%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE086+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 01:52:22 PM UTC 2026
% Result : Theorem 1.19s 1.09s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 69 unt; 2 def)
% Number of atoms : 158 ( 68 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 39 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f21,conjecture,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
domain(zero) != zero,
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
zero != domain(zero),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
zero != domain(zero),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
zero != antidomain(antidomain(zero)),
inference(definition_unfolding,[],[f43,f38]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f36]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f37]) ).
tcf(c_66,negated_conjecture,
antidomain(antidomain(zero)) != zero,
inference(cnf_transformation,[],[f44]) ).
tcf(c_82,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_128,definition,
iPr_def_10 = antidomain(zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_129,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_130,negated_conjecture,
iPr_def_11 != zero,
inference(demodulation,[status(thm)],[c_66,c_128,c_129]) ).
tcf(c_212,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_128,c_82]) ).
tcf(c_214,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_212,c_129]) ).
tcf(c_215,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_82,c_214]) ).
tcf(c_217,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_10,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_54,c_214]) ).
tcf(c_219,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_129,c_60]) ).
tcf(c_220,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_60,c_219]) ).
tcf(c_223,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_51,c_219]) ).
tcf(c_224,plain,
antidomain(multiplication(iPr_def_11,iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_128,c_219]) ).
tcf(c_225,plain,
multiplication(iPr_def_11,iPr_def_10) != iPr_def_11,
inference(demodulation,[status(thm)],[c_130,c_219]) ).
tcf(c_234,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_217,c_56]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(addition(iPr_def_10,iPr_def_11),X1),
inference(superposition,[status(thm)],[c_215,c_50]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(iPr_def_10,addition(iPr_def_11,X1)),
inference(theory_normalisation,[status(thm)],[c_265,c_50,c_49]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i] : addition(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) = multiplication(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_220,c_56]) ).
tcf(c_341,plain,
! [X0: $i] : addition(antidomain(X0),addition(iPr_def_10,iPr_def_11)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_215,c_264]) ).
tcf(c_356,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,antidomain(X0))) = addition(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_341,c_50,c_49]) ).
tcf(c_471,plain,
! [X0: $i] : addition(antidomain(multiplication(antidomain(antidomain(antidomain(X0))),X0)),antidomain(multiplication(iPr_def_11,iPr_def_10))) = antidomain(multiplication(iPr_def_11,iPr_def_10)),
inference(superposition,[status(thm)],[c_220,c_61]) ).
tcf(c_479,plain,
! [X0: $i] : addition(antidomain(multiplication(iPr_def_11,iPr_def_10)),antidomain(multiplication(antidomain(antidomain(antidomain(X0))),X0))) = antidomain(multiplication(iPr_def_11,iPr_def_10)),
inference(theory_normalisation,[status(thm)],[c_471,c_50,c_49]) ).
tcf(c_480,plain,
! [X0: $i] : addition(iPr_def_10,antidomain(multiplication(antidomain(antidomain(antidomain(X0))),X0))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_479,c_224]) ).
tcf(c_939,plain,
addition(iPr_def_10,antidomain(multiplication(antidomain(antidomain(iPr_def_11)),iPr_def_10))) = iPr_def_10,
inference(superposition,[status(thm)],[c_129,c_480]) ).
tcf(c_1864,plain,
antidomain(addition(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_314,c_234]) ).
tcf(c_2202,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),addition(antidomain(multiplication(iPr_def_11,iPr_def_10)),X0)) = addition(iPr_def_10,addition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_1864,c_277]) ).
tcf(c_2218,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),addition(iPr_def_10,X0)) = addition(iPr_def_10,addition(iPr_def_11,X0)),
inference(light_normalisation,[status(thm)],[c_2202,c_224]) ).
tcf(c_2219,plain,
! [X0: $i] : addition(iPr_def_10,addition(X0,multiplication(iPr_def_11,iPr_def_10))) = addition(iPr_def_10,addition(iPr_def_11,X0)),
inference(theory_normalisation,[status(thm)],[c_2218,c_50,c_49]) ).
tcf(c_2220,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,X0)) = addition(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_2219,c_223]) ).
tcf(c_2225,plain,
! [X0: $i] : addition(iPr_def_10,antidomain(X0)) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_356,c_2220]) ).
tcf(c_2230,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_939,c_2225]) ).
tcf(c_2231,plain,
multiplication(iPr_def_11,iPr_def_10) = antidomain(iPr_def_10),
inference(demodulation,[status(thm)],[c_1864,c_2230]) ).
tcf(c_2237,plain,
multiplication(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2231,c_129]) ).
tcf(c_2238,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2237,c_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE086+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 18:53:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 1.19/1.09 % SZS status Started for theBenchmark.p
% 1.19/1.09 % SZS status Theorem for theBenchmark.p
% 1.19/1.09
% 1.19/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/1.09
% 1.19/1.09 % ------ iProver source info
% 1.19/1.09
% 1.19/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/1.09 % git: non_committed_changes: false
% 1.19/1.09
% 1.19/1.09 % ------ Parsing...
% 1.19/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 1.19/1.09 %
% 1.19/1.09
% 1.19/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.19/1.09
% 1.19/1.09 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 1.19/1.09 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.19/1.09
% 1.19/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.19/1.09 % ------ Proving...
% 1.19/1.09 % ------ Problem Properties
% 1.19/1.09
% 1.19/1.09 %
% 1.19/1.09 % clauses 20
% 1.19/1.09 % conjectures 1
% 1.19/1.09 % EPR 1
% 1.19/1.09 % Horn 20
% 1.19/1.09 % unary 20
% 1.19/1.09 % binary 0
% 1.19/1.09 % lits 20
% 1.19/1.09 % lits eq 20
% 1.19/1.09 % fd_pure 0
% 1.19/1.09 % fd_pseudo 0
% 1.19/1.09 % fd_cond 0
% 1.19/1.09 % fd_pseudo_cond 0
% 1.19/1.09 % AC symbols 1
% 1.19/1.09
% 1.19/1.09 % ------ Schedule UEQ
% 1.19/1.09
% 1.19/1.09 % ------ Option_UEQ Time Limit: 10.
% 1.19/1.09
% 1.19/1.09
% 1.19/1.09 % ------
% 1.19/1.09 % Current options:
% 1.19/1.09 % ------
% 1.19/1.09
% 1.19/1.09
% 1.19/1.09 %
% 1.19/1.09
% 1.19/1.09 % ------ Proving...
% 1.19/1.09 %
% 1.19/1.09
% 1.19/1.09 % SZS status Theorem for theBenchmark.p
% 1.19/1.09
% 1.19/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/1.09
% 1.19/1.09
%------------------------------------------------------------------------------