%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE092+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 : n002.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 01:52:23 PM UTC 2026
% Result : Theorem 64.65s 12.29s
% Output : CNFRefutation 64.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 179 ( 166 unt; 3 def)
% Number of atoms : 373 ( 204 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 33 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 186 !; 1 ?; 126 :)
% 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(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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(f21,conjecture,
! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] : coantidomain(X0) != domain(coantidomain(X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f25,plain,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(cnf_transformation,[],[f24]) ).
fof(f26,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f31,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(f32,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f44,plain,
coantidomain(sK0) != antidomain(antidomain(coantidomain(sK0))),
inference(definition_unfolding,[],[f25,f26]) ).
tcf(c_49,negated_conjecture,
antidomain(antidomain(coantidomain(sK0))) != coantidomain(sK0),
inference(cnf_transformation,[],[f44]) ).
tcf(c_50,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,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,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f43]) ).
tcf(c_82,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_50,c_59,c_60]) ).
tcf(c_83,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_53,c_59,c_60]) ).
tcf(c_128,definition,
iPr_def_10 = coantidomain(sK0),
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,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_131,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_49,c_128,c_129,c_130]) ).
tcf(c_132,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_705,plain,
! [X0: $i] :
( ( iPr_def_12 = iPr_def_10 )
| ( iPr_def_12 != X0 )
| ( iPr_def_10 != X0 ) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_730,plain,
( ( iPr_def_12 = iPr_def_10 )
| ( iPr_def_12 != iPr_def_12 )
| ( iPr_def_10 != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_705]) ).
tcf(c_731,plain,
iPr_def_12 = iPr_def_12,
inference(instantiation,[status(thm)],[c_132]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_12 = X0 )
| ( iPr_def_12 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_807,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_12 != X0 )
| ( iPr_def_10 != X0 ) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_946,plain,
! [X0: $i] :
( ( iPr_def_12 = X0 )
| ( iPr_def_12 != iPr_def_12 )
| ( X0 != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_10 = X0 )
| ( iPr_def_10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_1098,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_132]) ).
tcf(c_1642,plain,
( ( iPr_def_12 = multiplication(one,iPr_def_12) )
| ( iPr_def_12 != iPr_def_12 )
| ( multiplication(one,iPr_def_12) != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_946]) ).
tcf(c_1643,plain,
multiplication(one,iPr_def_12) = iPr_def_12,
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2251,plain,
! [X0: $i] :
( ( iPr_def_12 = X0 )
| ( iPr_def_12 != multiplication(one,iPr_def_12) )
| ( X0 != multiplication(one,iPr_def_12) ) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_2731,plain,
! [X0: $i] :
( ( iPr_def_10 = X0 )
| ( iPr_def_10 != iPr_def_10 )
| ( X0 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_6733,plain,
( ( iPr_def_10 = addition(iPr_def_10,zero) )
| ( iPr_def_10 != iPr_def_10 )
| ( addition(iPr_def_10,zero) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_2731]) ).
tcf(c_6734,plain,
addition(iPr_def_10,zero) = iPr_def_10,
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_20214,plain,
( ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_12 != addition(iPr_def_10,zero) )
| ( iPr_def_10 != addition(iPr_def_10,zero) ) ),
inference(instantiation,[status(thm)],[c_807]) ).
tcf(c_79157,plain,
( ( iPr_def_12 = addition(iPr_def_10,zero) )
| ( iPr_def_12 != multiplication(one,iPr_def_12) )
| ( addition(iPr_def_10,zero) != multiplication(one,iPr_def_12) ) ),
inference(instantiation,[status(thm)],[c_2251]) ).
tcf(c_143832,plain,
addition(iPr_def_10,coantidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_128,c_82]) ).
tcf(c_143836,plain,
coantidomain(one) = zero,
inference(superposition,[status(thm)],[c_52,c_61]) ).
tcf(c_143840,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_55,c_62]) ).
tcf(c_143842,plain,
addition(zero,coantidomain(zero)) = one,
inference(superposition,[status(thm)],[c_143836,c_82]) ).
tcf(c_143844,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_66,c_60]) ).
tcf(c_143848,plain,
coantidomain(zero) = one,
inference(demodulation,[status(thm)],[c_143842,c_143844]) ).
tcf(c_143859,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_129,c_83]) ).
tcf(c_143860,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_130,c_83]) ).
tcf(c_143861,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_143840,c_83]) ).
tcf(c_143862,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_143859,c_130]) ).
tcf(c_143865,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_58,c_59]) ).
tcf(c_143868,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(one,X1),
inference(superposition,[status(thm)],[c_83,c_59]) ).
tcf(c_143870,plain,
! [X0: $i] : addition(iPr_def_10,addition(coantidomain(iPr_def_10),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_143832,c_59]) ).
tcf(c_143879,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_55,c_63]) ).
tcf(c_143887,plain,
! [X0: $i,X1: $i] : multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(superposition,[status(thm)],[c_63,c_52]) ).
tcf(c_143896,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(superposition,[status(thm)],[c_52,c_56]) ).
tcf(c_143897,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_143898,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_61,c_56]) ).
tcf(c_143937,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_52,c_57]) ).
tcf(c_143938,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_143940,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_62,c_57]) ).
tcf(c_143943,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(zero,X1)),
inference(superposition,[status(thm)],[c_65,c_57]) ).
tcf(c_143973,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_143861,c_143844]) ).
tcf(c_144024,plain,
! [X0: $i] : addition(coantidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_82,c_143865]) ).
tcf(c_144025,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_143865]) ).
tcf(c_144026,plain,
addition(iPr_def_10,one) = one,
inference(superposition,[status(thm)],[c_143832,c_143865]) ).
tcf(c_144027,plain,
addition(iPr_def_12,one) = one,
inference(superposition,[status(thm)],[c_143860,c_143865]) ).
tcf(c_144028,plain,
addition(iPr_def_11,one) = one,
inference(superposition,[status(thm)],[c_143862,c_143865]) ).
tcf(c_144031,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_144025,c_59,c_60]) ).
tcf(c_144032,plain,
! [X0: $i] : addition(one,coantidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_144024,c_59,c_60]) ).
tcf(c_144054,plain,
! [X0: $i,X1: $i] : addition(one,addition(coantidomain(X0),X1)) = addition(one,X1),
inference(superposition,[status(thm)],[c_144032,c_59]) ).
tcf(c_144087,plain,
! [X0: $i] : addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(X0)),coantidomain(X0)))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),coantidomain(X0))),
inference(superposition,[status(thm)],[c_52,c_51]) ).
tcf(c_144121,plain,
! [X0: $i] : addition(one,coantidomain(multiplication(coantidomain(coantidomain(X0)),coantidomain(X0)))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),coantidomain(X0))),
inference(light_normalisation,[status(thm)],[c_144087,c_143848]) ).
tcf(c_144125,plain,
! [X0: $i] : addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))) = antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(superposition,[status(thm)],[c_52,c_54]) ).
tcf(c_144162,plain,
! [X0: $i] : addition(one,antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))) = antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(light_normalisation,[status(thm)],[c_144125,c_143973]) ).
tcf(c_144265,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(superposition,[status(thm)],[c_143868,c_143865]) ).
tcf(c_144268,plain,
! [X0: $i,X1: $i] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(theory_normalisation,[status(thm)],[c_144265,c_59,c_60]) ).
tcf(c_144319,plain,
! [X0: $i] : addition(iPr_def_10,addition(X0,coantidomain(iPr_def_10))) = addition(one,X0),
inference(superposition,[status(thm)],[c_60,c_143870]) ).
tcf(c_144408,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_143879,c_64]) ).
tcf(c_144510,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(demodulation,[status(thm)],[c_143896,c_143844,c_143943]) ).
tcf(c_144514,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(superposition,[status(thm)],[c_60,c_144510]) ).
tcf(c_144671,plain,
! [X0: $i,X1: $i] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(superposition,[status(thm)],[c_60,c_144054]) ).
tcf(c_144702,plain,
! [X0: $i,X1: $i] : addition(one,antidomain(multiplication(X0,antidomain(antidomain(X1))))) = addition(one,antidomain(multiplication(X0,X1))),
inference(superposition,[status(thm)],[c_54,c_144268]) ).
tcf(c_144787,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_143897,c_143844,c_143943]) ).
tcf(c_144794,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_83,c_144787]) ).
tcf(c_144816,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_144794,c_61]) ).
tcf(c_144829,plain,
multiplication(antidomain(iPr_def_11),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_129,c_144816]) ).
tcf(c_144845,plain,
multiplication(iPr_def_12,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_144829,c_130]) ).
tcf(c_145192,plain,
! [X0: $i,X1: $i] : addition(one,coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = addition(one,coantidomain(multiplication(X0,X1))),
inference(superposition,[status(thm)],[c_51,c_144671]) ).
tcf(c_146464,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_144408,c_143898]) ).
tcf(c_146590,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_146464,c_59,c_60]) ).
tcf(c_146591,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(zero,X1)) = multiplication(one,multiplication(X0,X1)),
inference(light_normalisation,[status(thm)],[c_146590,c_143943,c_144031]) ).
tcf(c_146695,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,addition(zero,X1)),
inference(light_normalisation,[status(thm)],[c_143937,c_143943]) ).
tcf(c_146696,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(demodulation,[status(thm)],[c_146695,c_143844]) ).
tcf(c_146700,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_60,c_146696]) ).
tcf(c_146704,plain,
! [X0: $i] : multiplication(X0,coantidomain(coantidomain(X0))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_82,c_146696]) ).
tcf(c_146744,plain,
! [X0: $i] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_146704,c_62]) ).
tcf(c_147139,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_143938,c_61,c_143943,c_146591]) ).
tcf(c_147154,plain,
multiplication(antidomain(iPr_def_10),coantidomain(iPr_def_10)) = multiplication(antidomain(iPr_def_10),one),
inference(superposition,[status(thm)],[c_143832,c_147139]) ).
tcf(c_147198,plain,
multiplication(iPr_def_11,coantidomain(iPr_def_10)) = multiplication(iPr_def_11,one),
inference(light_normalisation,[status(thm)],[c_147154,c_129]) ).
tcf(c_147347,plain,
multiplication(iPr_def_11,coantidomain(iPr_def_10)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_147198,c_62]) ).
tcf(c_147354,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(coantidomain(iPr_def_10),X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_147347,c_63]) ).
tcf(c_147895,plain,
multiplication(iPr_def_11,coantidomain(coantidomain(iPr_def_10))) = multiplication(iPr_def_11,zero),
inference(superposition,[status(thm)],[c_52,c_147354]) ).
tcf(c_147927,plain,
multiplication(iPr_def_11,coantidomain(coantidomain(iPr_def_10))) = zero,
inference(demodulation,[status(thm)],[c_147895,c_65]) ).
tcf(c_147942,plain,
multiplication(addition(one,iPr_def_11),coantidomain(coantidomain(iPr_def_10))) = addition(coantidomain(coantidomain(iPr_def_10)),zero),
inference(superposition,[status(thm)],[c_147927,c_143898]) ).
tcf(c_147945,plain,
multiplication(addition(iPr_def_11,one),coantidomain(coantidomain(iPr_def_10))) = addition(zero,coantidomain(coantidomain(iPr_def_10))),
inference(theory_normalisation,[status(thm)],[c_147942,c_59,c_60]) ).
tcf(c_147946,plain,
addition(zero,coantidomain(coantidomain(iPr_def_10))) = multiplication(one,coantidomain(coantidomain(iPr_def_10))),
inference(light_normalisation,[status(thm)],[c_147945,c_144028]) ).
tcf(c_148874,plain,
multiplication(iPr_def_12,addition(one,iPr_def_10)) = addition(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_144845,c_143940]) ).
tcf(c_149011,plain,
multiplication(iPr_def_12,addition(iPr_def_10,one)) = addition(iPr_def_10,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_148874,c_59,c_60]) ).
tcf(c_149012,plain,
addition(iPr_def_10,iPr_def_12) = multiplication(iPr_def_12,one),
inference(light_normalisation,[status(thm)],[c_149011,c_144026]) ).
tcf(c_149183,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_149012,c_62]) ).
tcf(c_149184,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_12,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_149183,c_59]) ).
tcf(c_149273,plain,
addition(iPr_def_12,coantidomain(iPr_def_10)) = addition(one,iPr_def_12),
inference(superposition,[status(thm)],[c_149184,c_144319]) ).
tcf(c_149275,plain,
addition(iPr_def_12,coantidomain(iPr_def_10)) = addition(iPr_def_12,one),
inference(theory_normalisation,[status(thm)],[c_149273,c_59,c_60]) ).
tcf(c_149276,plain,
addition(iPr_def_12,coantidomain(iPr_def_10)) = one,
inference(light_normalisation,[status(thm)],[c_149275,c_144027]) ).
tcf(c_149300,plain,
multiplication(iPr_def_10,one) = multiplication(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_149276,c_146700]) ).
tcf(c_149309,plain,
multiplication(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(demodulation,[status(thm)],[c_149300,c_62]) ).
tcf(c_149316,plain,
! [X0: $i] : addition(iPr_def_10,multiplication(X0,iPr_def_12)) = multiplication(addition(iPr_def_10,X0),iPr_def_12),
inference(superposition,[status(thm)],[c_149309,c_56]) ).
tcf(c_150838,plain,
multiplication(one,coantidomain(coantidomain(iPr_def_10))) = multiplication(iPr_def_10,coantidomain(coantidomain(iPr_def_10))),
inference(superposition,[status(thm)],[c_143832,c_144514]) ).
tcf(c_159065,plain,
! [X0: $i] : coantidomain(multiplication(coantidomain(coantidomain(X0)),coantidomain(X0))) = one,
inference(demodulation,[status(thm)],[c_144121,c_144032,c_145192]) ).
tcf(c_159113,plain,
! [X0: $i] : multiplication(coantidomain(coantidomain(X0)),multiplication(coantidomain(X0),one)) = zero,
inference(superposition,[status(thm)],[c_159065,c_143887]) ).
tcf(c_159518,plain,
! [X0: $i] : multiplication(coantidomain(coantidomain(X0)),coantidomain(X0)) = zero,
inference(demodulation,[status(thm)],[c_159113,c_62]) ).
tcf(c_159536,plain,
! [X0: $i] : multiplication(coantidomain(coantidomain(X0)),addition(one,coantidomain(X0))) = addition(coantidomain(coantidomain(X0)),zero),
inference(superposition,[status(thm)],[c_159518,c_143940]) ).
tcf(c_159563,plain,
! [X0: $i] : multiplication(coantidomain(coantidomain(X0)),addition(one,coantidomain(X0))) = addition(zero,coantidomain(coantidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_159536,c_59,c_60]) ).
tcf(c_159564,plain,
! [X0: $i] : addition(zero,coantidomain(coantidomain(X0))) = multiplication(coantidomain(coantidomain(X0)),one),
inference(light_normalisation,[status(thm)],[c_159563,c_144032]) ).
tcf(c_167069,plain,
addition(zero,coantidomain(coantidomain(iPr_def_10))) = multiplication(iPr_def_10,coantidomain(coantidomain(iPr_def_10))),
inference(light_normalisation,[status(thm)],[c_147946,c_150838]) ).
tcf(c_167070,plain,
coantidomain(coantidomain(iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_167069,c_62,c_146744,c_159564]) ).
tcf(c_168346,plain,
! [X0: $i] : antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = one,
inference(demodulation,[status(thm)],[c_144162,c_144031,c_144702]) ).
tcf(c_168389,plain,
! [X0: $i] : multiplication(one,multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = zero,
inference(superposition,[status(thm)],[c_168346,c_55]) ).
tcf(c_168426,plain,
! [X0: $i] : multiplication(X0,antidomain(antidomain(coantidomain(X0)))) = zero,
inference(demodulation,[status(thm)],[c_168389,c_61]) ).
tcf(c_168435,plain,
multiplication(coantidomain(iPr_def_10),antidomain(antidomain(iPr_def_10))) = zero,
inference(superposition,[status(thm)],[c_167070,c_168426]) ).
tcf(c_168508,plain,
multiplication(coantidomain(iPr_def_10),iPr_def_12) = zero,
inference(light_normalisation,[status(thm)],[c_168435,c_129,c_130]) ).
tcf(c_168578,plain,
multiplication(addition(iPr_def_10,coantidomain(iPr_def_10)),iPr_def_12) = addition(iPr_def_10,zero),
inference(superposition,[status(thm)],[c_168508,c_149316]) ).
tcf(c_168589,plain,
addition(iPr_def_10,zero) = multiplication(one,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_168578,c_143832]) ).
tcf(c_168614,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_168589,c_79157,c_20214,c_6734,c_6733,c_1643,c_1642,c_1098,c_731,c_730,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:57:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 64.65/12.29 % SZS status Started for theBenchmark.p
% 64.65/12.29 % SZS status Theorem for theBenchmark.p
% 64.65/12.29
% 64.65/12.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 64.65/12.29
% 64.65/12.29 % ------ iProver source info
% 64.65/12.29
% 64.65/12.29 % git: date: 2026-07-19 20:42:38 +0200
% 64.65/12.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 64.65/12.29 % git: non_committed_changes: false
% 64.65/12.29
% 64.65/12.29 % ------ Parsing...
% 64.65/12.29 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 64.65/12.29 %
% 64.65/12.29
% 64.65/12.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 64.65/12.29
% 64.65/12.29 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 64.65/12.29 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 64.65/12.29
% 64.65/12.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 64.65/12.29 % ------ Proving...
% 64.65/12.29 % ------ Problem Properties
% 64.65/12.29
% 64.65/12.29 %
% 64.65/12.29 % clauses 21
% 64.65/12.29 % conjectures 1
% 64.65/12.29 % EPR 1
% 64.65/12.29 % Horn 21
% 64.65/12.29 % unary 21
% 64.65/12.29 % binary 0
% 64.65/12.29 % lits 21
% 64.65/12.29 % lits eq 21
% 64.65/12.29 % fd_pure 0
% 64.65/12.29 % fd_pseudo 0
% 64.65/12.29 % fd_cond 0
% 64.65/12.29 % fd_pseudo_cond 0
% 64.65/12.29 % AC symbols 1
% 64.65/12.29
% 64.65/12.29 % ------ Schedule UEQ
% 64.65/12.29
% 64.65/12.29 % ------ Option_UEQ Time Limit: 10.
% 64.65/12.29
% 64.65/12.29
% 64.65/12.29 % ------
% 64.65/12.29 % Current options:
% 64.65/12.29 % ------
% 64.65/12.29
% 64.65/12.29
% 64.65/12.29 %
% 64.65/12.29
% 64.65/12.29 % ------ Proving...
% 64.65/12.29 % Proof_search_loop: time out after: 2642 full_loop iterations
% 64.65/12.29
% 64.65/12.29 % ------ Option_UEQ Time Limit: 15.
% 64.65/12.29
% 64.65/12.29
% 64.65/12.29 % ------
% 64.65/12.29 % Current options:
% 64.65/12.29 % ------
% 64.65/12.29
% 64.65/12.29
% 64.65/12.29 %
% 64.65/12.29
% 64.65/12.29 % ------ Proving...
% 64.65/12.29 %
% 64.65/12.29
% 64.65/12.29 % SZS status Theorem for theBenchmark.p
% 64.65/12.29
% 64.65/12.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 64.65/12.29
% 64.65/12.29
%------------------------------------------------------------------------------