%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE169-10 : 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 : 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 01:52:34 PM UTC 2026
% Result : Unsatisfiable 16.18s 3.07s
% Output : CNFRefutation 16.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 83 ( 83 unt; 8 def)
% Number of atoms : 160 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq3(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f4,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f5,axiom,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f7,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f10,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f12,axiom,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f17,axiom,
! [X0,X1] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
fof(f18,axiom,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,plain,
! [X0,X1] : true = ifeq3(addition(X0,X1),X1,leq(X0,X1),true),
inference(reorient_equations,[],[f18]) ).
fof(f22,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f23,plain,
! [X0] : true = leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(reorient_equations,[],[f22]) ).
fof(f28,axiom,
sigma = addition(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an) ).
fof(f29,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
fof(f30,plain,
true != leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(reorient_equations,[],[f29]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_77,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f17]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_91,plain,
addition(a,b) = sigma,
inference(cnf_transformation,[],[f28]) ).
tcf(c_92,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
inference(cnf_transformation,[],[f30]) ).
tcf(c_166,definition,
iPr_def_10 = multiplication(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_167,definition,
iPr_def_11 = multiplication(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_168,definition,
iPr_def_12 = star(sigma),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_169,definition,
iPr_def_13 = multiplication(sigma,a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_170,definition,
iPr_def_14 = multiplication(a,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_171,definition,
iPr_def_15 = multiplication(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_172,definition,
iPr_def_16 = leq(iPr_def_11,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_173,definition,
iPr_def_17 = addition(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_174,negated_conjecture,
iPr_def_16 != true,
inference(demodulation,[status(thm)],[c_92,c_169,c_170,c_168,c_171,c_166,c_167,c_172]) ).
tcf(c_175,plain,
iPr_def_17 = sigma,
inference(demodulation,[status(thm)],[c_91,c_173]) ).
tcf(c_178,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_186,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_189,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_328,plain,
star(iPr_def_17) = iPr_def_12,
inference(demodulation,[status(thm)],[c_168,c_175]) ).
tcf(c_329,plain,
multiplication(iPr_def_17,a) = iPr_def_13,
inference(demodulation,[status(thm)],[c_169,c_175]) ).
tcf(c_330,plain,
addition(b,a) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_173,c_191,c_192]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_191,c_192]) ).
tcf(c_343,plain,
leq(addition(one,multiplication(iPr_def_12,iPr_def_17)),iPr_def_12) = true,
inference(superposition,[status(thm)],[c_328,c_178]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X1,X0),X1) = X1,
inference(superposition,[status(thm)],[c_192,c_181]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_189,c_191]) ).
tcf(c_430,plain,
! [X0: $i] : addition(iPr_def_10,multiplication(X0,a)) = multiplication(addition(b,X0),a),
inference(superposition,[status(thm)],[c_166,c_184]) ).
tcf(c_433,plain,
! [X0: $i] : addition(iPr_def_15,multiplication(X0,iPr_def_14)) = multiplication(addition(iPr_def_12,X0),iPr_def_14),
inference(superposition,[status(thm)],[c_171,c_184]) ).
tcf(c_472,plain,
! [X0: $i] : addition(iPr_def_14,multiplication(a,X0)) = multiplication(a,addition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_170,c_185]) ).
tcf(c_992,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),addition(X0,X1),leq(X0,addition(X0,X1)),true) = true,
inference(superposition,[status(thm)],[c_390,c_180]) ).
tcf(c_1056,plain,
ifeq2(true,true,addition(iPr_def_12,addition(one,multiplication(iPr_def_12,iPr_def_17))),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_343,c_364]) ).
tcf(c_1121,plain,
addition(iPr_def_10,multiplication(a,a)) = multiplication(iPr_def_17,a),
inference(superposition,[status(thm)],[c_330,c_430]) ).
tcf(c_1157,plain,
addition(iPr_def_10,multiplication(a,a)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1121,c_329]) ).
tcf(c_1168,plain,
addition(iPr_def_12,addition(one,multiplication(iPr_def_12,iPr_def_17))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1056,c_194]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)) = true,
inference(demodulation,[status(thm)],[c_992,c_195]) ).
tcf(c_1742,plain,
addition(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_1157,c_390]) ).
tcf(c_1749,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)) = true,
inference(superposition,[status(thm)],[c_192,c_1200]) ).
tcf(c_1758,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))) = true,
inference(superposition,[status(thm)],[c_331,c_1200]) ).
tcf(c_1937,plain,
addition(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_1742,c_191,c_192]) ).
tcf(c_2245,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))) = true,
inference(superposition,[status(thm)],[c_191,c_1749]) ).
tcf(c_2959,plain,
leq(one,iPr_def_12) = true,
inference(superposition,[status(thm)],[c_1168,c_1758]) ).
tcf(c_3279,plain,
ifeq2(true,true,addition(one,iPr_def_12),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_2959,c_181]) ).
tcf(c_3359,plain,
addition(iPr_def_14,multiplication(a,iPr_def_10)) = multiplication(a,iPr_def_13),
inference(superposition,[status(thm)],[c_1937,c_472]) ).
tcf(c_3511,plain,
addition(iPr_def_14,iPr_def_11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3359,c_167,c_170]) ).
tcf(c_3513,plain,
ifeq2(true,true,addition(iPr_def_12,one),iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_3279,c_191,c_192]) ).
tcf(c_3514,plain,
addition(iPr_def_12,one) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3513,c_194]) ).
tcf(c_3712,plain,
! [X0: $i] : leq(iPr_def_11,addition(X0,iPr_def_14)) = true,
inference(superposition,[status(thm)],[c_3511,c_2245]) ).
tcf(c_3726,plain,
addition(iPr_def_15,multiplication(one,iPr_def_14)) = multiplication(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_3514,c_433]) ).
tcf(c_3998,plain,
addition(iPr_def_15,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3726,c_186,c_171]) ).
tcf(c_4191,plain,
leq(iPr_def_11,iPr_def_15) = true,
inference(superposition,[status(thm)],[c_3998,c_3712]) ).
tcf(c_4382,plain,
true = iPr_def_16,
inference(demodulation,[status(thm)],[c_4191,c_172]) ).
tcf(c_4740,plain,
$false,
inference(superposition,[status(thm)],[c_4382,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.46 % Computer : n007.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Wed Sep 23 19:09:07 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.52 Running UEQ theorem proving
% 0.24/0.52 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
% 0.24/0.54
% 0.24/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.54
% 0.24/0.55 % Detected problem language: tptp
% 0.24/0.57 % Proving...
% 16.18/3.07 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 16.18/3.07 % SZS status Started for theBenchmark.p
% 16.18/3.07 % SZS status Unsatisfiable for theBenchmark.p
% 16.18/3.07
% 16.18/3.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.18/3.07
% 16.18/3.07 % ------ iProver source info
% 16.18/3.07
% 16.18/3.07 % git: date: 2026-07-19 20:42:38 +0200
% 16.18/3.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.18/3.07 % git: non_committed_changes: false
% 16.18/3.07
% 16.18/3.07 % ------ Parsing...% successful
% 16.18/3.07
% 16.18/3.07
% 16.18/3.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.18/3.07
% 16.18/3.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 16.18/3.07
% 16.18/3.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.18/3.07
% 16.18/3.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 16.18/3.07 % ------ Proving...
% 16.18/3.07 % ------ Problem Properties
% 16.18/3.07
% 16.18/3.07 %
% 16.18/3.07 % clauses 30
% 16.18/3.07 % conjectures 1
% 16.18/3.07 % EPR 2
% 16.18/3.07 % Horn 30
% 16.18/3.07 % unary 30
% 16.18/3.07 % binary 0
% 16.18/3.07 % lits 30
% 16.18/3.07 % lits eq 30
% 16.18/3.07 % fd_pure 0
% 16.18/3.07 % fd_pseudo 0
% 16.18/3.07 % fd_cond 0
% 16.18/3.07 % fd_pseudo_cond 0
% 16.18/3.07 % AC symbols 1
% 16.18/3.07
% 16.18/3.07 % ------ Input Options Time Limit: Unbounded
% 16.18/3.07
% 16.18/3.07
% 16.18/3.07 % ------
% 16.18/3.07 % Current options:
% 16.18/3.07 % ------
% 16.18/3.07
% 16.18/3.07
% 16.18/3.07 %
% 16.18/3.07
% 16.18/3.07 % ------ Proving...
% 16.18/3.07 %
% 16.18/3.07
% 16.18/3.07 % SZS status Unsatisfiable for theBenchmark.p
% 16.18/3.07
% 16.18/3.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.18/3.07
% 16.18/3.07
%------------------------------------------------------------------------------