%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE078+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 : n007.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 31.68s 6.85s
% Output : CNFRefutation 31.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 97 ( 93 unt; 2 def)
% Number of atoms : 161 ( 104 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 : 101 ( 0 sgn 100 !; 1 ?; 52 :)
% 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(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
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(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain4) ).
fof(f18,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> domain(antidomain(X0)) = antidomain(X0) ),
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 )
=> domain(antidomain(X0)) = antidomain(X0) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
& antidomain(X0) != domain(antidomain(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
& antidomain(sK0) != domain(antidomain(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
fof(f22,plain,
! [X1] : zero = multiplication(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
! [X1] : one = addition(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f24,plain,
antidomain(sK0) != domain(antidomain(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f25,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,negated_conjecture,
domain(antidomain(sK0)) != antidomain(sK0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[],[f22]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_54,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
domain(zero) = zero,
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_62,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f35]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_67,plain,
! [X0: $i] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_83,plain,
! [X0: $i] : addition(one,domain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_55,c_56]) ).
tcf(c_129,definition,
iPr_def_10 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = domain(iPr_def_10),
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_51]) ).
tcf(c_132,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_133,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_49,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_55,c_56]) ).
tcf(c_217,plain,
addition(domain(sK0),iPr_def_10) = one,
inference(superposition,[status(thm)],[c_129,c_132]) ).
tcf(c_219,plain,
addition(iPr_def_10,domain(sK0)) = one,
inference(theory_normalisation,[status(thm)],[c_217,c_55,c_56]) ).
tcf(c_223,plain,
addition(iPr_def_11,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_130,c_132]) ).
tcf(c_224,plain,
multiplication(iPr_def_11,antidomain(iPr_def_10)) = zero,
inference(superposition,[status(thm)],[c_130,c_131]) ).
tcf(c_226,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_60,c_56]) ).
tcf(c_270,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_427,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(antidomain(X0),one),
inference(superposition,[status(thm)],[c_54,c_270]) ).
tcf(c_454,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(theory_normalisation,[status(thm)],[c_427,c_55,c_56]) ).
tcf(c_455,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(light_normalisation,[status(thm)],[c_454,c_132]) ).
tcf(c_462,plain,
addition(one,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_129,c_455]) ).
tcf(c_469,plain,
addition(iPr_def_10,one) = one,
inference(theory_normalisation,[status(thm)],[c_462,c_55,c_56]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i] : addition(multiplication(one,X0),multiplication(domain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_83,c_52]) ).
tcf(c_623,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(domain(sK0),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_219,c_52]) ).
tcf(c_646,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(domain(sK0),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_623,c_63]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_620,c_63]) ).
tcf(c_649,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_67,c_647]) ).
tcf(c_665,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,antidomain(iPr_def_10))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_223,c_53]) ).
tcf(c_689,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,antidomain(iPr_def_10))) = X0,
inference(light_normalisation,[status(thm)],[c_665,c_64]) ).
tcf(c_699,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_469,c_53]) ).
tcf(c_705,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = X0,
inference(light_normalisation,[status(thm)],[c_699,c_64]) ).
tcf(c_706,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = X0,
inference(theory_normalisation,[status(thm)],[c_705,c_55,c_56]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(X0,domain(X1)),
inference(superposition,[status(thm)],[c_66,c_649]) ).
tcf(c_716,plain,
multiplication(iPr_def_11,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_130,c_649]) ).
tcf(c_1069,plain,
addition(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_716,c_706]) ).
tcf(c_1081,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1069,c_55,c_56]) ).
tcf(c_1360,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_1081,c_52]) ).
tcf(c_32417,plain,
addition(multiplication(iPr_def_10,antidomain(iPr_def_10)),zero) = zero,
inference(superposition,[status(thm)],[c_224,c_1360]) ).
tcf(c_32444,plain,
addition(zero,multiplication(iPr_def_10,antidomain(iPr_def_10))) = zero,
inference(theory_normalisation,[status(thm)],[c_32417,c_55,c_56]) ).
tcf(c_32763,plain,
multiplication(iPr_def_10,antidomain(iPr_def_10)) = zero,
inference(demodulation,[status(thm)],[c_32444,c_226]) ).
tcf(c_32827,plain,
addition(multiplication(iPr_def_10,iPr_def_11),zero) = iPr_def_10,
inference(superposition,[status(thm)],[c_32763,c_689]) ).
tcf(c_33559,plain,
multiplication(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_32827,c_60]) ).
tcf(c_71534,plain,
! [X0: $i] : multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))) = multiplication(domain(X0),domain(antidomain(X0))),
inference(superposition,[status(thm)],[c_131,c_715]) ).
tcf(c_71826,plain,
! [X0: $i] : multiplication(zero,multiplication(domain(X0),domain(antidomain(X0)))) = multiplication(domain(X0),domain(antidomain(X0))),
inference(light_normalisation,[status(thm)],[c_71534,c_57]) ).
tcf(c_72211,plain,
! [X0: $i] : multiplication(domain(X0),domain(antidomain(X0))) = zero,
inference(demodulation,[status(thm)],[c_71826,c_58]) ).
tcf(c_72320,plain,
addition(multiplication(iPr_def_10,domain(antidomain(sK0))),zero) = domain(antidomain(sK0)),
inference(superposition,[status(thm)],[c_72211,c_646]) ).
tcf(c_72367,plain,
addition(zero,multiplication(iPr_def_10,domain(antidomain(sK0)))) = domain(antidomain(sK0)),
inference(theory_normalisation,[status(thm)],[c_72320,c_55,c_56]) ).
tcf(c_72368,plain,
addition(zero,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_72367,c_129,c_130,c_33559]) ).
tcf(c_72369,plain,
addition(iPr_def_10,zero) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_72368,c_55,c_56]) ).
tcf(c_73359,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_72369,c_60]) ).
tcf(c_73524,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_133,c_73359]) ).
tcf(c_73525,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_73524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE078+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:50:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 31.68/6.85 % SZS status Started for theBenchmark.p
% 31.68/6.85 % SZS status Theorem for theBenchmark.p
% 31.68/6.85
% 31.68/6.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.68/6.85
% 31.68/6.85 % ------ iProver source info
% 31.68/6.85
% 31.68/6.85 % git: date: 2026-07-19 20:42:38 +0200
% 31.68/6.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.68/6.85 % git: non_committed_changes: false
% 31.68/6.85
% 31.68/6.85 % ------ Parsing...
% 31.68/6.85 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 31.68/6.85 %
% 31.68/6.85
% 31.68/6.85 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 31.68/6.85
% 31.68/6.85 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 31.68/6.85 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.68/6.85
% 31.68/6.85 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 31.68/6.85 % ------ Proving...
% 31.68/6.85 % ------ Problem Properties
% 31.68/6.85
% 31.68/6.85 %
% 31.68/6.85 % clauses 21
% 31.68/6.85 % conjectures 3
% 31.68/6.85 % EPR 1
% 31.68/6.85 % Horn 21
% 31.68/6.85 % unary 21
% 31.68/6.85 % binary 0
% 31.68/6.85 % lits 21
% 31.68/6.85 % lits eq 21
% 31.68/6.85 % fd_pure 0
% 31.68/6.85 % fd_pseudo 0
% 31.68/6.85 % fd_cond 0
% 31.68/6.85 % fd_pseudo_cond 0
% 31.68/6.85 % AC symbols 1
% 31.68/6.85
% 31.68/6.85 % ------ Schedule UEQ
% 31.68/6.85
% 31.68/6.85 % ------ Option_UEQ Time Limit: 10.
% 31.68/6.85
% 31.68/6.85
% 31.68/6.85 % ------
% 31.68/6.85 % Current options:
% 31.68/6.85 % ------
% 31.68/6.85
% 31.68/6.85
% 31.68/6.85 %
% 31.68/6.85
% 31.68/6.85 % ------ Proving...
% 31.68/6.85 %
% 31.68/6.85
% 31.68/6.85 % SZS status Theorem for theBenchmark.p
% 31.68/6.85
% 31.68/6.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.68/6.86
% 31.68/6.86
%------------------------------------------------------------------------------