%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE097+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 01:52:23 PM UTC 2026
% Result : Theorem 123.87s 20.46s
% Output : CNFRefutation 123.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 31
% Syntax : Number of formulae : 254 ( 238 unt; 13 def)
% Number of atoms : 743 ( 281 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 32 ~; 24 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 184 !; 3 ?; 124 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0)
=> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0)
=> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0)
& domain(X2) != addition(forward_diamond(X0,domain(X1)),domain(X2)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( multiplication(domain(sK2),sK0) = addition(multiplication(sK0,domain(sK1)),multiplication(domain(sK2),sK0))
& domain(sK2) != addition(forward_diamond(sK0,domain(sK1)),domain(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
multiplication(domain(sK2),sK0) = addition(multiplication(sK0,domain(sK1)),multiplication(domain(sK2),sK0)),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
domain(sK2) != addition(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
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,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f42,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(f43,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f50,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f40,f39,f39]) ).
fof(f53,plain,
antidomain(antidomain(sK2)) != addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f32,f39,f52,f39,f39]) ).
fof(f54,plain,
multiplication(antidomain(antidomain(sK2)),sK0) = addition(multiplication(sK0,antidomain(antidomain(sK1))),multiplication(antidomain(antidomain(sK2)),sK0)),
inference(definition_unfolding,[],[f31,f39,f39,f39]) ).
tcf(c_49,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))) != antidomain(antidomain(sK2)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
addition(multiplication(sK0,antidomain(antidomain(sK1))),multiplication(antidomain(antidomain(sK2)),sK0)) = multiplication(antidomain(antidomain(sK2)),sK0),
inference(cnf_transformation,[],[f54]) ).
tcf(c_51,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_52,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_53,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,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,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f48]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f50]) ).
tcf(c_83,negated_conjecture,
addition(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) != antidomain(antidomain(sK2)),
inference(theory_normalisation,[status(thm)],[c_49,c_54,c_55]) ).
tcf(c_84,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_57,c_54,c_55]) ).
tcf(c_132,definition,
iPr_def_10 = antidomain(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_137,definition,
iPr_def_15 = antidomain(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_138,definition,
iPr_def_16 = multiplication(sK0,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_139,definition,
iPr_def_17 = antidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_140,definition,
iPr_def_18 = antidomain(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_141,definition,
iPr_def_19 = addition(iPr_def_11,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_142,definition,
iPr_def_20 = multiplication(sK0,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_143,definition,
iPr_def_21 = multiplication(iPr_def_11,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_144,definition,
iPr_def_22 = addition(iPr_def_20,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_145,negated_conjecture,
iPr_def_19 != iPr_def_11,
inference(demodulation,[status(thm)],[c_83,c_134,c_135,c_136,c_137,c_138,c_139,c_140,c_132,c_133,c_141]) ).
tcf(c_146,negated_conjecture,
iPr_def_22 = iPr_def_21,
inference(demodulation,[status(thm)],[c_50,c_143,c_142,c_144]) ).
tcf(c_147,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_256,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_84]) ).
tcf(c_257,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_134,c_84]) ).
tcf(c_259,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_135,c_84]) ).
tcf(c_260,plain,
addition(iPr_def_14,antidomain(iPr_def_14)) = one,
inference(superposition,[status(thm)],[c_136,c_84]) ).
tcf(c_262,plain,
addition(iPr_def_14,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_260,c_137]) ).
tcf(c_263,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_259,c_136]) ).
tcf(c_264,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_257,c_135]) ).
tcf(c_265,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_256,c_133]) ).
tcf(c_267,plain,
! [X0: $i] : multiplication(addition(iPr_def_14,iPr_def_15),X0) = X0,
inference(light_normalisation,[status(thm)],[c_61,c_262]) ).
tcf(c_268,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = X0,
inference(demodulation,[status(thm)],[c_267,c_51]) ).
tcf(c_269,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_14,iPr_def_15)) = X0,
inference(light_normalisation,[status(thm)],[c_62,c_262]) ).
tcf(c_270,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),multiplication(X0,iPr_def_15)) = X0,
inference(demodulation,[status(thm)],[c_269,c_52]) ).
tcf(c_280,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_262,c_263]) ).
tcf(c_281,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_263,c_264]) ).
tcf(c_282,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_280,c_281]) ).
tcf(c_283,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_264,c_265]) ).
tcf(c_284,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_281,c_283]) ).
tcf(c_288,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_133,c_59]) ).
tcf(c_289,plain,
multiplication(iPr_def_13,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_135,c_59]) ).
tcf(c_290,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_136,c_59]) ).
tcf(c_291,plain,
multiplication(iPr_def_15,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_137,c_59]) ).
tcf(c_294,plain,
addition(zero,multiplication(antidomain(iPr_def_14),iPr_def_15)) = antidomain(iPr_def_14),
inference(superposition,[status(thm)],[c_59,c_270]) ).
tcf(c_297,plain,
addition(zero,multiplication(iPr_def_15,iPr_def_15)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_294,c_137]) ).
tcf(c_298,plain,
addition(multiplication(iPr_def_15,iPr_def_15),zero) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_297,c_54,c_55]) ).
tcf(c_300,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_66,c_288]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_582,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_15,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_138,c_56]) ).
tcf(c_631,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_283,c_52]) ).
tcf(c_687,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_289,c_288]) ).
tcf(c_692,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_290,c_288]) ).
tcf(c_695,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_15,iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_692,c_268]) ).
tcf(c_698,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_15,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_291,c_288]) ).
tcf(c_1027,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_282,c_283]) ).
tcf(c_1031,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),multiplication(X0,iPr_def_15)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_1027,c_52]) ).
tcf(c_1034,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = X0,
inference(light_normalisation,[status(thm)],[c_1031,c_270,c_631]) ).
tcf(c_1039,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,iPr_def_14)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_284,c_52]) ).
tcf(c_1042,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,iPr_def_14)) = X0,
inference(light_normalisation,[status(thm)],[c_1039,c_631,c_1034]) ).
tcf(c_1044,plain,
addition(multiplication(iPr_def_15,iPr_def_15),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_298,c_288]) ).
tcf(c_1045,plain,
multiplication(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1044,c_300]) ).
tcf(c_1064,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_300,c_55]) ).
tcf(c_1073,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_11 )
| ( iPr_def_19 != X0 )
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_1265,plain,
! [X0: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != iPr_def_11 )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1266,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_1328,plain,
iPr_def_19 = iPr_def_19,
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_19 = X0 )
| ( iPr_def_19 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_1469,plain,
( ( iPr_def_11 = addition(iPr_def_11,zero) )
| ( iPr_def_11 != iPr_def_11 )
| ( addition(iPr_def_11,zero) != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_1265]) ).
tcf(c_1470,plain,
addition(iPr_def_11,zero) = iPr_def_11,
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1919,plain,
multiplication(sK0,iPr_def_15) = multiplication(iPr_def_16,iPr_def_15),
inference(superposition,[status(thm)],[c_1045,c_582]) ).
tcf(c_1927,plain,
multiplication(iPr_def_16,iPr_def_15) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1919,c_138]) ).
tcf(c_1945,plain,
! [X0: $i] : multiplication(iPr_def_16,multiplication(iPr_def_15,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_1927,c_56]) ).
tcf(c_2236,plain,
multiplication(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_695,c_1064]) ).
tcf(c_2240,plain,
multiplication(sK0,iPr_def_13) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_2236,c_582]) ).
tcf(c_2244,plain,
multiplication(iPr_def_16,iPr_def_13) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_2240,c_142]) ).
tcf(c_2248,plain,
! [X0: $i] : multiplication(iPr_def_16,multiplication(iPr_def_13,X0)) = multiplication(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_2244,c_56]) ).
tcf(c_2704,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),X0) = X0,
inference(superposition,[status(thm)],[c_1034,c_308]) ).
tcf(c_2713,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_12)) = X0,
inference(theory_normalisation,[status(thm)],[c_2704,c_54,c_55]) ).
tcf(c_3115,plain,
! [X0: $i] :
( ( iPr_def_19 = X0 )
| ( iPr_def_19 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_3125,plain,
addition(iPr_def_20,multiplication(iPr_def_16,iPr_def_14)) = iPr_def_16,
inference(superposition,[status(thm)],[c_2244,c_1042]) ).
tcf(c_4165,plain,
multiplication(iPr_def_16,multiplication(iPr_def_11,iPr_def_10)) = multiplication(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_698,c_1945]) ).
tcf(c_4260,plain,
addition(iPr_def_20,multiplication(iPr_def_16,multiplication(iPr_def_13,iPr_def_12))) = iPr_def_20,
inference(superposition,[status(thm)],[c_2248,c_2713]) ).
tcf(c_4282,plain,
iPr_def_16 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_4260,c_687,c_3125,c_4165]) ).
tcf(c_4303,plain,
! [X0: $i] : multiplication(iPr_def_16,multiplication(iPr_def_13,X0)) = multiplication(iPr_def_16,X0),
inference(demodulation,[status(thm)],[c_2248,c_4282]) ).
tcf(c_7338,plain,
( ( iPr_def_19 = multiplication(one,iPr_def_19) )
| ( iPr_def_19 != iPr_def_19 )
| ( multiplication(one,iPr_def_19) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_3115]) ).
tcf(c_7339,plain,
multiplication(one,iPr_def_19) = iPr_def_19,
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_49291,plain,
! [X0: $i,X1: $i] : multiplication(iPr_def_16,multiplication(multiplication(iPr_def_13,X0),X1)) = multiplication(multiplication(iPr_def_16,X0),X1),
inference(superposition,[status(thm)],[c_4303,c_56]) ).
tcf(c_87971,plain,
( ( iPr_def_19 = iPr_def_11 )
| ( iPr_def_19 != multiplication(one,iPr_def_19) )
| ( iPr_def_11 != multiplication(one,iPr_def_19) ) ),
inference(instantiation,[status(thm)],[c_1073]) ).
tcf(c_159688,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_159695,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_84]) ).
tcf(c_159697,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_133,c_84]) ).
tcf(c_159704,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_159695,c_133]) ).
tcf(c_159707,plain,
addition(iPr_def_18,antidomain(iPr_def_18)) = one,
inference(superposition,[status(thm)],[c_140,c_84]) ).
tcf(c_159708,plain,
addition(iPr_def_20,iPr_def_21) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_144,c_146]) ).
tcf(c_159710,plain,
multiplication(iPr_def_10,sK2) = zero,
inference(superposition,[status(thm)],[c_132,c_59]) ).
tcf(c_159712,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_133,c_59]) ).
tcf(c_159718,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_59,c_62]) ).
tcf(c_159721,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_66,c_55]) ).
tcf(c_159727,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_159731,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_18,X0)) = addition(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_141,c_54]) ).
tcf(c_159739,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_159718,c_84]) ).
tcf(c_159742,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_159704,c_54]) ).
tcf(c_159900,plain,
! [X0: $i,X1: $i] : multiplication(iPr_def_16,multiplication(iPr_def_13,multiplication(X0,X1))) = multiplication(iPr_def_16,multiplication(X0,X1)),
inference(demodulation,[status(thm)],[c_49291,c_56]) ).
tcf(c_159902,plain,
! [X0: $i] : multiplication(iPr_def_16,multiplication(iPr_def_13,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_61,c_159900]) ).
tcf(c_159915,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_59,c_56]) ).
tcf(c_159921,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_15,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_138,c_56]) ).
tcf(c_159923,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(sK0,X0)) = multiplication(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_143,c_56]) ).
tcf(c_159931,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_59,c_51]) ).
tcf(c_159932,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_159938,plain,
! [X0: $i] : multiplication(addition(sK0,X0),iPr_def_13) = addition(iPr_def_20,multiplication(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_142,c_51]) ).
tcf(c_159972,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_59,c_52]) ).
tcf(c_160012,plain,
! [X0: $i] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(superposition,[status(thm)],[c_59,c_58]) ).
tcf(c_160031,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_16)),antidomain(multiplication(X0,antidomain(iPr_def_17)))) = antidomain(multiplication(X0,antidomain(iPr_def_17))),
inference(superposition,[status(thm)],[c_139,c_58]) ).
tcf(c_160042,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_16)),antidomain(multiplication(X0,iPr_def_18))) = antidomain(multiplication(X0,iPr_def_18)),
inference(light_normalisation,[status(thm)],[c_160031,c_140]) ).
tcf(c_160055,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(sK2,X0)) = addition(zero,multiplication(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_159710,c_52]) ).
tcf(c_160077,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(iPr_def_10,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_159712,c_56]) ).
tcf(c_160079,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(iPr_def_10,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_160077,c_64]) ).
tcf(c_161195,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_159739,c_159721]) ).
tcf(c_161656,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_84,c_159727]) ).
tcf(c_161658,plain,
addition(iPr_def_11,iPr_def_19) = iPr_def_19,
inference(superposition,[status(thm)],[c_141,c_159727]) ).
tcf(c_161660,plain,
addition(iPr_def_11,one) = one,
inference(superposition,[status(thm)],[c_159697,c_159727]) ).
tcf(c_161667,plain,
addition(iPr_def_18,one) = one,
inference(superposition,[status(thm)],[c_159707,c_159727]) ).
tcf(c_161755,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_161656,c_54,c_55]) ).
tcf(c_161783,plain,
! [X0: $i,X1: $i] : addition(one,addition(X0,antidomain(X1))) = addition(X0,one),
inference(superposition,[status(thm)],[c_161755,c_159688]) ).
tcf(c_162003,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_163137,plain,
addition(iPr_def_11,one) = addition(iPr_def_19,one),
inference(superposition,[status(thm)],[c_161667,c_159731]) ).
tcf(c_163138,plain,
addition(iPr_def_19,one) = one,
inference(light_normalisation,[status(thm)],[c_163137,c_161660]) ).
tcf(c_164109,plain,
addition(one,iPr_def_19) = addition(iPr_def_10,iPr_def_19),
inference(superposition,[status(thm)],[c_161658,c_159742]) ).
tcf(c_164216,plain,
addition(iPr_def_10,iPr_def_19) = addition(iPr_def_19,one),
inference(theory_normalisation,[status(thm)],[c_164109,c_54,c_55]) ).
tcf(c_164217,plain,
addition(iPr_def_10,iPr_def_19) = one,
inference(light_normalisation,[status(thm)],[c_164216,c_163138]) ).
tcf(c_164803,plain,
multiplication(iPr_def_16,one) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_62,c_159902]) ).
tcf(c_164816,plain,
multiplication(iPr_def_16,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_164803,c_62]) ).
tcf(c_164821,plain,
! [X0: $i] : multiplication(addition(iPr_def_16,X0),iPr_def_13) = addition(iPr_def_16,multiplication(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_164816,c_51]) ).
tcf(c_164993,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_159915,c_64]) ).
tcf(c_165327,plain,
multiplication(iPr_def_11,iPr_def_20) = multiplication(iPr_def_21,iPr_def_13),
inference(superposition,[status(thm)],[c_142,c_159923]) ).
tcf(c_165425,plain,
! [X0: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != addition(iPr_def_11,zero) )
| ( X0 != addition(iPr_def_11,zero) ) ),
inference(instantiation,[status(thm)],[c_162003]) ).
tcf(c_167403,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_159931,c_159721]) ).
tcf(c_167410,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_84,c_167403]) ).
tcf(c_167442,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_167410,c_61]) ).
tcf(c_167453,plain,
multiplication(antidomain(iPr_def_11),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_133,c_167442]) ).
tcf(c_167455,plain,
multiplication(antidomain(iPr_def_14),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_136,c_167442]) ).
tcf(c_167477,plain,
multiplication(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_167455,c_137]) ).
tcf(c_167515,plain,
multiplication(sK0,iPr_def_13) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_167477,c_159921]) ).
tcf(c_167517,plain,
iPr_def_16 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_167515,c_142,c_164816]) ).
tcf(c_167527,plain,
multiplication(iPr_def_11,iPr_def_16) = multiplication(iPr_def_21,iPr_def_13),
inference(demodulation,[status(thm)],[c_165327,c_167517]) ).
tcf(c_167557,plain,
addition(iPr_def_16,iPr_def_21) = iPr_def_21,
inference(demodulation,[status(thm)],[c_159708,c_167517]) ).
tcf(c_167558,plain,
multiplication(sK0,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_142,c_167517]) ).
tcf(c_167856,plain,
multiplication(addition(one,iPr_def_11),sK0) = addition(sK0,iPr_def_21),
inference(superposition,[status(thm)],[c_143,c_159932]) ).
tcf(c_167878,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_164993,c_159932]) ).
tcf(c_167879,plain,
! [X0: $i] : multiplication(addition(one,iPr_def_11),multiplication(iPr_def_10,X0)) = addition(multiplication(iPr_def_10,X0),zero),
inference(superposition,[status(thm)],[c_160079,c_159932]) ).
tcf(c_167949,plain,
multiplication(addition(iPr_def_11,one),sK0) = addition(iPr_def_21,sK0),
inference(theory_normalisation,[status(thm)],[c_167856,c_54,c_55]) ).
tcf(c_167950,plain,
multiplication(one,sK0) = addition(iPr_def_21,sK0),
inference(light_normalisation,[status(thm)],[c_167949,c_161660]) ).
tcf(c_167964,plain,
! [X0: $i] : multiplication(addition(iPr_def_11,one),multiplication(iPr_def_10,X0)) = addition(zero,multiplication(iPr_def_10,X0)),
inference(theory_normalisation,[status(thm)],[c_167879,c_54,c_55]) ).
tcf(c_167965,plain,
! [X0: $i] : multiplication(one,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(sK2,X0)),
inference(light_normalisation,[status(thm)],[c_167964,c_160055,c_161660]) ).
tcf(c_167985,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_167878,c_54,c_55]) ).
tcf(c_167986,plain,
! [X0: $i,X1: $i] : multiplication(one,multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(light_normalisation,[status(thm)],[c_167985,c_161755]) ).
tcf(c_168066,plain,
! [X0: $i] : multiplication(addition(sK0,X0),iPr_def_13) = addition(iPr_def_16,multiplication(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_167558,c_51]) ).
tcf(c_168068,plain,
! [X0: $i] : multiplication(addition(X0,sK0),iPr_def_13) = addition(multiplication(X0,iPr_def_13),iPr_def_16),
inference(superposition,[status(thm)],[c_167558,c_51]) ).
tcf(c_168073,plain,
! [X0: $i] : multiplication(addition(X0,sK0),iPr_def_13) = addition(iPr_def_16,multiplication(X0,iPr_def_13)),
inference(theory_normalisation,[status(thm)],[c_168068,c_54,c_55]) ).
tcf(c_168074,plain,
! [X0: $i] : multiplication(addition(sK0,X0),iPr_def_13) = multiplication(addition(iPr_def_16,X0),iPr_def_13),
inference(light_normalisation,[status(thm)],[c_168066,c_164821]) ).
tcf(c_170210,plain,
! [X0: $i] : multiplication(addition(X0,sK0),iPr_def_13) = multiplication(addition(iPr_def_16,X0),iPr_def_13),
inference(light_normalisation,[status(thm)],[c_159938,c_167517,c_168073,c_168074]) ).
tcf(c_170452,plain,
addition(iPr_def_21,sK0) = sK0,
inference(demodulation,[status(thm)],[c_167950,c_61]) ).
tcf(c_170461,plain,
multiplication(addition(iPr_def_16,iPr_def_21),iPr_def_13) = multiplication(sK0,iPr_def_13),
inference(superposition,[status(thm)],[c_170452,c_170210]) ).
tcf(c_170462,plain,
multiplication(iPr_def_11,iPr_def_16) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_170461,c_167527,c_167557,c_167558]) ).
tcf(c_177384,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_159972,c_61,c_167986]) ).
tcf(c_177392,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(sK2,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_132,c_177384]) ).
tcf(c_177405,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(superposition,[status(thm)],[c_55,c_177384]) ).
tcf(c_177411,plain,
multiplication(antidomain(iPr_def_11),iPr_def_18) = multiplication(antidomain(iPr_def_11),iPr_def_19),
inference(superposition,[status(thm)],[c_141,c_177384]) ).
tcf(c_177418,plain,
multiplication(antidomain(iPr_def_10),one) = multiplication(antidomain(iPr_def_10),iPr_def_11),
inference(superposition,[status(thm)],[c_159704,c_177384]) ).
tcf(c_177442,plain,
multiplication(antidomain(iPr_def_10),one) = multiplication(antidomain(iPr_def_10),iPr_def_19),
inference(superposition,[status(thm)],[c_164217,c_177384]) ).
tcf(c_177491,plain,
multiplication(iPr_def_11,one) = multiplication(iPr_def_11,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_177442,c_133]) ).
tcf(c_177493,plain,
multiplication(iPr_def_11,one) = multiplication(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_177418,c_133]) ).
tcf(c_177779,plain,
multiplication(iPr_def_11,iPr_def_11) = multiplication(iPr_def_11,iPr_def_19),
inference(demodulation,[status(thm)],[c_177491,c_177493]) ).
tcf(c_178907,plain,
multiplication(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_177493,c_62]) ).
tcf(c_178908,plain,
multiplication(iPr_def_11,iPr_def_19) = iPr_def_11,
inference(demodulation,[status(thm)],[c_177779,c_178907]) ).
tcf(c_178952,plain,
! [X0: $i] : multiplication(addition(iPr_def_11,X0),iPr_def_19) = addition(iPr_def_11,multiplication(X0,iPr_def_19)),
inference(superposition,[status(thm)],[c_178908,c_51]) ).
tcf(c_192113,plain,
! [X0: $i] : addition(one,antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(light_normalisation,[status(thm)],[c_160012,c_161195]) ).
tcf(c_192114,plain,
! [X0: $i] : antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))) = one,
inference(demodulation,[status(thm)],[c_192113,c_161755]) ).
tcf(c_192125,plain,
antidomain(multiplication(iPr_def_10,antidomain(iPr_def_10))) = one,
inference(superposition,[status(thm)],[c_132,c_192114]) ).
tcf(c_192154,plain,
antidomain(multiplication(iPr_def_10,iPr_def_11)) = one,
inference(light_normalisation,[status(thm)],[c_192125,c_133]) ).
tcf(c_192191,plain,
multiplication(one,multiplication(iPr_def_10,iPr_def_11)) = zero,
inference(superposition,[status(thm)],[c_192154,c_59]) ).
tcf(c_192286,plain,
multiplication(iPr_def_10,iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_192191,c_167965,c_177392]) ).
tcf(c_192303,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_11,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_192286,c_56]) ).
tcf(c_192317,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_11,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_192303,c_64]) ).
tcf(c_193169,plain,
multiplication(iPr_def_10,iPr_def_16) = zero,
inference(superposition,[status(thm)],[c_170462,c_192317]) ).
tcf(c_193364,plain,
addition(antidomain(zero),antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_16))))) = antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_16)))),
inference(superposition,[status(thm)],[c_193169,c_58]) ).
tcf(c_193395,plain,
addition(one,antidomain(multiplication(iPr_def_10,iPr_def_18))) = antidomain(multiplication(iPr_def_10,iPr_def_18)),
inference(light_normalisation,[status(thm)],[c_193364,c_139,c_140,c_161195]) ).
tcf(c_239812,plain,
( ( iPr_def_11 = multiplication(one,iPr_def_19) )
| ( iPr_def_11 != addition(iPr_def_11,zero) )
| ( multiplication(one,iPr_def_19) != addition(iPr_def_11,zero) ) ),
inference(instantiation,[status(thm)],[c_165425]) ).
tcf(c_264951,plain,
multiplication(antidomain(iPr_def_11),one) = multiplication(antidomain(iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_159704,c_177405]) ).
tcf(c_265315,plain,
multiplication(antidomain(iPr_def_11),one) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_264951,c_167453]) ).
tcf(c_265556,plain,
antidomain(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_265315,c_62]) ).
tcf(c_265599,plain,
multiplication(iPr_def_10,iPr_def_18) = multiplication(iPr_def_10,iPr_def_19),
inference(demodulation,[status(thm)],[c_177411,c_265556]) ).
tcf(c_291603,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_16)),one) = addition(one,antidomain(multiplication(X0,iPr_def_18))),
inference(superposition,[status(thm)],[c_160042,c_161783]) ).
tcf(c_291765,plain,
! [X0: $i] : addition(one,antidomain(multiplication(X0,iPr_def_16))) = addition(one,antidomain(multiplication(X0,iPr_def_18))),
inference(theory_normalisation,[status(thm)],[c_291603,c_54,c_55]) ).
tcf(c_313170,plain,
antidomain(multiplication(iPr_def_10,iPr_def_18)) = one,
inference(demodulation,[status(thm)],[c_193395,c_161755,c_291765]) ).
tcf(c_313188,plain,
multiplication(one,multiplication(iPr_def_10,iPr_def_18)) = zero,
inference(superposition,[status(thm)],[c_313170,c_59]) ).
tcf(c_313222,plain,
multiplication(iPr_def_10,iPr_def_18) = zero,
inference(demodulation,[status(thm)],[c_313188,c_167965,c_177392]) ).
tcf(c_313224,plain,
multiplication(iPr_def_10,iPr_def_19) = zero,
inference(demodulation,[status(thm)],[c_265599,c_313222]) ).
tcf(c_313478,plain,
multiplication(addition(iPr_def_11,iPr_def_10),iPr_def_19) = addition(iPr_def_11,zero),
inference(superposition,[status(thm)],[c_313224,c_178952]) ).
tcf(c_313494,plain,
multiplication(addition(iPr_def_10,iPr_def_11),iPr_def_19) = addition(iPr_def_11,zero),
inference(theory_normalisation,[status(thm)],[c_313478,c_54,c_55]) ).
tcf(c_313495,plain,
multiplication(one,iPr_def_19) = addition(iPr_def_11,zero),
inference(light_normalisation,[status(thm)],[c_313494,c_159704]) ).
tcf(c_313619,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_313495,c_239812,c_87971,c_7339,c_7338,c_1470,c_1469,c_1328,c_1266,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE097+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.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 18:58:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 123.87/20.46 % SZS status Started for theBenchmark.p
% 123.87/20.46 % SZS status Theorem for theBenchmark.p
% 123.87/20.46
% 123.87/20.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 123.87/20.46
% 123.87/20.46 % ------ iProver source info
% 123.87/20.46
% 123.87/20.46 % git: date: 2026-07-19 20:42:38 +0200
% 123.87/20.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 123.87/20.46 % git: non_committed_changes: false
% 123.87/20.46
% 123.87/20.46 % ------ Parsing...
% 123.87/20.46 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 123.87/20.46 %
% 123.87/20.46
% 123.87/20.46 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 123.87/20.46
% 123.87/20.46 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 123.87/20.46 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 123.87/20.46
% 123.87/20.46 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 123.87/20.46 % ------ Proving...
% 123.87/20.46 % ------ Problem Properties
% 123.87/20.46
% 123.87/20.46 %
% 123.87/20.46 % clauses 32
% 123.87/20.46 % conjectures 2
% 123.87/20.46 % EPR 2
% 123.87/20.46 % Horn 32
% 123.87/20.46 % unary 32
% 123.87/20.46 % binary 0
% 123.87/20.46 % lits 32
% 123.87/20.46 % lits eq 32
% 123.87/20.46 % fd_pure 0
% 123.87/20.46 % fd_pseudo 0
% 123.87/20.46 % fd_cond 0
% 123.87/20.46 % fd_pseudo_cond 0
% 123.87/20.46 % AC symbols 1
% 123.87/20.46
% 123.87/20.46 % ------ Schedule UEQ
% 123.87/20.46
% 123.87/20.46 % ------ Option_UEQ Time Limit: 10.
% 123.87/20.46
% 123.87/20.46
% 123.87/20.46 % ------
% 123.87/20.46 % Current options:
% 123.87/20.46 % ------
% 123.87/20.46
% 123.87/20.46
% 123.87/20.46 %
% 123.87/20.46
% 123.87/20.46 % ------ Proving...
% 123.87/20.46 % Proof_search_loop: time out after: 2594 full_loop iterations
% 123.87/20.46
% 123.87/20.46 % ------ Option_UEQ Time Limit: 15.
% 123.87/20.46
% 123.87/20.46
% 123.87/20.46 % ------
% 123.87/20.46 % Current options:
% 123.87/20.46 % ------
% 123.87/20.46
% 123.87/20.46
% 123.87/20.46 %
% 123.87/20.46
% 123.87/20.46 % ------ Proving...
% 123.87/20.46 %
% 123.87/20.46
% 123.87/20.46 % SZS status Theorem for theBenchmark.p
% 123.87/20.46
% 123.87/20.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 123.87/20.47
% 123.87/20.47
%------------------------------------------------------------------------------