%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE081+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 : n001.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 01:52:21 PM UTC 2026
% Result : Theorem 3.98s 1.17s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 86 ( 82 unt; 2 def)
% Number of atoms : 133 ( 93 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 102 !; 1 ?; 56 :)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
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] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),X0) = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
& zero != multiplication(antidomain(X0),X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
& zero != multiplication(antidomain(sK0),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(f24,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
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(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(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X1] : zero = multiplication(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X1] : one = addition(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
zero != multiplication(antidomain(sK0),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_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f25]) ).
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_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_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
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,
multiplication(antidomain(sK0),sK0) != zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[],[f39]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_83,plain,
! [X0: $i] : addition(one,domain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_129,definition,
iPr_def_10 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = multiplication(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,negated_conjecture,
! [X0: $i] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_132,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_133,negated_conjecture,
iPr_def_11 != zero,
inference(demodulation,[status(thm)],[c_65,c_129,c_130]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_218,plain,
multiplication(domain(sK0),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_129,c_131]) ).
tcf(c_222,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] : addition(domain(X0),addition(X1,antidomain(X0))) = addition(X1,one),
inference(superposition,[status(thm)],[c_132,c_214]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] : multiplication(addition(domain(X0),domain(X1)),antidomain(addition(X0,X1))) = zero,
inference(superposition,[status(thm)],[c_64,c_131]) ).
tcf(c_377,plain,
! [X0: $i] : multiplication(domain(sK0),multiplication(iPr_def_10,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_218,c_53]) ).
tcf(c_387,plain,
! [X0: $i] : multiplication(domain(sK0),multiplication(iPr_def_10,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_377,c_59]) ).
tcf(c_448,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(antidomain(X0),one),
inference(superposition,[status(thm)],[c_52,c_311]) ).
tcf(c_466,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(theory_normalisation,[status(thm)],[c_448,c_50,c_49]) ).
tcf(c_467,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(light_normalisation,[status(thm)],[c_466,c_132]) ).
tcf(c_476,plain,
addition(one,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_129,c_467]) ).
tcf(c_484,plain,
addition(iPr_def_10,one) = one,
inference(theory_normalisation,[status(thm)],[c_476,c_50,c_49]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] : addition(multiplication(domain(X0),antidomain(addition(X0,X1))),multiplication(domain(X1),antidomain(addition(X0,X1)))) = zero,
inference(demodulation,[status(thm)],[c_340,c_57]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] : addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = multiplication(one,X1),
inference(superposition,[status(thm)],[c_132,c_57]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i] : addition(multiplication(one,X0),multiplication(domain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_83,c_57]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_736,c_55]) ).
tcf(c_765,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_60,c_763]) ).
tcf(c_772,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(one,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_484,c_57]) ).
tcf(c_776,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_772,c_55]) ).
tcf(c_777,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_776,c_50,c_49]) ).
tcf(c_829,plain,
! [X0: $i] : addition(multiplication(domain(X0),antidomain(X0)),multiplication(domain(multiplication(iPr_def_10,X0)),antidomain(X0))) = zero,
inference(superposition,[status(thm)],[c_777,c_543]) ).
tcf(c_842,plain,
! [X0: $i] : addition(zero,multiplication(domain(multiplication(iPr_def_10,X0)),antidomain(X0))) = zero,
inference(light_normalisation,[status(thm)],[c_829,c_131]) ).
tcf(c_922,plain,
! [X0: $i] : multiplication(domain(multiplication(iPr_def_10,X0)),antidomain(X0)) = zero,
inference(demodulation,[status(thm)],[c_842,c_222]) ).
tcf(c_928,plain,
multiplication(domain(iPr_def_11),antidomain(sK0)) = zero,
inference(superposition,[status(thm)],[c_130,c_922]) ).
tcf(c_935,plain,
multiplication(domain(iPr_def_11),iPr_def_10) = zero,
inference(light_normalisation,[status(thm)],[c_928,c_129]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i] : addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_735,c_55]) ).
tcf(c_1205,plain,
! [X0: $i] : multiplication(domain(iPr_def_11),multiplication(iPr_def_10,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_935,c_53]) ).
tcf(c_1213,plain,
! [X0: $i] : multiplication(domain(iPr_def_11),multiplication(iPr_def_10,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_1205,c_59]) ).
tcf(c_1351,plain,
multiplication(domain(sK0),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_130,c_387]) ).
tcf(c_1391,plain,
addition(zero,multiplication(antidomain(sK0),iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1351,c_969]) ).
tcf(c_1392,plain,
addition(zero,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1391,c_129]) ).
tcf(c_1393,plain,
addition(multiplication(iPr_def_10,iPr_def_11),zero) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1392,c_50,c_49]) ).
tcf(c_1399,plain,
multiplication(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1393,c_51]) ).
tcf(c_2557,plain,
multiplication(domain(iPr_def_11),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_1399,c_1213]) ).
tcf(c_2656,plain,
zero = iPr_def_11,
inference(demodulation,[status(thm)],[c_2557,c_765]) ).
tcf(c_2685,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_133,c_2656]) ).
tcf(c_2686,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE081+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:57:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.98/1.17 % SZS status Started for theBenchmark.p
% 3.98/1.17 % SZS status Theorem for theBenchmark.p
% 3.98/1.17
% 3.98/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.98/1.17
% 3.98/1.17 % ------ iProver source info
% 3.98/1.17
% 3.98/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.98/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.98/1.17 % git: non_committed_changes: false
% 3.98/1.17
% 3.98/1.17 % ------ Parsing...
% 3.98/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.98/1.17 %
% 3.98/1.17
% 3.98/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.98/1.17
% 3.98/1.17 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.98/1.17 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.98/1.17
% 3.98/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.98/1.17 % ------ Proving...
% 3.98/1.17 % ------ Problem Properties
% 3.98/1.17
% 3.98/1.17 %
% 3.98/1.17 % clauses 21
% 3.98/1.17 % conjectures 3
% 3.98/1.17 % EPR 1
% 3.98/1.17 % Horn 21
% 3.98/1.17 % unary 21
% 3.98/1.17 % binary 0
% 3.98/1.17 % lits 21
% 3.98/1.17 % lits eq 21
% 3.98/1.17 % fd_pure 0
% 3.98/1.17 % fd_pseudo 0
% 3.98/1.17 % fd_cond 0
% 3.98/1.17 % fd_pseudo_cond 0
% 3.98/1.17 % AC symbols 1
% 3.98/1.17
% 3.98/1.17 % ------ Schedule UEQ
% 3.98/1.17
% 3.98/1.17 % ------ Option_UEQ Time Limit: 10.
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 % ------
% 3.98/1.17 % Current options:
% 3.98/1.17 % ------
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 %
% 3.98/1.17
% 3.98/1.17 % ------ Proving...
% 3.98/1.17 %
% 3.98/1.17
% 3.98/1.17 % SZS status Theorem for theBenchmark.p
% 3.98/1.17
% 3.98/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.98/1.17
% 3.98/1.17
%------------------------------------------------------------------------------