%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE056+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 : n015.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 01:52:18 PM UTC 2026
% Result : Theorem 2.66s 1.28s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 51 unt; 1 def)
% Number of atoms : 73 ( 58 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 57 !; 1 ?; 25 :)
% 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(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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain4) ).
fof(f18,conjecture,
! [X0] :
( domain(X0) = zero
=> X0 = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( domain(X0) = zero
=> X0 = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] :
( domain(X0) = zero
& zero != X0 ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( zero = domain(sK0)
& zero != 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(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(f31,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
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(f36,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f38,plain,
zero = domain(sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
zero != 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_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_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f32]) ).
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_63,plain,
domain(zero) = zero,
inference(cnf_transformation,[],[f36]) ).
tcf(c_65,negated_conjecture,
zero != sK0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_66,negated_conjecture,
domain(sK0) = zero,
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_123,definition,
iPr_def_10 = domain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_124,negated_conjecture,
iPr_def_10 = zero,
inference(demodulation,[status(thm)],[c_66,c_123]) ).
tcf(c_125,negated_conjecture,
zero != sK0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_197,plain,
sK0 != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_125,c_124]) ).
tcf(c_198,plain,
domain(iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_63,c_124]) ).
tcf(c_203,plain,
! [X0: $i] : multiplication(X0,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_58,c_124]) ).
tcf(c_204,plain,
! [X0: $i] : multiplication(iPr_def_10,X0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_59,c_124]) ).
tcf(c_212,plain,
! [X0: $i] : domain(multiplication(X0,sK0)) = domain(multiplication(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_123,c_61]) ).
tcf(c_217,plain,
! [X0: $i] : domain(multiplication(X0,sK0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_212,c_198,c_203]) ).
tcf(c_228,plain,
domain(sK0) = iPr_def_10,
inference(superposition,[status(thm)],[c_55,c_217]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] : addition(multiplication(one,X0),multiplication(domain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_80,c_57]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_535,c_55]) ).
tcf(c_582,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_580]) ).
tcf(c_588,plain,
multiplication(iPr_def_10,sK0) = sK0,
inference(superposition,[status(thm)],[c_228,c_582]) ).
tcf(c_648,plain,
sK0 = iPr_def_10,
inference(demodulation,[status(thm)],[c_588,c_204]) ).
tcf(c_649,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_648,c_197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:51:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.66/1.28 % SZS status Started for theBenchmark.p
% 2.66/1.28 % SZS status Theorem for theBenchmark.p
% 2.66/1.28
% 2.66/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.66/1.28
% 2.66/1.28 % ------ iProver source info
% 2.66/1.28
% 2.66/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.66/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.66/1.28 % git: non_committed_changes: false
% 2.66/1.28
% 2.66/1.28 % ------ Parsing...
% 2.66/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.66/1.28 %
% 2.66/1.28
% 2.66/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.66/1.28
% 2.66/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.66/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.66/1.28
% 2.66/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.66/1.28 % ------ Proving...
% 2.66/1.28 % ------ Problem Properties
% 2.66/1.28
% 2.66/1.28 %
% 2.66/1.28 % clauses 19
% 2.66/1.28 % conjectures 2
% 2.66/1.28 % EPR 2
% 2.66/1.28 % Horn 19
% 2.66/1.28 % unary 19
% 2.66/1.28 % binary 0
% 2.66/1.28 % lits 19
% 2.66/1.28 % lits eq 19
% 2.66/1.28 % fd_pure 0
% 2.66/1.28 % fd_pseudo 0
% 2.66/1.28 % fd_cond 0
% 2.66/1.28 % fd_pseudo_cond 0
% 2.66/1.28 % AC symbols 1
% 2.66/1.28
% 2.66/1.28 % ------ Schedule UEQ
% 2.66/1.28
% 2.66/1.28 % ------ Option_UEQ Time Limit: 10.
% 2.66/1.28
% 2.66/1.28
% 2.66/1.28 % ------
% 2.66/1.28 % Current options:
% 2.66/1.28 % ------
% 2.66/1.28
% 2.66/1.28
% 2.66/1.28 %
% 2.66/1.28
% 2.66/1.28 % ------ Proving...
% 2.66/1.28 %
% 2.66/1.28
% 2.66/1.28 % SZS status Theorem for theBenchmark.p
% 2.66/1.28
% 2.66/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.66/1.28
% 2.66/1.28
%------------------------------------------------------------------------------