%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE089+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 : n003.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 01:52:22 PM UTC 2026
% Result : Theorem 3.50s 1.27s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 43 unt; 5 def)
% Number of atoms : 94 ( 50 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 38 !; 2 ?; 12 :)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f21,conjecture,
! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
& zero != multiplication(domain(X0),X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
( antidomain(sK1) = addition(domain(sK0),antidomain(sK1))
& zero != multiplication(domain(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
antidomain(sK1) = addition(domain(sK0),antidomain(sK1)),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
zero != multiplication(domain(sK0),sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
zero != multiplication(antidomain(antidomain(sK0)),sK1),
inference(definition_unfolding,[],[f45,f39]) ).
fof(f47,plain,
antidomain(sK1) = addition(antidomain(antidomain(sK0)),antidomain(sK1)),
inference(definition_unfolding,[],[f44,f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f27]) ).
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,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f36]) ).
tcf(c_66,negated_conjecture,
multiplication(antidomain(antidomain(sK0)),sK1) != zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,negated_conjecture,
addition(antidomain(antidomain(sK0)),antidomain(sK1)) = antidomain(sK1),
inference(cnf_transformation,[],[f47]) ).
tcf(c_85,negated_conjecture,
addition(antidomain(sK1),antidomain(antidomain(sK0))) = antidomain(sK1),
inference(theory_normalisation,[status(thm)],[c_67,c_50,c_49]) ).
tcf(c_132,definition,
iPr_def_10 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = addition(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,definition,
iPr_def_14 = multiplication(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_137,negated_conjecture,
iPr_def_13 = iPr_def_10,
inference(demodulation,[status(thm)],[c_85,c_133,c_134,c_132,c_135]) ).
tcf(c_138,negated_conjecture,
iPr_def_14 != zero,
inference(demodulation,[status(thm)],[c_66,c_136]) ).
tcf(c_240,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_135,c_137]) ).
tcf(c_244,plain,
multiplication(iPr_def_10,sK1) = zero,
inference(superposition,[status(thm)],[c_132,c_60]) ).
tcf(c_245,plain,
multiplication(iPr_def_12,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_134,c_60]) ).
tcf(c_249,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_12,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_51,c_245]) ).
tcf(c_250,plain,
multiplication(iPr_def_12,iPr_def_11) != iPr_def_14,
inference(demodulation,[status(thm)],[c_138,c_245]) ).
tcf(c_253,plain,
multiplication(iPr_def_10,sK1) = multiplication(iPr_def_12,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_244,c_245]) ).
tcf(c_311,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_12,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_240,c_57]) ).
tcf(c_368,plain,
addition(multiplication(iPr_def_10,sK1),iPr_def_14) = multiplication(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_136,c_311]) ).
tcf(c_372,plain,
addition(iPr_def_14,multiplication(iPr_def_10,sK1)) = multiplication(iPr_def_10,sK1),
inference(theory_normalisation,[status(thm)],[c_368,c_50,c_49]) ).
tcf(c_373,plain,
addition(iPr_def_14,multiplication(iPr_def_12,iPr_def_11)) = multiplication(iPr_def_12,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_372,c_253]) ).
tcf(c_1065,plain,
multiplication(iPr_def_12,iPr_def_11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_373,c_249]) ).
tcf(c_1066,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1065,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 18:55:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.50/1.27 % SZS status Started for theBenchmark.p
% 3.50/1.27 % SZS status Theorem for theBenchmark.p
% 3.50/1.27
% 3.50/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/1.27
% 3.50/1.27 % ------ iProver source info
% 3.50/1.27
% 3.50/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/1.27 % git: non_committed_changes: false
% 3.50/1.27
% 3.50/1.27 % ------ Parsing...
% 3.50/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.50/1.27 %
% 3.50/1.27
% 3.50/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.50/1.27
% 3.50/1.27 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.50/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.50/1.27
% 3.50/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.50/1.27 % ------ Proving...
% 3.50/1.27 % ------ Problem Properties
% 3.50/1.27
% 3.50/1.27 %
% 3.50/1.27 % clauses 24
% 3.50/1.27 % conjectures 2
% 3.50/1.27 % EPR 2
% 3.50/1.27 % Horn 24
% 3.50/1.27 % unary 24
% 3.50/1.27 % binary 0
% 3.50/1.27 % lits 24
% 3.50/1.27 % lits eq 24
% 3.50/1.27 % fd_pure 0
% 3.50/1.27 % fd_pseudo 0
% 3.50/1.27 % fd_cond 0
% 3.50/1.27 % fd_pseudo_cond 0
% 3.50/1.27 % AC symbols 1
% 3.50/1.27
% 3.50/1.27 % ------ Schedule UEQ
% 3.50/1.27
% 3.50/1.27 % ------ Option_UEQ Time Limit: 10.
% 3.50/1.27
% 3.50/1.27
% 3.50/1.27 % ------
% 3.50/1.27 % Current options:
% 3.50/1.27 % ------
% 3.50/1.27
% 3.50/1.27
% 3.50/1.27 %
% 3.50/1.27
% 3.50/1.27 % ------ Proving...
% 3.50/1.27 %
% 3.50/1.27
% 3.50/1.27 % SZS status Theorem for theBenchmark.p
% 3.50/1.27
% 3.50/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.27
% 3.50/1.27
%------------------------------------------------------------------------------