%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE055+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 : n020.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 2.97s 1.09s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 52 unt; 3 def)
% Number of atoms : 87 ( 59 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 58 !; 1 ?; 26 :)
% 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(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(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f18,conjecture,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] :
( addition(X0,one) = one
& domain(X0) != addition(X0,domain(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( one = addition(sK0,one)
& domain(sK0) != addition(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(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,
one = addition(sK0,one),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
domain(sK0) != addition(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_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,
addition(sK0,domain(sK0)) != domain(sK0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_66,negated_conjecture,
addition(sK0,one) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_80,plain,
! [X0: $i] : addition(one,domain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_81,negated_conjecture,
addition(one,sK0) = one,
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_124,definition,
iPr_def_10 = addition(one,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_125,definition,
iPr_def_11 = domain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_126,definition,
iPr_def_12 = addition(sK0,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_127,negated_conjecture,
iPr_def_10 = one,
inference(demodulation,[status(thm)],[c_81,c_124]) ).
tcf(c_128,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_65,c_125,c_126]) ).
tcf(c_204,plain,
! [X0: $i] : multiplication(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_54,c_127]) ).
tcf(c_205,plain,
! [X0: $i] : multiplication(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_55,c_127]) ).
tcf(c_206,plain,
! [X0: $i] : addition(iPr_def_10,domain(X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_80,c_127]) ).
tcf(c_209,plain,
addition(iPr_def_10,sK0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_124,c_127]) ).
tcf(c_210,plain,
addition(iPr_def_11,sK0) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_126,c_50,c_49]) ).
tcf(c_392,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,sK0)) = multiplication(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_209,c_56]) ).
tcf(c_403,plain,
! [X0: $i] : addition(X0,multiplication(X0,sK0)) = X0,
inference(light_normalisation,[status(thm)],[c_392,c_204]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),multiplication(domain(X1),X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_206,c_57]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_600,c_205]) ).
tcf(c_639,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_629]) ).
tcf(c_670,plain,
addition(domain(sK0),sK0) = domain(sK0),
inference(superposition,[status(thm)],[c_639,c_403]) ).
tcf(c_672,plain,
addition(sK0,domain(sK0)) = domain(sK0),
inference(theory_normalisation,[status(thm)],[c_670,c_50,c_49]) ).
tcf(c_673,plain,
addition(sK0,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_672,c_125]) ).
tcf(c_674,plain,
addition(iPr_def_11,sK0) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_673,c_50,c_49]) ).
tcf(c_684,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_210,c_674]) ).
tcf(c_687,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_128,c_684]) ).
tcf(c_688,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_687]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Wed Sep 23 18:49:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.97/1.09 % SZS status Started for theBenchmark.p
% 2.97/1.09 % SZS status Theorem for theBenchmark.p
% 2.97/1.09
% 2.97/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.97/1.09
% 2.97/1.09 % ------ iProver source info
% 2.97/1.09
% 2.97/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 2.97/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.97/1.09 % git: non_committed_changes: false
% 2.97/1.09
% 2.97/1.09 % ------ Parsing...
% 2.97/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.97/1.09 %
% 2.97/1.09
% 2.97/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.97/1.09
% 2.97/1.09 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.97/1.09 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.97/1.09
% 2.97/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.97/1.09 % ------ Proving...
% 2.97/1.09 % ------ Problem Properties
% 2.97/1.09
% 2.97/1.09 %
% 2.97/1.09 % clauses 21
% 2.97/1.09 % conjectures 2
% 2.97/1.09 % EPR 2
% 2.97/1.09 % Horn 21
% 2.97/1.09 % unary 21
% 2.97/1.09 % binary 0
% 2.97/1.09 % lits 21
% 2.97/1.09 % lits eq 21
% 2.97/1.09 % fd_pure 0
% 2.97/1.09 % fd_pseudo 0
% 2.97/1.09 % fd_cond 0
% 2.97/1.09 % fd_pseudo_cond 0
% 2.97/1.09 % AC symbols 1
% 2.97/1.09
% 2.97/1.09 % ------ Schedule UEQ
% 2.97/1.09
% 2.97/1.09 % ------ Option_UEQ Time Limit: 10.
% 2.97/1.09
% 2.97/1.09
% 2.97/1.09 % ------
% 2.97/1.09 % Current options:
% 2.97/1.09 % ------
% 2.97/1.09
% 2.97/1.09
% 2.97/1.09 %
% 2.97/1.09
% 2.97/1.09 % ------ Proving...
% 2.97/1.09 %
% 2.97/1.09
% 2.97/1.09 % SZS status Theorem for theBenchmark.p
% 2.97/1.09
% 2.97/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.97/1.09
%------------------------------------------------------------------------------