(or(not(X0),X1)),true,ifeq(axiom(or(not(X2),X0)),true,theorem(or(not(X2),X1)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
fof(f16,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,ifeq(axiom(or(not(X2),X0)),true,theorem(or(not(X2),X1)),true),true),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f18,plain,
true != theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),
inference(reorient_equations,[],[f17]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i] : axiom(or(not(or(X0,X0)),X0)) = true,
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : axiom(or(not(X0),or(X1,X0))) = true,
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : axiom(or(not(or(X0,X1)),or(X1,X0))) = true,
inference(cnf_transformation,[],[f6]) ).
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,[],[f8]) ).
tcf(c_65,plain,
! [X0: $i] : ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(cnf_transformation,[],[f12]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : ifeq(theorem(X0),true,ifeq(axiom(or(not(X0),X1)),true,theorem(X1),true),true) = true,
inference(cnf_transformation,[],[f14]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(theorem(or(not(X0),X1)),true,ifeq(axiom(or(not(X2),X0)),true,theorem(or(not(X2),X1)),true),true) = true,
inference(cnf_transformation,[],[f16]) ).
tcf(c_68,negated_conjecture,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != true,
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,definition,
iPr_def_10 = or(p,q),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_106,definition,
iPr_def_11 = not(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_107,definition,
iPr_def_12 = or(iPr_def_11,q),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_108,definition,
iPr_def_13 = not(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_109,definition,
iPr_def_14 = not(p),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_110,definition,
iPr_def_15 = or(iPr_def_14,q),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_111,definition,
iPr_def_16 = or(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_112,definition,
iPr_def_17 = theorem(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_113,negated_conjecture,
iPr_def_17 != true,
inference(demodulation,[status(thm)],[c_68,c_109,c_110,c_105,c_106,c_107,c_108,c_111,c_112]) ).
tcf(c_230,plain,
axiom(or(not(or(q,p)),iPr_def_10)) = true,
inference(superposition,[status(thm)],[c_105,c_62]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] : ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true) = true,
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(X0,X1)),or(X1,X0))) = true,
inference(demodulation,[status(thm)],[c_269,c_59]) ).
tcf(c_328,plain,
! [X0: $i] : axiom(or(not(or(X0,iPr_def_12)),or(iPr_def_11,or(X0,q)))) = true,
inference(superposition,[status(thm)],[c_107,c_63]) ).
tcf(c_333,plain,
! [X0: $i] : axiom(or(not(or(iPr_def_14,or(X0,q))),or(X0,iPr_def_15))) = true,
inference(superposition,[status(thm)],[c_110,c_63]) ).
tcf(c_334,plain,
! [X0: $i] : axiom(or(not(or(iPr_def_13,or(X0,iPr_def_15))),or(X0,iPr_def_16))) = true,
inference(superposition,[status(thm)],[c_111,c_63]) ).
tcf(c_560,plain,
! [X0: $i] : ifeq(theorem(or(X0,X0)),true,ifeq(true,true,theorem(X0),true),true) = true,
inference(superposition,[status(thm)],[c_60,c_66]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i] : ifeq(theorem(X0),true,ifeq(true,true,theorem(or(X1,X0)),true),true) = true,
inference(superposition,[status(thm)],[c_61,c_66]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i] : ifeq(theorem(or(X0,X1)),true,ifeq(true,true,theorem(or(X1,X0)),true),true) = true,
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(theorem(or(X0,or(X1,X2))),true,ifeq(true,true,theorem(or(X1,or(X0,X2))),true),true) = true,
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i] : ifeq(theorem(X0),true,theorem(or(X1,X0)),true) = true,
inference(demodulation,[status(thm)],[c_561,c_59]) ).
tcf(c_605,plain,
! [X0: $i] : ifeq(theorem(or(X0,X0)),true,theorem(X0),true) = true,
inference(demodulation,[status(thm)],[c_560,c_59]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] : ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true) = true,
inference(demodulation,[status(thm)],[c_562,c_59]) ).
tcf(c_616,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_563,c_59]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(theorem(or(not(or(X0,X1)),X2)),true,ifeq(true,true,theorem(or(not(X1),X2)),true),true) = true,
inference(superposition,[status(thm)],[c_61,c_67]) ).
tcf(c_834,plain,
! [X0: $i] : ifeq(theorem(or(not(iPr_def_10),X0)),true,ifeq(true,true,theorem(or(not(or(q,p)),X0)),true),true) = true,
inference(superposition,[status(thm)],[c_230,c_67]) ).
tcf(c_870,plain,
! [X0: $i] : ifeq(theorem(or(not(iPr_def_10),X0)),true,theorem(or(not(or(q,p)),X0)),true) = true,
inference(demodulation,[status(thm)],[c_834,c_59]) ).
tcf(c_871,plain,
! [X0: $i] : ifeq(theorem(or(iPr_def_11,X0)),true,theorem(or(not(or(q,p)),X0)),true) = true,
inference(light_normalisation,[status(thm)],[c_870,c_106]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(theorem(or(not(or(X0,X1)),X2)),true,theorem(or(not(X1),X2)),true) = true,
inference(demodulation,[status(thm)],[c_824,c_59]) ).
tcf(c_1205,plain,
! [X0: $i] : ifeq(theorem(or(X0,iPr_def_12)),true,ifeq(true,true,theorem(or(iPr_def_11,or(X0,q))),true),true) = true,
inference(superposition,[status(thm)],[c_328,c_66]) ).
tcf(c_1208,plain,
! [X0: $i] : ifeq(theorem(or(X0,iPr_def_12)),true,theorem(or(iPr_def_11,or(X0,q))),true) = true,
inference(demodulation,[status(thm)],[c_1205,c_59]) ).
tcf(c_1504,plain,
ifeq(theorem(or(iPr_def_16,iPr_def_16)),true,iPr_def_17,true) = true,
inference(superposition,[status(thm)],[c_112,c_605]) ).
tcf(c_2578,plain,
! [X0: $i] : ifeq(theorem(or(iPr_def_14,or(X0,q))),true,ifeq(true,true,theorem(or(X0,iPr_def_15)),true),true) = true,
inference(superposition,[status(thm)],[c_333,c_66]) ).
tcf(c_2581,plain,
! [X0: $i] : ifeq(theorem(or(iPr_def_14,or(X0,q))),true,theorem(or(X0,iPr_def_15)),true) = true,
inference(demodulation,[status(thm)],[c_2578,c_59]) ).
tcf(c_2696,plain,
! [X0: $i] : ifeq(theorem(or(iPr_def_13,or(X0,iPr_def_15))),true,ifeq(true,true,theorem(or(X0,iPr_def_16)),true),true) = true,
inference(superposition,[status(thm)],[c_334,c_66]) ).
tcf(c_2699,plain,
! [X0: $i] : ifeq(theorem(or(iPr_def_13,or(X0,iPr_def_15))),true,theorem(or(X0,iPr_def_16)),true) = true,
inference(demodulation,[status(thm)],[c_2696,c_59]) ).
tcf(c_81510,plain,
! [X0: $i,X1: $i] : ifeq(true,true,theorem(or(not(X0),or(X0,X1))),true) = true,
inference(superposition,[status(thm)],[c_291,c_874]) ).
tcf(c_81960,plain,
! [X0: $i,X1: $i] : theorem(or(not(X0),or(X0,X1))) = true,
inference(demodulation,[status(thm)],[c_81510,c_59]) ).
tcf(c_84248,plain,
! [X0: $i] : theorem(or(iPr_def_13,or(iPr_def_12,X0))) = true,
inference(superposition,[status(thm)],[c_108,c_81960]) ).
tcf(c_84694,plain,
! [X0: $i] : ifeq(true,true,theorem(or(iPr_def_12,or(iPr_def_13,X0))),true) = true,
inference(superposition,[status(thm)],[c_84248,c_616]) ).
tcf(c_84700,plain,
! [X0: $i] : theorem(or(iPr_def_12,or(iPr_def_13,X0))) = true,
inference(demodulation,[status(thm)],[c_84694,c_59]) ).
tcf(c_85422,plain,
theorem(or(iPr_def_12,iPr_def_16)) = true,
inference(superposition,[status(thm)],[c_111,c_84700]) ).
tcf(c_85532,plain,
ifeq(true,true,theorem(or(iPr_def_16,iPr_def_12)),true) = true,
inference(superposition,[status(thm)],[c_85422,c_606]) ).
tcf(c_85534,plain,
theorem(or(iPr_def_16,iPr_def_12)) = true,
inference(demodulation,[status(thm)],[c_85532,c_59]) ).
tcf(c_140355,plain,
ifeq(true,true,theorem(or(iPr_def_11,or(iPr_def_16,q))),true) = true,
inference(superposition,[status(thm)],[c_85534,c_1208]) ).
tcf(c_140410,plain,
theorem(or(iPr_def_11,or(iPr_def_16,q))) = true,
inference(demodulation,[status(thm)],[c_140355,c_59]) ).
tcf(c_141749,plain,
ifeq(true,true,theorem(or(not(or(q,p)),or(iPr_def_16,q))),true) = true,
inference(superposition,[status(thm)],[c_140410,c_871]) ).
tcf(c_141758,plain,
theorem(or(not(or(q,p)),or(iPr_def_16,q))) = true,
inference(demodulation,[status(thm)],[c_141749,c_59]) ).
tcf(c_406623,plain,
ifeq(true,true,theorem(or(not(p),or(iPr_def_16,q))),true) = true,
inference(superposition,[status(thm)],[c_141758,c_874]) ).
tcf(c_406628,plain,
theorem(or(not(p),or(iPr_def_16,q))) = true,
inference(demodulation,[status(thm)],[c_406623,c_59]) ).
tcf(c_406629,plain,
theorem(or(iPr_def_14,or(iPr_def_16,q))) = true,
inference(light_normalisation,[status(thm)],[c_406628,c_109]) ).
tcf(c_407960,plain,
ifeq(true,true,theorem(or(iPr_def_16,iPr_def_15)),true) = true,
inference(superposition,[status(thm)],[c_406629,c_2581]) ).
tcf(c_407962,plain,
theorem(or(iPr_def_16,iPr_def_15)) = true,
inference(demodulation,[status(thm)],[c_407960,c_59]) ).
tcf(c_408123,plain,
! [X0: $i] : ifeq(true,true,theorem(or(X0,or(iPr_def_16,iPr_def_15))),true) = true,
inference(superposition,[status(thm)],[c_407962,c_604]) ).
tcf(c_408162,plain,
! [X0: $i] : theorem(or(X0,or(iPr_def_16,iPr_def_15))) = true,
inference(demodulation,[status(thm)],[c_408123,c_59]) ).
tcf(c_408672,plain,
ifeq(true,true,theorem(or(iPr_def_16,iPr_def_16)),true) = true,
inference(superposition,[status(thm)],[c_408162,c_2699]) ).
tcf(c_408699,plain,
theorem(or(iPr_def_16,iPr_def_16)) = true,
inference(demodulation,[status(thm)],[c_408672,c_59]) ).
tcf(c_408709,plain,
ifeq(true,true,iPr_def_17,true) = true,
inference(demodulation,[status(thm)],[c_1504,c_408699]) ).
tcf(c_408710,plain,
true = iPr_def_17,
inference(demodulation,[status(thm)],[c_408709,c_59]) ).
tcf(c_410481,plain,
iPr_def_17 != iPr_def_17,
inference(demodulation,[status(thm)],[c_113,c_408710]) ).
tcf(c_410482,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_410481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 22:22:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 140.75/28.95 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 140.75/28.95 % SZS status Started for theBenchmark.p
% 140.75/28.95 % SZS status Unsatisfiable for theBenchmark.p
% 140.75/28.95
% 140.75/28.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 140.75/28.95
% 140.75/28.95 % ------ iProver source info
% 140.75/28.95
% 140.75/28.95 % git: date: 2026-07-19 20:42:38 +0200
% 140.75/28.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 140.75/28.95 % git: non_committed_changes: false
% 140.75/28.95
% 140.75/28.95 % ------ Parsing...% successful
% 140.75/28.95
% 140.75/28.95
% 140.75/28.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 140.75/28.95
% 140.75/28.95 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 140.75/28.95
% 140.75/28.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 140.75/28.95
% 140.75/28.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 140.75/28.95 % ------ Proving...
% 140.75/28.95 % ------ Problem Properties
% 140.75/28.95
% 140.75/28.95 %
% 140.75/28.95 % clauses 18
% 140.75/28.95 % conjectures 1
% 140.75/28.95 % EPR 1
% 140.75/28.95 % Horn 18
% 140.75/28.95 % unary 18
% 140.75/28.95 % binary 0
% 140.75/28.95 % lits 18
% 140.75/28.95 % lits eq 18
% 140.75/28.95 % fd_pure 0
% 140.75/28.95 % fd_pseudo 0
% 140.75/28.95 % fd_cond 0
% 140.75/28.95 % fd_pseudo_cond 0
% 140.75/28.95 % AC symbols 0
% 140.75/28.95
% 140.75/28.95 % ------ Input Options Time Limit: Unbounded
% 140.75/28.95
% 140.75/28.95
% 140.75/28.95 % ------
% 140.75/28.95 % Current options:
% 140.75/28.95 % ------
% 140.75/28.95
% 140.75/28.95
% 140.75/28.95 %
% 140.75/28.95
% 140.75/28.95 % ------ Proving...
% 140.75/28.95 %
% 140.75/28.95
% 140.75/28.95 % SZS status Unsatisfiable for theBenchmark.p
% 140.75/28.95
% 140.75/28.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 140.75/28.96
% 140.75/28.96
%------------------------------------------------------------------------------