%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 01:52:19 PM UTC 2026
% Result : Theorem 4.91s 7.23s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 78 unt; 4 def)
% Number of atoms : 142 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 80 !; 2 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(f18,conjecture,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] : domain(X0) != multiplication(domain(X0),addition(domain(X0),domain(X1))),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != multiplication(domain(sK0),addition(domain(sK0),domain(sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
domain(sK0) != multiplication(domain(sK0),addition(domain(sK0),domain(sK1))),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f30]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_65,negated_conjecture,
multiplication(domain(sK0),addition(domain(sK0),domain(sK1))) != domain(sK0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_79,plain,
! [X0: $i] : addition(one,domain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_115,plain,
multiplication(domain(sK0),domain(addition(sK0,sK1))) != domain(sK0),
inference(ac_demodulation,[status(thm)],[c_65,c_64,c_50,c_49]) ).
tcf(c_121,definition,
iPr_def_10 = domain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_122,definition,
iPr_def_11 = addition(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_123,definition,
iPr_def_12 = domain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_124,definition,
iPr_def_13 = multiplication(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_125,plain,
iPr_def_13 != iPr_def_10,
inference(demodulation,[status(thm)],[c_115,c_122,c_123,c_121,c_124]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_203,plain,
addition(one,iPr_def_12) = one,
inference(superposition,[status(thm)],[c_123,c_79]) ).
tcf(c_204,plain,
addition(iPr_def_12,one) = one,
inference(theory_normalisation,[status(thm)],[c_203,c_50,c_49]) ).
tcf(c_215,plain,
! [X0: $i] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_61]) ).
tcf(c_223,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_215,c_55]) ).
tcf(c_226,plain,
domain(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_121,c_223]) ).
tcf(c_257,plain,
! [X0: $i] : addition(sK0,addition(X0,sK1)) = addition(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_122,c_200]) ).
tcf(c_414,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_204,c_56]) ).
tcf(c_427,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),X0) = X0,
inference(light_normalisation,[status(thm)],[c_414,c_54]) ).
tcf(c_428,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_12)) = X0,
inference(theory_normalisation,[status(thm)],[c_427,c_50,c_49]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i] : addition(multiplication(one,X0),multiplication(domain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_79,c_57]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_446,c_55]) ).
tcf(c_472,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_470]) ).
tcf(c_485,plain,
multiplication(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_226,c_472]) ).
tcf(c_541,plain,
addition(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(superposition,[status(thm)],[c_124,c_428]) ).
tcf(c_730,plain,
addition(sK0,sK1) = addition(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_52,c_257]) ).
tcf(c_742,plain,
addition(sK0,sK1) = addition(iPr_def_11,sK1),
inference(theory_normalisation,[status(thm)],[c_730,c_50,c_49]) ).
tcf(c_743,plain,
addition(iPr_def_11,sK1) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_742,c_122]) ).
tcf(c_757,plain,
addition(sK0,iPr_def_11) = addition(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_743,c_257]) ).
tcf(c_758,plain,
addition(iPr_def_11,sK0) = addition(iPr_def_11,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_757,c_50,c_49]) ).
tcf(c_767,plain,
addition(iPr_def_11,sK0) = iPr_def_11,
inference(demodulation,[status(thm)],[c_758,c_52]) ).
tcf(c_769,plain,
addition(domain(iPr_def_11),domain(sK0)) = domain(iPr_def_11),
inference(superposition,[status(thm)],[c_767,c_64]) ).
tcf(c_774,plain,
addition(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_769,c_121,c_123]) ).
tcf(c_775,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_774,c_50,c_49]) ).
tcf(c_780,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_12)) = multiplication(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_775,c_56]) ).
tcf(c_10667,plain,
addition(multiplication(iPr_def_10,iPr_def_10),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_124,c_780]) ).
tcf(c_10676,plain,
addition(iPr_def_13,multiplication(iPr_def_10,iPr_def_10)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_10667,c_50,c_49]) ).
tcf(c_10677,plain,
addition(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_10676,c_485]) ).
tcf(c_10678,plain,
addition(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_10677,c_50,c_49]) ).
tcf(c_10679,plain,
iPr_def_10 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_10678,c_541]) ).
tcf(c_10739,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_125,c_10679]) ).
tcf(c_10740,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_10739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 18:50:11 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 4.91/7.23 % SZS status Started for theBenchmark.p
% 4.91/7.23 % SZS status Theorem for theBenchmark.p
% 4.91/7.23
% 4.91/7.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.91/7.23
% 4.91/7.23 % ------ iProver source info
% 4.91/7.23
% 4.91/7.23 % git: date: 2026-07-19 20:42:38 +0200
% 4.91/7.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.91/7.23 % git: non_committed_changes: false
% 4.91/7.23
% 4.91/7.23 % ------ Parsing...
% 4.91/7.23 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 4.91/7.23 %
% 4.91/7.23
% 4.91/7.23 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.91/7.23
% 4.91/7.23 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.91/7.23 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.91/7.23
% 4.91/7.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.91/7.23 % ------ Proving...
% 4.91/7.23 % ------ Problem Properties
% 4.91/7.23
% 4.91/7.23 %
% 4.91/7.23 % clauses 21
% 4.91/7.23 % conjectures 0
% 4.91/7.23 % EPR 1
% 4.91/7.23 % Horn 21
% 4.91/7.23 % unary 21
% 4.91/7.23 % binary 0
% 4.91/7.23 % lits 21
% 4.91/7.23 % lits eq 21
% 4.91/7.23 % fd_pure 0
% 4.91/7.23 % fd_pseudo 0
% 4.91/7.23 % fd_cond 0
% 4.91/7.23 % fd_pseudo_cond 0
% 4.91/7.23 % AC symbols 1
% 4.91/7.23
% 4.91/7.23 % ------ Schedule UEQ
% 4.91/7.23
% 4.91/7.23 % ------ Option_UEQ Time Limit: 10.
% 4.91/7.23
% 4.91/7.23
% 4.91/7.23 % ------
% 4.91/7.23 % Current options:
% 4.91/7.23 % ------
% 4.91/7.23
% 4.91/7.23
% 4.91/7.23 %
% 4.91/7.23
% 4.91/7.23 % ------ Proving...
% 4.91/7.23 %
% 4.91/7.23
% 4.91/7.23 % SZS status Theorem for theBenchmark.p
% 4.91/7.23
% 4.91/7.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.91/7.23
% 4.91/7.23
%------------------------------------------------------------------------------