%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE067+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 : 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 01:52:19 PM UTC 2026
% Result : Theorem 2.40s 1.49s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 32 unt; 3 def)
% Number of atoms : 45 ( 31 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 36 !; 2 ?; 12 :)
% 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(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
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] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] : addition(domain(X0),domain(X1)) != domain(addition(domain(X0),domain(X1))),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
addition(domain(sK0),domain(sK1)) != domain(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(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
addition(domain(sK0),domain(sK1)) != domain(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_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
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,
domain(addition(domain(sK0),domain(sK1))) != addition(domain(sK0),domain(sK1)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,plain,
domain(domain(addition(sK0,sK1))) != domain(addition(sK0,sK1)),
inference(ac_demodulation,[status(thm)],[c_65,c_64,c_64,c_50,c_49]) ).
tcf(c_121,definition,
iPr_def_10 = addition(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_122,definition,
iPr_def_11 = domain(iPr_def_10),
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,plain,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_115,c_121,c_122,c_123]) ).
tcf(c_212,plain,
! [X0: $i] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_61]) ).
tcf(c_220,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_212,c_55]) ).
tcf(c_223,plain,
domain(iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_122,c_220]) ).
tcf(c_226,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_123,c_223]) ).
tcf(c_228,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_124,c_226]) ).
tcf(c_229,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE067+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 % Computer : n006.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Wed Sep 23 18:49:46 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.47 Running first-order theorem proving
% 0.17/0.47 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
% 0.17/0.49
% 0.17/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.49
% 0.17/0.49 % Detected problem language: tptp
% 0.17/0.51 % Proving...
% 2.40/1.49 % SZS status Started for theBenchmark.p
% 2.40/1.49 % SZS status Theorem for theBenchmark.p
% 2.40/1.49
% 2.40/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.40/1.49
% 2.40/1.49 % ------ iProver source info
% 2.40/1.49
% 2.40/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.40/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.40/1.49 % git: non_committed_changes: false
% 2.40/1.49
% 2.40/1.49 % ------ Parsing...
% 2.40/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.40/1.49 %
% 2.40/1.49
% 2.40/1.49 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.40/1.49
% 2.40/1.49 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.40/1.49 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.40/1.49
% 2.40/1.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.40/1.49 % ------ Proving...
% 2.40/1.49 % ------ Problem Properties
% 2.40/1.49
% 2.40/1.49 %
% 2.40/1.49 % clauses 20
% 2.40/1.49 % conjectures 0
% 2.40/1.49 % EPR 1
% 2.40/1.49 % Horn 20
% 2.40/1.49 % unary 20
% 2.40/1.49 % binary 0
% 2.40/1.49 % lits 20
% 2.40/1.49 % lits eq 20
% 2.40/1.49 % fd_pure 0
% 2.40/1.49 % fd_pseudo 0
% 2.40/1.49 % fd_cond 0
% 2.40/1.49 % fd_pseudo_cond 0
% 2.40/1.49 % AC symbols 1
% 2.40/1.49
% 2.40/1.49 % ------ Schedule UEQ
% 2.40/1.49
% 2.40/1.49 % ------ Option_UEQ Time Limit: 10.
% 2.40/1.49
% 2.40/1.49
% 2.40/1.49 % ------
% 2.40/1.49 % Current options:
% 2.40/1.49 % ------
% 2.40/1.49
% 2.40/1.49
% 2.40/1.49 %
% 2.40/1.49
% 2.40/1.49 % ------ Proving...
% 2.40/1.49 %
% 2.40/1.49
% 2.40/1.49 % SZS status Theorem for theBenchmark.p
% 2.40/1.49
% 2.40/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.40/1.49
% 2.40/1.49
%------------------------------------------------------------------------------