%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE102+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 : n011.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 01:52:24 PM UTC 2026
% Result : Theorem 32.45s 23.23s
% Output : CNFRefutation 32.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 36
% Syntax : Number of formulae : 236 ( 232 unt; 16 def)
% Number of atoms : 726 ( 239 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 179 ( 0 sgn 176 !; 3 ?; 104 :)
% 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(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).
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(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero
=> multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero
=> multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero
& zero != multiplication(forward_diamond(X0,domain(X1)),domain(X2)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( zero = multiplication(domain(sK1),backward_diamond(sK0,domain(sK2)))
& zero != multiplication(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,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f43,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(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f56,plain,
zero = multiplication(domain(sK1),backward_diamond(sK0,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
zero != multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f53,f49,f49]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f64,plain,
zero != multiplication(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f57,f62,f45,f45]) ).
fof(f65,plain,
zero = multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))),
inference(definition_unfolding,[],[f56,f45,f59,f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
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,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
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,[],[f43]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f48]) ).
tcf(c_66,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))) != zero,
inference(cnf_transformation,[],[f64]) ).
tcf(c_67,negated_conjecture,
multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))) = zero,
inference(cnf_transformation,[],[f65]) ).
tcf(c_83,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_84,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).
tcf(c_131,definition,
iPr_def_10 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = antidomain(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_135,definition,
iPr_def_14 = coantidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_136,definition,
iPr_def_15 = coantidomain(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_137,definition,
iPr_def_16 = multiplication(iPr_def_15,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_138,definition,
iPr_def_17 = coantidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_139,definition,
iPr_def_18 = coantidomain(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_140,definition,
iPr_def_19 = multiplication(iPr_def_11,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_141,definition,
iPr_def_20 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_142,definition,
iPr_def_21 = antidomain(iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_143,definition,
iPr_def_22 = multiplication(sK0,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_144,definition,
iPr_def_23 = antidomain(iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_145,definition,
iPr_def_24 = antidomain(iPr_def_23),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_146,definition,
iPr_def_25 = multiplication(iPr_def_24,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_147,negated_conjecture,
iPr_def_19 = zero,
inference(demodulation,[status(thm)],[c_67,c_133,c_134,c_135,c_136,c_137,c_138,c_139,c_131,c_132,c_140]) ).
tcf(c_148,negated_conjecture,
iPr_def_25 != zero,
inference(demodulation,[status(thm)],[c_66,c_141,c_142,c_143,c_144,c_145,c_146]) ).
tcf(c_258,plain,
iPr_def_19 != iPr_def_25,
inference(light_normalisation,[status(thm)],[c_148,c_147]) ).
tcf(c_263,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_131,c_83]) ).
tcf(c_264,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_133,c_83]) ).
tcf(c_265,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_132,c_83]) ).
tcf(c_267,plain,
addition(iPr_def_11,iPr_def_20) = one,
inference(light_normalisation,[status(thm)],[c_265,c_141]) ).
tcf(c_268,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_264,c_134]) ).
tcf(c_269,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_263,c_132]) ).
tcf(c_270,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_11,iPr_def_20),
inference(demodulation,[status(thm)],[c_83,c_267]) ).
tcf(c_271,plain,
! [X0: $i] : addition(X0,iPr_def_19) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_147]) ).
tcf(c_272,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_11,iPr_def_20)) = X0,
inference(light_normalisation,[status(thm)],[c_54,c_267]) ).
tcf(c_273,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_20)) = X0,
inference(demodulation,[status(thm)],[c_272,c_56]) ).
tcf(c_274,plain,
! [X0: $i] : multiplication(addition(iPr_def_11,iPr_def_20),X0) = X0,
inference(light_normalisation,[status(thm)],[c_55,c_267]) ).
tcf(c_275,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_20,X0)) = X0,
inference(demodulation,[status(thm)],[c_274,c_57]) ).
tcf(c_280,plain,
! [X0: $i] : multiplication(iPr_def_19,X0) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_59,c_147]) ).
tcf(c_284,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(iPr_def_11,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_84,c_267]) ).
tcf(c_289,plain,
addition(iPr_def_14,coantidomain(iPr_def_14)) = addition(iPr_def_11,iPr_def_20),
inference(superposition,[status(thm)],[c_135,c_284]) ).
tcf(c_291,plain,
addition(iPr_def_17,coantidomain(iPr_def_17)) = addition(iPr_def_11,iPr_def_20),
inference(superposition,[status(thm)],[c_138,c_284]) ).
tcf(c_293,plain,
addition(iPr_def_11,iPr_def_20) = addition(iPr_def_17,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_291,c_139]) ).
tcf(c_294,plain,
addition(iPr_def_11,iPr_def_20) = addition(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_289,c_136]) ).
tcf(c_295,plain,
addition(iPr_def_19,multiplication(iPr_def_20,iPr_def_18)) = iPr_def_18,
inference(superposition,[status(thm)],[c_140,c_275]) ).
tcf(c_296,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_11,iPr_def_20),
inference(demodulation,[status(thm)],[c_267,c_269]) ).
tcf(c_298,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_268,c_269]) ).
tcf(c_299,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_60,c_147]) ).
tcf(c_302,plain,
multiplication(iPr_def_11,iPr_def_10) = iPr_def_19,
inference(superposition,[status(thm)],[c_132,c_299]) ).
tcf(c_303,plain,
multiplication(iPr_def_13,iPr_def_12) = iPr_def_19,
inference(superposition,[status(thm)],[c_134,c_299]) ).
tcf(c_304,plain,
multiplication(iPr_def_20,iPr_def_11) = iPr_def_19,
inference(superposition,[status(thm)],[c_141,c_299]) ).
tcf(c_305,plain,
multiplication(iPr_def_21,iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_142,c_299]) ).
tcf(c_313,plain,
addition(iPr_def_19,multiplication(iPr_def_20,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_302,c_275]) ).
tcf(c_320,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_63,c_147]) ).
tcf(c_321,plain,
multiplication(iPr_def_13,iPr_def_14) = iPr_def_19,
inference(superposition,[status(thm)],[c_135,c_320]) ).
tcf(c_323,plain,
multiplication(iPr_def_16,iPr_def_17) = iPr_def_19,
inference(superposition,[status(thm)],[c_138,c_320]) ).
tcf(c_328,plain,
! [X0: $i] : addition(iPr_def_19,X0) = X0,
inference(superposition,[status(thm)],[c_271,c_49]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_350,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK0,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_137,c_53]) ).
tcf(c_359,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_303,c_53]) ).
tcf(c_361,plain,
! [X0: $i] : multiplication(iPr_def_21,multiplication(iPr_def_20,X0)) = multiplication(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_305,c_53]) ).
tcf(c_370,plain,
! [X0: $i] : multiplication(iPr_def_21,multiplication(iPr_def_20,X0)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_361,c_280]) ).
tcf(c_372,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_359,c_280]) ).
tcf(c_430,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_270,c_296]) ).
tcf(c_445,plain,
addition(iPr_def_23,antidomain(iPr_def_23)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_144,c_430]) ).
tcf(c_448,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_23,iPr_def_24),
inference(light_normalisation,[status(thm)],[c_445,c_145]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_430,c_56]) ).
tcf(c_463,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_20)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_296,c_56]) ).
tcf(c_464,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_298,c_56]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] : addition(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) = iPr_def_19,
inference(superposition,[status(thm)],[c_56,c_299]) ).
tcf(c_485,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_10,iPr_def_11)) = X0,
inference(light_normalisation,[status(thm)],[c_463,c_273]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i] : addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(addition(iPr_def_10,iPr_def_11),X1),
inference(superposition,[status(thm)],[c_430,c_57]) ).
tcf(c_499,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_298,c_57]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(addition(X0,X1))),multiplication(X1,coantidomain(addition(X0,X1)))) = iPr_def_19,
inference(superposition,[status(thm)],[c_57,c_320]) ).
tcf(c_540,plain,
! [X0: $i] : addition(antidomain(iPr_def_19),antidomain(multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0)))))) = antidomain(multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0))))),
inference(superposition,[status(thm)],[c_372,c_61]) ).
tcf(c_631,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_17,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_293,c_296]) ).
tcf(c_633,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_17),multiplication(X0,iPr_def_18)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_631,c_56]) ).
tcf(c_634,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_631,c_57]) ).
tcf(c_636,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)),
inference(light_normalisation,[status(thm)],[c_634,c_499]) ).
tcf(c_637,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = addition(multiplication(X0,iPr_def_17),multiplication(X0,iPr_def_18)),
inference(light_normalisation,[status(thm)],[c_633,c_464]) ).
tcf(c_638,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_294,c_296]) ).
tcf(c_641,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_638,c_57]) ).
tcf(c_643,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)),
inference(light_normalisation,[status(thm)],[c_641,c_499]) ).
tcf(c_645,plain,
multiplication(iPr_def_20,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_295,c_328]) ).
tcf(c_649,plain,
multiplication(iPr_def_21,iPr_def_18) = iPr_def_19,
inference(superposition,[status(thm)],[c_645,c_370]) ).
tcf(c_760,plain,
! [X0: $i] : addition(multiplication(iPr_def_23,X0),multiplication(iPr_def_24,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_448,c_57]) ).
tcf(c_762,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = addition(multiplication(iPr_def_23,X0),multiplication(iPr_def_24,X0)),
inference(light_normalisation,[status(thm)],[c_760,c_499]) ).
tcf(c_764,plain,
multiplication(iPr_def_20,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_313,c_328]) ).
tcf(c_930,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_485,c_56]) ).
tcf(c_942,plain,
addition(multiplication(iPr_def_20,iPr_def_10),iPr_def_19) = iPr_def_20,
inference(superposition,[status(thm)],[c_304,c_930]) ).
tcf(c_952,plain,
addition(iPr_def_19,multiplication(iPr_def_20,iPr_def_10)) = iPr_def_20,
inference(theory_normalisation,[status(thm)],[c_942,c_50,c_49]) ).
tcf(c_953,plain,
addition(iPr_def_19,iPr_def_10) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_952,c_764]) ).
tcf(c_954,plain,
addition(iPr_def_10,iPr_def_19) = iPr_def_20,
inference(theory_normalisation,[status(thm)],[c_953,c_50,c_49]) ).
tcf(c_968,plain,
iPr_def_10 = iPr_def_20,
inference(demodulation,[status(thm)],[c_954,c_271]) ).
tcf(c_979,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_10,X0)) = X0,
inference(demodulation,[status(thm)],[c_275,c_968]) ).
tcf(c_981,plain,
antidomain(iPr_def_10) = iPr_def_21,
inference(demodulation,[status(thm)],[c_142,c_968]) ).
tcf(c_982,plain,
antidomain(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_141,c_968]) ).
tcf(c_983,plain,
iPr_def_11 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_981,c_132]) ).
tcf(c_985,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_979,c_50,c_49]) ).
tcf(c_992,plain,
multiplication(iPr_def_11,iPr_def_18) = iPr_def_19,
inference(demodulation,[status(thm)],[c_649,c_983]) ).
tcf(c_993,plain,
multiplication(sK0,iPr_def_11) = iPr_def_22,
inference(demodulation,[status(thm)],[c_143,c_983]) ).
tcf(c_1182,plain,
antidomain(addition(iPr_def_10,iPr_def_11)) = iPr_def_19,
inference(superposition,[status(thm)],[c_471,c_930]) ).
tcf(c_1447,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_430,c_334]) ).
tcf(c_1460,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_930,c_334]) ).
tcf(c_1467,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = X0,
inference(theory_normalisation,[status(thm)],[c_1460,c_50,c_49]) ).
tcf(c_1479,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_1447,c_50,c_49]) ).
tcf(c_1512,plain,
multiplication(iPr_def_15,iPr_def_22) = multiplication(iPr_def_16,iPr_def_11),
inference(superposition,[status(thm)],[c_993,c_350]) ).
tcf(c_1518,plain,
addition(iPr_def_19,antidomain(iPr_def_19)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1182,c_430]) ).
tcf(c_2158,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,iPr_def_10))) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_1467,c_56]) ).
tcf(c_2177,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_15,iPr_def_22),X0) = multiplication(iPr_def_16,multiplication(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_1512,c_53]) ).
tcf(c_2178,plain,
addition(multiplication(iPr_def_16,iPr_def_10),multiplication(iPr_def_15,iPr_def_22)) = iPr_def_16,
inference(superposition,[status(thm)],[c_1512,c_930]) ).
tcf(c_2181,plain,
addition(multiplication(iPr_def_15,iPr_def_22),multiplication(iPr_def_16,iPr_def_10)) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_2178,c_50,c_49]) ).
tcf(c_3345,plain,
addition(iPr_def_10,iPr_def_11) = antidomain(iPr_def_19),
inference(demodulation,[status(thm)],[c_1518,c_328]) ).
tcf(c_6052,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_461,c_464]) ).
tcf(c_6078,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,antidomain(iPr_def_10))) = addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_982,c_6052]) ).
tcf(c_6103,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = X0,
inference(light_normalisation,[status(thm)],[c_6078,c_132,c_930]) ).
tcf(c_6550,plain,
addition(multiplication(iPr_def_15,iPr_def_22),iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_2181,c_334]) ).
tcf(c_6563,plain,
addition(iPr_def_16,multiplication(iPr_def_15,iPr_def_22)) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_6550,c_50,c_49]) ).
tcf(c_6592,plain,
addition(multiplication(iPr_def_16,coantidomain(iPr_def_16)),multiplication(multiplication(iPr_def_15,iPr_def_22),coantidomain(iPr_def_16))) = iPr_def_19,
inference(superposition,[status(thm)],[c_6563,c_506]) ).
tcf(c_6607,plain,
addition(iPr_def_19,multiplication(multiplication(iPr_def_15,iPr_def_22),iPr_def_17)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_6592,c_138,c_323]) ).
tcf(c_8274,plain,
addition(multiplication(antidomain(iPr_def_13),iPr_def_12),iPr_def_19) = antidomain(iPr_def_13),
inference(superposition,[status(thm)],[c_299,c_6103]) ).
tcf(c_8299,plain,
addition(iPr_def_19,multiplication(antidomain(iPr_def_13),iPr_def_12)) = antidomain(iPr_def_13),
inference(theory_normalisation,[status(thm)],[c_8274,c_50,c_49]) ).
tcf(c_8557,plain,
multiplication(antidomain(iPr_def_13),iPr_def_12) = antidomain(iPr_def_13),
inference(demodulation,[status(thm)],[c_8299,c_328]) ).
tcf(c_9349,plain,
multiplication(iPr_def_16,multiplication(iPr_def_11,iPr_def_17)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_6607,c_328,c_2177]) ).
tcf(c_10372,plain,
! [X0: $i,X1: $i] : addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = addition(multiplication(iPr_def_12,X1),multiplication(iPr_def_13,X1)),
inference(demodulation,[status(thm)],[c_496,c_499]) ).
tcf(c_10375,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = addition(iPr_def_19,multiplication(antidomain(antidomain(X0)),X0)),
inference(superposition,[status(thm)],[c_299,c_10372]) ).
tcf(c_10427,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(antidomain(iPr_def_10),X0)) = addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_982,c_10372]) ).
tcf(c_10451,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_10427,c_132,c_985]) ).
tcf(c_10704,plain,
! [X0: $i] : addition(iPr_def_19,multiplication(antidomain(antidomain(X0)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_10375,c_10451]) ).
tcf(c_10705,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_10704,c_328]) ).
tcf(c_10713,plain,
multiplication(antidomain(iPr_def_13),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_134,c_10705]) ).
tcf(c_10792,plain,
antidomain(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_8557,c_10713]) ).
tcf(c_10990,plain,
multiplication(iPr_def_12,iPr_def_13) = iPr_def_19,
inference(superposition,[status(thm)],[c_10792,c_299]) ).
tcf(c_13428,plain,
addition(multiplication(iPr_def_12,iPr_def_14),iPr_def_19) = iPr_def_14,
inference(superposition,[status(thm)],[c_321,c_10451]) ).
tcf(c_13469,plain,
addition(iPr_def_19,multiplication(iPr_def_12,iPr_def_14)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_13428,c_50,c_49]) ).
tcf(c_13825,plain,
multiplication(iPr_def_12,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_13469,c_328]) ).
tcf(c_13830,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(iPr_def_14,X0)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_13825,c_53]) ).
tcf(c_23857,plain,
! [X0: $i] : addition(addition(iPr_def_10,iPr_def_11),antidomain(multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0)))))) = antidomain(multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0))))),
inference(light_normalisation,[status(thm)],[c_540,c_3345]) ).
tcf(c_23858,plain,
! [X0: $i] : antidomain(multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0))))) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_23857,c_50,c_1479]) ).
tcf(c_23898,plain,
! [X0: $i] : multiplication(addition(iPr_def_10,iPr_def_11),multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0))))) = iPr_def_19,
inference(superposition,[status(thm)],[c_23858,c_299]) ).
tcf(c_25049,plain,
! [X0: $i] : multiplication(iPr_def_13,antidomain(antidomain(multiplication(iPr_def_12,X0)))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_23898,c_57,c_985]) ).
tcf(c_83980,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_636,c_10451]) ).
tcf(c_84046,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),X0) = X0,
inference(superposition,[status(thm)],[c_83980,c_334]) ).
tcf(c_84076,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_17,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_84046,c_50,c_49]) ).
tcf(c_84527,plain,
! [X0: $i] : addition(multiplication(antidomain(X0),X0),multiplication(antidomain(X0),multiplication(iPr_def_17,X0))) = iPr_def_19,
inference(superposition,[status(thm)],[c_84076,c_471]) ).
tcf(c_84630,plain,
! [X0: $i] : addition(iPr_def_19,multiplication(antidomain(X0),multiplication(iPr_def_17,X0))) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_84527,c_299]) ).
tcf(c_84770,plain,
! [X0: $i] : multiplication(antidomain(X0),multiplication(iPr_def_17,X0)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_84630,c_328]) ).
tcf(c_84774,plain,
multiplication(iPr_def_11,multiplication(iPr_def_17,iPr_def_10)) = iPr_def_19,
inference(superposition,[status(thm)],[c_132,c_84770]) ).
tcf(c_85551,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_17),multiplication(X0,iPr_def_18)) = X0,
inference(light_normalisation,[status(thm)],[c_637,c_6103]) ).
tcf(c_85565,plain,
addition(multiplication(iPr_def_11,iPr_def_17),iPr_def_19) = iPr_def_11,
inference(superposition,[status(thm)],[c_992,c_85551]) ).
tcf(c_85613,plain,
addition(iPr_def_19,multiplication(iPr_def_11,iPr_def_17)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_85565,c_50,c_49]) ).
tcf(c_85897,plain,
addition(multiplication(iPr_def_11,iPr_def_17),iPr_def_19) = multiplication(iPr_def_11,iPr_def_17),
inference(superposition,[status(thm)],[c_84774,c_2158]) ).
tcf(c_85903,plain,
addition(iPr_def_19,multiplication(iPr_def_11,iPr_def_17)) = multiplication(iPr_def_11,iPr_def_17),
inference(theory_normalisation,[status(thm)],[c_85897,c_50,c_49]) ).
tcf(c_85904,plain,
multiplication(iPr_def_11,iPr_def_17) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_85903,c_85613]) ).
tcf(c_85942,plain,
multiplication(iPr_def_16,iPr_def_11) = iPr_def_19,
inference(demodulation,[status(thm)],[c_9349,c_85904]) ).
tcf(c_85943,plain,
multiplication(iPr_def_15,iPr_def_22) = iPr_def_19,
inference(demodulation,[status(thm)],[c_1512,c_85942]) ).
tcf(c_86849,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_643,c_10451]) ).
tcf(c_86925,plain,
addition(multiplication(iPr_def_14,iPr_def_22),iPr_def_19) = iPr_def_22,
inference(superposition,[status(thm)],[c_85943,c_86849]) ).
tcf(c_86977,plain,
addition(iPr_def_19,multiplication(iPr_def_14,iPr_def_22)) = iPr_def_22,
inference(theory_normalisation,[status(thm)],[c_86925,c_50,c_49]) ).
tcf(c_101905,plain,
multiplication(iPr_def_14,iPr_def_22) = iPr_def_22,
inference(demodulation,[status(thm)],[c_86977,c_328]) ).
tcf(c_101947,plain,
multiplication(iPr_def_12,iPr_def_22) = iPr_def_22,
inference(superposition,[status(thm)],[c_101905,c_13830]) ).
tcf(c_102030,plain,
multiplication(iPr_def_13,antidomain(antidomain(iPr_def_22))) = iPr_def_19,
inference(superposition,[status(thm)],[c_101947,c_25049]) ).
tcf(c_102043,plain,
multiplication(iPr_def_13,iPr_def_24) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_102030,c_144,c_145]) ).
tcf(c_104285,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_24,X0)) = multiplication(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_102043,c_53]) ).
tcf(c_104313,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_24,X0)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_104285,c_280]) ).
tcf(c_104772,plain,
multiplication(iPr_def_13,iPr_def_25) = iPr_def_19,
inference(superposition,[status(thm)],[c_146,c_104313]) ).
tcf(c_106166,plain,
addition(multiplication(iPr_def_12,iPr_def_25),iPr_def_19) = iPr_def_25,
inference(superposition,[status(thm)],[c_104772,c_10451]) ).
tcf(c_106174,plain,
addition(iPr_def_19,multiplication(iPr_def_12,iPr_def_25)) = iPr_def_25,
inference(theory_normalisation,[status(thm)],[c_106166,c_50,c_49]) ).
tcf(c_128415,plain,
! [X0: $i] : addition(multiplication(iPr_def_23,X0),multiplication(iPr_def_24,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_762,c_10451]) ).
tcf(c_128463,plain,
addition(multiplication(iPr_def_23,iPr_def_13),iPr_def_25) = iPr_def_13,
inference(superposition,[status(thm)],[c_146,c_128415]) ).
tcf(c_128560,plain,
addition(iPr_def_25,multiplication(iPr_def_23,iPr_def_13)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_128463,c_50,c_49]) ).
tcf(c_128654,plain,
addition(iPr_def_25,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_128560,c_334]) ).
tcf(c_128672,plain,
addition(iPr_def_13,iPr_def_25) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_128654,c_50,c_49]) ).
tcf(c_129101,plain,
addition(multiplication(antidomain(iPr_def_13),iPr_def_13),multiplication(antidomain(iPr_def_13),iPr_def_25)) = iPr_def_19,
inference(superposition,[status(thm)],[c_128672,c_471]) ).
tcf(c_129121,plain,
iPr_def_19 = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_129101,c_10792,c_10990,c_106174]) ).
tcf(c_129122,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_129121,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE102+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/16.47 % CPULimit : 300
% 0.03/16.47 % WCLimit : 300
% 0.03/16.47 % DateTime : Wed Sep 23 18:55:48 UTC 2026
% 0.03/16.47 % CPUTime :
% 0.03/16.47 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/16.49 Running first-order theorem proving
% 0.03/16.49 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
% 0.03/16.49
% 0.03/16.49 % ======== iProver multi-core TPTP/SMT =========
% 0.03/16.49
% 0.03/16.49 % Detected problem language: tptp
% 0.14/16.50 % Proving...
% 32.45/23.23 % SZS status Started for theBenchmark.p
% 32.45/23.23 % SZS status Theorem for theBenchmark.p
% 32.45/23.23
% 32.45/23.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.45/23.23
% 32.45/23.23 % ------ iProver source info
% 32.45/23.23
% 32.45/23.23 % git: date: 2026-07-19 20:42:38 +0200
% 32.45/23.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.45/23.23 % git: non_committed_changes: false
% 32.45/23.23
% 32.45/23.23 % ------ Parsing...
% 32.45/23.23 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 32.45/23.23 %
% 32.45/23.23
% 32.45/23.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 32.45/23.23
% 32.45/23.23 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 32.45/23.23 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.45/23.23
% 32.45/23.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 32.45/23.23 % ------ Proving...
% 32.45/23.23 % ------ Problem Properties
% 32.45/23.23
% 32.45/23.23 %
% 32.45/23.23 % clauses 35
% 32.45/23.23 % conjectures 2
% 32.45/23.23 % EPR 2
% 32.45/23.23 % Horn 35
% 32.45/23.23 % unary 35
% 32.45/23.23 % binary 0
% 32.45/23.23 % lits 35
% 32.45/23.23 % lits eq 35
% 32.45/23.23 % fd_pure 0
% 32.45/23.23 % fd_pseudo 0
% 32.45/23.23 % fd_cond 0
% 32.45/23.23 % fd_pseudo_cond 0
% 32.45/23.23 % AC symbols 1
% 32.45/23.23
% 32.45/23.23 % ------ Schedule UEQ
% 32.45/23.23
% 32.45/23.23 % ------ Option_UEQ Time Limit: 10.
% 32.45/23.23
% 32.45/23.23
% 32.45/23.23 % ------
% 32.45/23.23 % Current options:
% 32.45/23.23 % ------
% 32.45/23.23
% 32.45/23.23
% 32.45/23.23 %
% 32.45/23.23
% 32.45/23.23 % ------ Proving...
% 32.45/23.23 %
% 32.45/23.23
% 32.45/23.23 % SZS status Theorem for theBenchmark.p
% 32.45/23.23
% 32.45/23.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.45/23.23
% 32.45/23.23
%------------------------------------------------------------------------------