%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE052+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 : n019.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 01:52:17 PM UTC 2026
% Result : Theorem 4.18s 1.28s
% Output : CNFRefutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 2 def)
% Number of atoms : 43 ( 34 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 : 42 ( 0 sgn 41 !; 1 ?; 17 :)
% 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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f18,conjecture,
! [X0] : multiplication(domain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),X0) = X0,
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] : multiplication(domain(X0),X0) != X0,
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
sK0 != multiplication(domain(sK0),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(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
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(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
sK0 != multiplication(domain(sK0),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_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
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_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,negated_conjecture,
multiplication(domain(sK0),sK0) != 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,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_122,negated_conjecture,
iPr_def_11 != sK0,
inference(demodulation,[status(thm)],[c_65,c_120,c_121]) ).
tcf(c_439,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_462,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_439,c_55]) ).
tcf(c_466,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_462]) ).
tcf(c_473,plain,
multiplication(iPr_def_10,sK0) = sK0,
inference(superposition,[status(thm)],[c_120,c_466]) ).
tcf(c_489,plain,
sK0 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_473,c_121]) ).
tcf(c_505,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_122,c_489]) ).
tcf(c_506,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE052+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:48:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 4.18/1.28 % SZS status Started for theBenchmark.p
% 4.18/1.28 % SZS status Theorem for theBenchmark.p
% 4.18/1.28
% 4.18/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.18/1.28
% 4.18/1.28 % ------ iProver source info
% 4.18/1.28
% 4.18/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.18/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.18/1.28 % git: non_committed_changes: false
% 4.18/1.28
% 4.18/1.28 % ------ Parsing...
% 4.18/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 4.18/1.28 %
% 4.18/1.28
% 4.18/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.18/1.28
% 4.18/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.18/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.18/1.28
% 4.18/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.18/1.28 % ------ Proving...
% 4.18/1.28 % ------ Problem Properties
% 4.18/1.28
% 4.18/1.28 %
% 4.18/1.28 % clauses 19
% 4.18/1.28 % conjectures 1
% 4.18/1.28 % EPR 1
% 4.18/1.28 % Horn 19
% 4.18/1.28 % unary 19
% 4.18/1.28 % binary 0
% 4.18/1.28 % lits 19
% 4.18/1.28 % lits eq 19
% 4.18/1.28 % fd_pure 0
% 4.18/1.28 % fd_pseudo 0
% 4.18/1.28 % fd_cond 0
% 4.18/1.28 % fd_pseudo_cond 0
% 4.18/1.28 % AC symbols 1
% 4.18/1.28
% 4.18/1.28 % ------ Schedule UEQ
% 4.18/1.28
% 4.18/1.28 % ------ Option_UEQ Time Limit: 10.
% 4.18/1.28
% 4.18/1.28
% 4.18/1.28 % ------
% 4.18/1.28 % Current options:
% 4.18/1.28 % ------
% 4.18/1.28
% 4.18/1.28
% 4.18/1.28 %
% 4.18/1.28
% 4.18/1.28 % ------ Proving...
% 4.18/1.28 %
% 4.18/1.28
% 4.18/1.28 % SZS status Theorem for theBenchmark.p
% 4.18/1.28
% 4.18/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.18/1.28
% 4.18/1.28
%------------------------------------------------------------------------------