%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE070+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 : n016.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 01:52:20 PM UTC 2026
% Result : Theorem 4.06s 6.30s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 36 unt; 4 def)
% Number of atoms : 58 ( 35 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 38 !; 2 ?; 14 :)
% 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(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(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f18,conjecture,
! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] : domain(X0) != addition(domain(X0),multiplication(domain(X0),domain(X1))),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != addition(domain(sK0),multiplication(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(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
domain(sK0) != addition(domain(sK0),multiplication(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_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f27]) ).
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_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,negated_conjecture,
addition(domain(sK0),multiplication(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_120,definition,
iPr_def_10 = domain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_121,definition,
iPr_def_11 = domain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_122,definition,
iPr_def_12 = multiplication(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_123,definition,
iPr_def_13 = addition(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_124,negated_conjecture,
iPr_def_13 != iPr_def_10,
inference(demodulation,[status(thm)],[c_65,c_121,c_122,c_120,c_123]) ).
tcf(c_202,plain,
addition(one,iPr_def_11) = one,
inference(superposition,[status(thm)],[c_121,c_79]) ).
tcf(c_203,plain,
addition(iPr_def_11,one) = one,
inference(theory_normalisation,[status(thm)],[c_202,c_50,c_49]) ).
tcf(c_408,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_203,c_56]) ).
tcf(c_420,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),X0) = X0,
inference(light_normalisation,[status(thm)],[c_408,c_54]) ).
tcf(c_421,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_11)) = X0,
inference(theory_normalisation,[status(thm)],[c_420,c_50,c_49]) ).
tcf(c_534,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_122,c_421]) ).
tcf(c_547,plain,
iPr_def_10 = iPr_def_13,
inference(demodulation,[status(thm)],[c_123,c_534]) ).
tcf(c_549,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_124,c_547]) ).
tcf(c_550,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE070+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n016.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 18:55:32 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 4.06/6.30 % SZS status Started for theBenchmark.p
% 4.06/6.30 % SZS status Theorem for theBenchmark.p
% 4.06/6.30
% 4.06/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.06/6.30
% 4.06/6.30 % ------ iProver source info
% 4.06/6.30
% 4.06/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.06/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.06/6.30 % git: non_committed_changes: false
% 4.06/6.30
% 4.06/6.30 % ------ Parsing...
% 4.06/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 4.06/6.30 %
% 4.06/6.30
% 4.06/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.06/6.30
% 4.06/6.30 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.06/6.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.06/6.30
% 4.06/6.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.06/6.30 % ------ Proving...
% 4.06/6.30 % ------ Problem Properties
% 4.06/6.30
% 4.06/6.30 %
% 4.06/6.30 % clauses 21
% 4.06/6.30 % conjectures 1
% 4.06/6.30 % EPR 1
% 4.06/6.30 % Horn 21
% 4.06/6.30 % unary 21
% 4.06/6.30 % binary 0
% 4.06/6.30 % lits 21
% 4.06/6.30 % lits eq 21
% 4.06/6.30 % fd_pure 0
% 4.06/6.30 % fd_pseudo 0
% 4.06/6.30 % fd_cond 0
% 4.06/6.30 % fd_pseudo_cond 0
% 4.06/6.30 % AC symbols 1
% 4.06/6.30
% 4.06/6.30 % ------ Schedule UEQ
% 4.06/6.30
% 4.06/6.30 % ------ Option_UEQ Time Limit: 10.
% 4.06/6.30
% 4.06/6.30
% 4.06/6.30 % ------
% 4.06/6.30 % Current options:
% 4.06/6.30 % ------
% 4.06/6.30
% 4.06/6.30
% 4.06/6.30 %
% 4.06/6.30
% 4.06/6.30 % ------ Proving...
% 4.06/6.30 %
% 4.06/6.30
% 4.06/6.30 % SZS status Theorem for theBenchmark.p
% 4.06/6.30
% 4.06/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.06/6.30
% 4.06/6.30
%------------------------------------------------------------------------------