%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE061+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 01:52:18 PM UTC 2026
% Result : Theorem 3.61s 1.42s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 48 unt; 2 def)
% Number of atoms : 76 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 50 !; 1 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f18,conjecture,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] : domain(X0) != multiplication(domain(X0),domain(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != multiplication(domain(sK0),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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(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(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(f38,plain,
domain(sK0) != multiplication(domain(sK0),domain(sK0)),
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_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_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_65,negated_conjecture,
multiplication(domain(sK0),domain(sK0)) != 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_120,definition,
iPr_def_10 = domain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_121,definition,
iPr_def_11 = multiplication(iPr_def_10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_122,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_65,c_120,c_121]) ).
tcf(c_195,plain,
addition(one,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_120,c_79]) ).
tcf(c_196,plain,
addition(iPr_def_10,one) = one,
inference(theory_normalisation,[status(thm)],[c_195,c_50,c_49]) ).
tcf(c_202,plain,
! [X0: $i] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_61]) ).
tcf(c_209,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_202,c_55]) ).
tcf(c_216,plain,
domain(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_120,c_209]) ).
tcf(c_338,plain,
addition(iPr_def_10,multiplication(iPr_def_10,iPr_def_10)) = multiplication(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_216,c_60]) ).
tcf(c_342,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_338,c_121]) ).
tcf(c_356,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_196,c_56]) ).
tcf(c_368,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = X0,
inference(light_normalisation,[status(thm)],[c_356,c_54]) ).
tcf(c_369,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = X0,
inference(theory_normalisation,[status(thm)],[c_368,c_50,c_49]) ).
tcf(c_395,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_121,c_369]) ).
tcf(c_401,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_342,c_395]) ).
tcf(c_403,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_122,c_401]) ).
tcf(c_404,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.44 % Computer : n006.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Wed Sep 23 18:48:56 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.52
% 0.24/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.52
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 3.61/1.42 % SZS status Started for theBenchmark.p
% 3.61/1.42 % SZS status Theorem for theBenchmark.p
% 3.61/1.42
% 3.61/1.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.61/1.42
% 3.61/1.42 % ------ iProver source info
% 3.61/1.42
% 3.61/1.42 % git: date: 2026-07-19 20:42:38 +0200
% 3.61/1.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.61/1.42 % git: non_committed_changes: false
% 3.61/1.42
% 3.61/1.42 % ------ Parsing...
% 3.61/1.42 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.61/1.42 %
% 3.61/1.42
% 3.61/1.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.61/1.42
% 3.61/1.42 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.61/1.42 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.61/1.42
% 3.61/1.42 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.61/1.42 % ------ Proving...
% 3.61/1.42 % ------ Problem Properties
% 3.61/1.42
% 3.61/1.42 %
% 3.61/1.42 % clauses 19
% 3.61/1.42 % conjectures 1
% 3.61/1.42 % EPR 1
% 3.61/1.42 % Horn 19
% 3.61/1.42 % unary 19
% 3.61/1.42 % binary 0
% 3.61/1.42 % lits 19
% 3.61/1.42 % lits eq 19
% 3.61/1.42 % fd_pure 0
% 3.61/1.42 % fd_pseudo 0
% 3.61/1.42 % fd_cond 0
% 3.61/1.42 % fd_pseudo_cond 0
% 3.61/1.42 % AC symbols 1
% 3.61/1.42
% 3.61/1.42 % ------ Schedule UEQ
% 3.61/1.42
% 3.61/1.42 % ------ Option_UEQ Time Limit: 10.
% 3.61/1.42
% 3.61/1.42
% 3.61/1.42 % ------
% 3.61/1.42 % Current options:
% 3.61/1.42 % ------
% 3.61/1.42
% 3.61/1.42
% 3.61/1.42 %
% 3.61/1.42
% 3.61/1.42 % ------ Proving...
% 3.61/1.42 %
% 3.61/1.42
% 3.61/1.42 % SZS status Theorem for theBenchmark.p
% 3.61/1.42
% 3.61/1.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.61/1.42
% 3.61/1.42
%------------------------------------------------------------------------------