%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE074+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 : n004.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 2.24s 1.31s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 62 unt; 7 def)
% Number of atoms : 111 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 65 !; 3 ?; 27 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f18,conjecture,
! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) != domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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(f26,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
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(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
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_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
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_61,plain,
! [X0: $i,X1: $i] : domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,negated_conjecture,
domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))) != domain(multiplication(multiplication(sK0,sK1),domain(sK2))),
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_115,plain,
domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) != domain(multiplication(sK0,multiplication(sK1,sK2))),
inference(demodulation,[status(thm)],[c_65,c_53,c_61]) ).
tcf(c_121,definition,
iPr_def_10 = domain(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_122,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_123,definition,
iPr_def_12 = multiplication(sK0,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_124,definition,
iPr_def_13 = domain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_125,definition,
iPr_def_14 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_126,definition,
iPr_def_15 = multiplication(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_127,definition,
iPr_def_16 = domain(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_128,plain,
iPr_def_13 != iPr_def_16,
inference(demodulation,[status(thm)],[c_115,c_125,c_126,c_127,c_121,c_122,c_123,c_124]) ).
tcf(c_226,plain,
! [X0: $i] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_61]) ).
tcf(c_229,plain,
! [X0: $i] : domain(multiplication(X0,sK2)) = domain(multiplication(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_121,c_61]) ).
tcf(c_235,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_226,c_55]) ).
tcf(c_238,plain,
domain(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_121,c_235]) ).
tcf(c_294,plain,
! [X0: $i] : multiplication(sK1,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_122,c_53]) ).
tcf(c_295,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_11,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_123,c_53]) ).
tcf(c_410,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_433,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_410,c_55]) ).
tcf(c_435,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_433]) ).
tcf(c_442,plain,
multiplication(iPr_def_10,sK2) = sK2,
inference(superposition,[status(thm)],[c_121,c_435]) ).
tcf(c_449,plain,
multiplication(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_238,c_435]) ).
tcf(c_848,plain,
multiplication(sK1,sK2) = multiplication(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_442,c_294]) ).
tcf(c_849,plain,
multiplication(sK1,iPr_def_10) = multiplication(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_449,c_294]) ).
tcf(c_852,plain,
multiplication(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_849,c_122]) ).
tcf(c_853,plain,
multiplication(iPr_def_11,sK2) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_848,c_125]) ).
tcf(c_867,plain,
multiplication(sK0,iPr_def_14) = multiplication(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_853,c_295]) ).
tcf(c_868,plain,
multiplication(sK0,iPr_def_11) = multiplication(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_852,c_295]) ).
tcf(c_871,plain,
multiplication(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_868,c_123]) ).
tcf(c_872,plain,
multiplication(iPr_def_12,sK2) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_867,c_126]) ).
tcf(c_878,plain,
domain(multiplication(iPr_def_12,iPr_def_10)) = domain(iPr_def_15),
inference(superposition,[status(thm)],[c_872,c_229]) ).
tcf(c_879,plain,
iPr_def_13 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_878,c_124,c_127,c_871]) ).
tcf(c_880,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_879,c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE074+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 18:51:20 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.45
% 0.13/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.45
% 0.13/0.45 % Detected problem language: tptp
% 0.19/0.46 % Proving...
% 2.24/1.31 % SZS status Started for theBenchmark.p
% 2.24/1.31 % SZS status Theorem for theBenchmark.p
% 2.24/1.31
% 2.24/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/1.31
% 2.24/1.31 % ------ iProver source info
% 2.24/1.31
% 2.24/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/1.31 % git: non_committed_changes: false
% 2.24/1.31
% 2.24/1.31 % ------ Parsing...
% 2.24/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.24/1.31 %
% 2.24/1.31
% 2.24/1.31 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.24/1.31
% 2.24/1.31 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.24/1.31 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.24/1.31
% 2.24/1.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.24/1.31 % ------ Proving...
% 2.24/1.31 % ------ Problem Properties
% 2.24/1.31
% 2.24/1.31 %
% 2.24/1.31 % clauses 24
% 2.24/1.31 % conjectures 0
% 2.24/1.31 % EPR 1
% 2.24/1.31 % Horn 24
% 2.24/1.31 % unary 24
% 2.24/1.31 % binary 0
% 2.24/1.31 % lits 24
% 2.24/1.31 % lits eq 24
% 2.24/1.31 % fd_pure 0
% 2.24/1.31 % fd_pseudo 0
% 2.24/1.31 % fd_cond 0
% 2.24/1.31 % fd_pseudo_cond 0
% 2.24/1.31 % AC symbols 1
% 2.24/1.31
% 2.24/1.31 % ------ Schedule UEQ
% 2.24/1.31
% 2.24/1.31 % ------ Option_UEQ Time Limit: 10.
% 2.24/1.31
% 2.24/1.31
% 2.24/1.31 % ------
% 2.24/1.31 % Current options:
% 2.24/1.31 % ------
% 2.24/1.31
% 2.24/1.31
% 2.24/1.31 %
% 2.24/1.31
% 2.24/1.31 % ------ Proving...
% 2.24/1.31 %
% 2.24/1.31
% 2.24/1.31 % SZS status Theorem for theBenchmark.p
% 2.24/1.31
% 2.24/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/1.31
% 2.24/1.31
%------------------------------------------------------------------------------