%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE104+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 : n009.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 01:52:25 PM UTC 2026
% Result : Theorem 69.25s 10.36s
% Output : CNFRefutation 69.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 52
% Syntax : Number of formulae : 396 ( 392 unt; 28 def)
% Number of atoms : 1330 ( 399 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 267 ( 0 sgn 264 !; 3 ?; 175 :)
% 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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
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(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',complement) ).
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(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_box) ).
fof(f26,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_box) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(domain(X1),backward_box(X0,domain(X2))) = one
=> addition(forward_box(X0,domain(X1)),domain(X2)) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(domain(X1),backward_box(X0,domain(X2))) = one
=> addition(forward_box(X0,domain(X1)),domain(X2)) = one ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( addition(domain(X1),backward_box(X0,domain(X2))) = one
& one != addition(forward_box(X0,domain(X1)),domain(X2)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( one = addition(domain(sK1),backward_box(sK0,domain(sK2)))
& one != addition(forward_box(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,
one = addition(domain(sK1),backward_box(sK0,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
one != addition(forward_box(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,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,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(f49,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f50,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f52,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f53,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f54,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f55,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f57,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f50,f42]) ).
fof(f58,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f52,f56,f56]) ).
fof(f59,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X0)))))),
inference(definition_unfolding,[],[f44,f57,f58,f57]) ).
fof(f60,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f51,f42,f42]) ).
fof(f61,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))))))),
inference(definition_unfolding,[],[f43,f57,f60,f57]) ).
fof(f62,plain,
one != addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1))))))))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f32,f61,f42,f42]) ).
fof(f63,plain,
one = addition(antidomain(antidomain(sK1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))),sK0))))))),
inference(definition_unfolding,[],[f31,f42,f59,f42]) ).
tcf(c_49,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1))))))))))))),antidomain(antidomain(sK2))) != one,
inference(cnf_transformation,[],[f62]) ).
tcf(c_50,negated_conjecture,
addition(antidomain(antidomain(sK1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))),sK0))))))) = one,
inference(cnf_transformation,[],[f63]) ).
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] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,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,[],[f48]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f49]) ).
tcf(c_65,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f53]) ).
tcf(c_66,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f55]) ).
tcf(c_83,negated_conjecture,
addition(antidomain(antidomain(sK2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1)))))))))))))) != one,
inference(theory_normalisation,[status(thm)],[c_49,c_54,c_55]) ).
tcf(c_84,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_56,c_54,c_55]) ).
tcf(c_85,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 = antidomain(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 = multiplication(sK0,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_142,definition,
iPr_def_20 = antidomain(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_143,definition,
iPr_def_21 = antidomain(iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_144,definition,
iPr_def_22 = antidomain(iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_145,definition,
iPr_def_23 = antidomain(iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_146,definition,
iPr_def_24 = antidomain(iPr_def_23),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_147,definition,
iPr_def_25 = addition(iPr_def_11,iPr_def_24),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_148,definition,
iPr_def_26 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_149,definition,
iPr_def_27 = antidomain(iPr_def_26),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_150,definition,
iPr_def_28 = antidomain(iPr_def_27),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_151,definition,
iPr_def_29 = coantidomain(iPr_def_28),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_152,definition,
iPr_def_30 = coantidomain(iPr_def_29),
introduced(definition,[new_symbols(definition,[iPr_def_30])],[]) ).
tcf(c_153,definition,
iPr_def_31 = multiplication(iPr_def_30,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_31])],[]) ).
tcf(c_154,definition,
iPr_def_32 = coantidomain(iPr_def_31),
introduced(definition,[new_symbols(definition,[iPr_def_32])],[]) ).
tcf(c_155,definition,
iPr_def_33 = coantidomain(iPr_def_32),
introduced(definition,[new_symbols(definition,[iPr_def_33])],[]) ).
tcf(c_156,definition,
iPr_def_34 = antidomain(iPr_def_33),
introduced(definition,[new_symbols(definition,[iPr_def_34])],[]) ).
tcf(c_157,definition,
iPr_def_35 = antidomain(iPr_def_34),
introduced(definition,[new_symbols(definition,[iPr_def_35])],[]) ).
tcf(c_158,definition,
iPr_def_36 = antidomain(iPr_def_35),
introduced(definition,[new_symbols(definition,[iPr_def_36])],[]) ).
tcf(c_159,definition,
iPr_def_37 = addition(iPr_def_13,iPr_def_36),
introduced(definition,[new_symbols(definition,[iPr_def_37])],[]) ).
tcf(c_160,negated_conjecture,
iPr_def_25 != one,
inference(demodulation,[status(thm)],[c_83,c_134,c_135,c_136,c_137,c_138,c_139,c_140,c_141,c_142,c_143,c_144,c_145,c_146,c_132,c_133,c_147]) ).
tcf(c_161,negated_conjecture,
iPr_def_37 = one,
inference(demodulation,[status(thm)],[c_50,c_148,c_149,c_150,c_151,c_152,c_153,c_154,c_155,c_156,c_157,c_158,c_159]) ).
tcf(c_294,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_295,plain,
iPr_def_25 != iPr_def_37,
inference(light_normalisation,[status(thm)],[c_160,c_161]) ).
tcf(c_296,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_84,c_161]) ).
tcf(c_297,plain,
addition(iPr_def_29,coantidomain(iPr_def_29)) = iPr_def_37,
inference(superposition,[status(thm)],[c_151,c_296]) ).
tcf(c_298,plain,
addition(iPr_def_29,iPr_def_30) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_297,c_152]) ).
tcf(c_302,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_85,c_161]) ).
tcf(c_320,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = iPr_def_37,
inference(superposition,[status(thm)],[c_134,c_302]) ).
tcf(c_321,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = iPr_def_37,
inference(superposition,[status(thm)],[c_132,c_302]) ).
tcf(c_322,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = iPr_def_37,
inference(superposition,[status(thm)],[c_133,c_302]) ).
tcf(c_323,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = iPr_def_37,
inference(superposition,[status(thm)],[c_135,c_302]) ).
tcf(c_329,plain,
addition(iPr_def_20,antidomain(iPr_def_20)) = iPr_def_37,
inference(superposition,[status(thm)],[c_142,c_302]) ).
tcf(c_330,plain,
addition(iPr_def_21,antidomain(iPr_def_21)) = iPr_def_37,
inference(superposition,[status(thm)],[c_143,c_302]) ).
tcf(c_334,plain,
addition(iPr_def_26,antidomain(iPr_def_26)) = iPr_def_37,
inference(superposition,[status(thm)],[c_148,c_302]) ).
tcf(c_338,plain,
addition(iPr_def_26,iPr_def_27) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_334,c_149]) ).
tcf(c_341,plain,
addition(iPr_def_21,iPr_def_22) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_330,c_144]) ).
tcf(c_342,plain,
addition(iPr_def_20,iPr_def_21) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_329,c_143]) ).
tcf(c_347,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_323,c_136]) ).
tcf(c_348,plain,
addition(iPr_def_11,iPr_def_26) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_322,c_148]) ).
tcf(c_349,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_321,c_133]) ).
tcf(c_350,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_320,c_135]) ).
tcf(c_352,plain,
addition(iPr_def_34,antidomain(iPr_def_34)) = iPr_def_37,
inference(superposition,[status(thm)],[c_156,c_302]) ).
tcf(c_353,plain,
addition(iPr_def_34,iPr_def_35) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_352,c_157]) ).
tcf(c_354,plain,
addition(iPr_def_35,antidomain(iPr_def_35)) = iPr_def_37,
inference(superposition,[status(thm)],[c_157,c_302]) ).
tcf(c_355,plain,
addition(iPr_def_35,iPr_def_36) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_354,c_158]) ).
tcf(c_357,plain,
! [X0: $i] : multiplication(iPr_def_37,X0) = X0,
inference(light_normalisation,[status(thm)],[c_58,c_161]) ).
tcf(c_358,plain,
! [X0: $i] : multiplication(X0,iPr_def_37) = X0,
inference(light_normalisation,[status(thm)],[c_59,c_161]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i] : addition(coantidomain(X0),addition(X1,coantidomain(coantidomain(X0)))) = addition(X1,iPr_def_37),
inference(superposition,[status(thm)],[c_296,c_294]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(X1,antidomain(antidomain(X0)))) = addition(X1,iPr_def_37),
inference(superposition,[status(thm)],[c_302,c_294]) ).
tcf(c_422,plain,
multiplication(iPr_def_28,iPr_def_29) = zero,
inference(superposition,[status(thm)],[c_151,c_62]) ).
tcf(c_423,plain,
multiplication(iPr_def_29,iPr_def_30) = zero,
inference(superposition,[status(thm)],[c_152,c_62]) ).
tcf(c_424,plain,
multiplication(iPr_def_31,iPr_def_32) = zero,
inference(superposition,[status(thm)],[c_154,c_62]) ).
tcf(c_425,plain,
multiplication(iPr_def_32,iPr_def_33) = zero,
inference(superposition,[status(thm)],[c_155,c_62]) ).
tcf(c_426,plain,
coantidomain(iPr_def_37) = zero,
inference(superposition,[status(thm)],[c_62,c_357]) ).
tcf(c_428,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_28,iPr_def_29)) = X0,
inference(demodulation,[status(thm)],[c_67,c_422]) ).
tcf(c_429,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_28,iPr_def_29)) = multiplication(iPr_def_28,iPr_def_29),
inference(demodulation,[status(thm)],[c_66,c_422]) ).
tcf(c_430,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_28,iPr_def_29),X0) = multiplication(iPr_def_28,iPr_def_29),
inference(demodulation,[status(thm)],[c_65,c_422]) ).
tcf(c_431,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_28,iPr_def_29),
inference(light_normalisation,[status(thm)],[c_64,c_422]) ).
tcf(c_434,plain,
multiplication(iPr_def_10,sK2) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_132,c_431]) ).
tcf(c_435,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_133,c_431]) ).
tcf(c_436,plain,
multiplication(iPr_def_13,iPr_def_12) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_135,c_431]) ).
tcf(c_437,plain,
multiplication(iPr_def_14,iPr_def_13) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_136,c_431]) ).
tcf(c_443,plain,
multiplication(iPr_def_21,iPr_def_20) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_143,c_431]) ).
tcf(c_444,plain,
multiplication(iPr_def_22,iPr_def_21) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_144,c_431]) ).
tcf(c_447,plain,
multiplication(iPr_def_26,iPr_def_11) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_148,c_431]) ).
tcf(c_448,plain,
multiplication(iPr_def_27,iPr_def_26) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_149,c_431]) ).
tcf(c_450,plain,
multiplication(iPr_def_28,iPr_def_29) = multiplication(iPr_def_34,iPr_def_33),
inference(superposition,[status(thm)],[c_156,c_431]) ).
tcf(c_451,plain,
multiplication(iPr_def_28,iPr_def_29) = multiplication(iPr_def_35,iPr_def_34),
inference(superposition,[status(thm)],[c_157,c_431]) ).
tcf(c_452,plain,
multiplication(iPr_def_28,iPr_def_29) = multiplication(iPr_def_36,iPr_def_35),
inference(superposition,[status(thm)],[c_158,c_431]) ).
tcf(c_453,plain,
multiplication(iPr_def_28,iPr_def_29) = antidomain(iPr_def_37),
inference(superposition,[status(thm)],[c_431,c_358]) ).
tcf(c_454,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_431,c_435]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i] : addition(coantidomain(X0),addition(coantidomain(coantidomain(X0)),X1)) = addition(iPr_def_37,X1),
inference(superposition,[status(thm)],[c_296,c_54]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(iPr_def_37,X1),
inference(superposition,[status(thm)],[c_302,c_54]) ).
tcf(c_483,plain,
multiplication(iPr_def_11,iPr_def_10) = coantidomain(iPr_def_37),
inference(light_normalisation,[status(thm)],[c_426,c_422,c_435]) ).
tcf(c_484,plain,
addition(multiplication(iPr_def_11,iPr_def_10),coantidomain(multiplication(iPr_def_11,iPr_def_10))) = iPr_def_37,
inference(superposition,[status(thm)],[c_483,c_296]) ).
tcf(c_485,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_350,c_54]) ).
tcf(c_496,plain,
multiplication(iPr_def_11,iPr_def_10) = antidomain(iPr_def_37),
inference(light_normalisation,[status(thm)],[c_453,c_435]) ).
tcf(c_497,plain,
addition(multiplication(iPr_def_11,iPr_def_10),antidomain(multiplication(iPr_def_11,iPr_def_10))) = iPr_def_37,
inference(superposition,[status(thm)],[c_496,c_302]) ).
tcf(c_515,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(coantidomain(coantidomain(X0)),iPr_def_37),
inference(superposition,[status(thm)],[c_53,c_391]) ).
tcf(c_530,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(iPr_def_37,coantidomain(coantidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_515,c_54,c_55]) ).
tcf(c_531,plain,
! [X0: $i] : addition(iPr_def_37,coantidomain(coantidomain(X0))) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_530,c_296]) ).
tcf(c_535,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,coantidomain(coantidomain(X0)))) = iPr_def_37,
inference(demodulation,[status(thm)],[c_531,c_485]) ).
tcf(c_538,plain,
addition(iPr_def_12,addition(iPr_def_13,coantidomain(iPr_def_32))) = iPr_def_37,
inference(superposition,[status(thm)],[c_154,c_535]) ).
tcf(c_544,plain,
addition(iPr_def_12,addition(iPr_def_13,iPr_def_33)) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_538,c_155]) ).
tcf(c_572,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(antidomain(X0)),iPr_def_37),
inference(superposition,[status(thm)],[c_53,c_392]) ).
tcf(c_617,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_37,antidomain(antidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_572,c_54,c_55]) ).
tcf(c_618,plain,
! [X0: $i] : addition(iPr_def_37,antidomain(antidomain(X0))) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_617,c_302]) ).
tcf(c_622,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,antidomain(antidomain(X0)))) = iPr_def_37,
inference(demodulation,[status(thm)],[c_618,c_485]) ).
tcf(c_625,plain,
addition(iPr_def_12,addition(iPr_def_13,antidomain(iPr_def_11))) = iPr_def_37,
inference(superposition,[status(thm)],[c_133,c_622]) ).
tcf(c_637,plain,
addition(iPr_def_12,addition(iPr_def_13,antidomain(iPr_def_26))) = iPr_def_37,
inference(superposition,[status(thm)],[c_148,c_622]) ).
tcf(c_640,plain,
addition(iPr_def_12,addition(iPr_def_13,antidomain(iPr_def_34))) = iPr_def_37,
inference(superposition,[status(thm)],[c_156,c_622]) ).
tcf(c_648,plain,
addition(iPr_def_12,addition(iPr_def_13,iPr_def_35)) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_640,c_157]) ).
tcf(c_650,plain,
addition(iPr_def_12,addition(iPr_def_13,iPr_def_27)) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_637,c_149]) ).
tcf(c_660,plain,
addition(iPr_def_12,addition(iPr_def_13,iPr_def_26)) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_625,c_148]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] : addition(coantidomain(X0),addition(coantidomain(coantidomain(X0)),X1)) = addition(iPr_def_12,addition(iPr_def_13,X1)),
inference(demodulation,[status(thm)],[c_457,c_485]) ).
tcf(c_684,plain,
! [X0: $i] : addition(iPr_def_32,addition(coantidomain(iPr_def_32),X0)) = addition(iPr_def_12,addition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_154,c_667]) ).
tcf(c_692,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(iPr_def_32,addition(iPr_def_33,X0)),
inference(light_normalisation,[status(thm)],[c_684,c_155]) ).
tcf(c_707,plain,
! [X0: $i] : multiplication(iPr_def_30,multiplication(sK0,X0)) = multiplication(iPr_def_31,X0),
inference(superposition,[status(thm)],[c_153,c_60]) ).
tcf(c_720,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_36,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_159,c_51]) ).
tcf(c_729,plain,
! [X0: $i] : addition(multiplication(iPr_def_26,X0),multiplication(iPr_def_27,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_338,c_51]) ).
tcf(c_732,plain,
! [X0: $i] : addition(multiplication(iPr_def_21,X0),multiplication(iPr_def_22,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_341,c_51]) ).
tcf(c_738,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_14,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_347,c_51]) ).
tcf(c_739,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_26,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_348,c_51]) ).
tcf(c_740,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_349,c_51]) ).
tcf(c_741,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_350,c_51]) ).
tcf(c_743,plain,
! [X0: $i] : addition(multiplication(iPr_def_34,X0),multiplication(iPr_def_35,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_353,c_51]) ).
tcf(c_744,plain,
! [X0: $i] : addition(multiplication(iPr_def_35,X0),multiplication(iPr_def_36,X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_355,c_51]) ).
tcf(c_756,plain,
! [X0: $i] : addition(multiplication(iPr_def_35,X0),multiplication(iPr_def_36,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_744,c_357]) ).
tcf(c_757,plain,
! [X0: $i] : addition(multiplication(iPr_def_34,X0),multiplication(iPr_def_35,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_743,c_357]) ).
tcf(c_758,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_741,c_357]) ).
tcf(c_759,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_740,c_357]) ).
tcf(c_760,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_26,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_739,c_357]) ).
tcf(c_761,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_14,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_738,c_357]) ).
tcf(c_767,plain,
! [X0: $i] : addition(multiplication(iPr_def_21,X0),multiplication(iPr_def_22,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_732,c_357]) ).
tcf(c_770,plain,
! [X0: $i] : addition(multiplication(iPr_def_26,X0),multiplication(iPr_def_27,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_729,c_357]) ).
tcf(c_774,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_36,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_720,c_357]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_296,c_52]) ).
tcf(c_798,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_29),multiplication(X0,iPr_def_30)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_298,c_52]) ).
tcf(c_809,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_20),multiplication(X0,iPr_def_21)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_342,c_52]) ).
tcf(c_815,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_26)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_348,c_52]) ).
tcf(c_816,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_11)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_349,c_52]) ).
tcf(c_817,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_350,c_52]) ).
tcf(c_819,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_34),multiplication(X0,iPr_def_35)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_353,c_52]) ).
tcf(c_835,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_34),multiplication(X0,iPr_def_35)) = X0,
inference(light_normalisation,[status(thm)],[c_819,c_358]) ).
tcf(c_836,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = X0,
inference(light_normalisation,[status(thm)],[c_817,c_358]) ).
tcf(c_837,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_11)) = X0,
inference(light_normalisation,[status(thm)],[c_816,c_358]) ).
tcf(c_838,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_26)) = X0,
inference(light_normalisation,[status(thm)],[c_815,c_358]) ).
tcf(c_844,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_20),multiplication(X0,iPr_def_21)) = X0,
inference(light_normalisation,[status(thm)],[c_809,c_358]) ).
tcf(c_851,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_29),multiplication(X0,iPr_def_30)) = X0,
inference(light_normalisation,[status(thm)],[c_798,c_358]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = X0,
inference(light_normalisation,[status(thm)],[c_793,c_358]) ).
tcf(c_893,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(light_normalisation,[status(thm)],[c_422,c_435]) ).
tcf(c_894,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_29,iPr_def_30),
inference(light_normalisation,[status(thm)],[c_423,c_893]) ).
tcf(c_896,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_29,multiplication(iPr_def_30,X0)),
inference(superposition,[status(thm)],[c_894,c_60]) ).
tcf(c_898,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_31,iPr_def_32),
inference(light_normalisation,[status(thm)],[c_424,c_893]) ).
tcf(c_900,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_31,multiplication(iPr_def_32,X0)),
inference(superposition,[status(thm)],[c_898,c_60]) ).
tcf(c_901,plain,
! [X0: $i] : multiplication(iPr_def_29,multiplication(iPr_def_30,X0)) = multiplication(iPr_def_31,multiplication(iPr_def_32,X0)),
inference(light_normalisation,[status(thm)],[c_900,c_896]) ).
tcf(c_903,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_32,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_425,c_893]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_12,X0),addition(multiplication(iPr_def_13,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_758,c_54]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_12,X0),addition(X1,multiplication(iPr_def_13,X0))) = addition(X1,X0),
inference(superposition,[status(thm)],[c_758,c_294]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),X2)) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),X2),
inference(superposition,[status(thm)],[c_63,c_51]) ).
tcf(c_1093,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(light_normalisation,[status(thm)],[c_428,c_435]) ).
tcf(c_1104,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_1093,c_55]) ).
tcf(c_1108,plain,
coantidomain(multiplication(iPr_def_11,iPr_def_10)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_484,c_1104]) ).
tcf(c_1109,plain,
antidomain(multiplication(iPr_def_11,iPr_def_10)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_497,c_1104]) ).
tcf(c_1139,plain,
multiplication(iPr_def_10,sK2) = multiplication(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_434,c_435]) ).
tcf(c_1142,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_10,multiplication(sK2,X0)),
inference(superposition,[status(thm)],[c_1139,c_60]) ).
tcf(c_1143,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK2,X0)) = multiplication(iPr_def_29,multiplication(iPr_def_30,X0)),
inference(light_normalisation,[status(thm)],[c_1142,c_896]) ).
tcf(c_1246,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_436,c_435]) ).
tcf(c_1249,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_13,multiplication(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_1246,c_60]) ).
tcf(c_1250,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_14,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_1246,c_761]) ).
tcf(c_1273,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_437,c_435]) ).
tcf(c_1421,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_21,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_443,c_435]) ).
tcf(c_1430,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_22,iPr_def_21),
inference(light_normalisation,[status(thm)],[c_444,c_435]) ).
tcf(c_1454,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_26,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_447,c_435]) ).
tcf(c_1463,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_27,iPr_def_26),
inference(light_normalisation,[status(thm)],[c_448,c_435]) ).
tcf(c_1480,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_22,iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_1421,c_767]) ).
tcf(c_1532,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_27,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1454,c_770]) ).
tcf(c_1589,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_34,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_450,c_435]) ).
tcf(c_1602,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_35,iPr_def_34),
inference(light_normalisation,[status(thm)],[c_451,c_435]) ).
tcf(c_1605,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_35,multiplication(iPr_def_34,X0)),
inference(superposition,[status(thm)],[c_1602,c_60]) ).
tcf(c_1607,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_36,iPr_def_34)) = iPr_def_34,
inference(superposition,[status(thm)],[c_1602,c_756]) ).
tcf(c_1609,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_35,multiplication(iPr_def_34,X0)),
inference(light_normalisation,[status(thm)],[c_1605,c_1249]) ).
tcf(c_1612,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_36,iPr_def_35),
inference(light_normalisation,[status(thm)],[c_452,c_435]) ).
tcf(c_1624,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,addition(iPr_def_13,iPr_def_33))) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_544,c_52]) ).
tcf(c_1628,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,addition(iPr_def_13,iPr_def_33))) = X0,
inference(light_normalisation,[status(thm)],[c_1624,c_358]) ).
tcf(c_1662,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,iPr_def_27),X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_650,c_51]) ).
tcf(c_1669,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,iPr_def_27),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1662,c_357]) ).
tcf(c_1733,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_36,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_1246,c_774]) ).
tcf(c_1863,plain,
addition(multiplication(iPr_def_36,iPr_def_34),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_36,
inference(superposition,[status(thm)],[c_1612,c_835]) ).
tcf(c_1870,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_36,iPr_def_34)) = iPr_def_36,
inference(theory_normalisation,[status(thm)],[c_1863,c_54,c_55]) ).
tcf(c_1871,plain,
iPr_def_34 = iPr_def_36,
inference(light_normalisation,[status(thm)],[c_1870,c_1607]) ).
tcf(c_1877,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_34,iPr_def_35),
inference(demodulation,[status(thm)],[c_1612,c_1871]) ).
tcf(c_1907,plain,
addition(multiplication(iPr_def_14,iPr_def_12),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_14,
inference(superposition,[status(thm)],[c_1273,c_836]) ).
tcf(c_1908,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,iPr_def_12),addition(multiplication(X0,iPr_def_13),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_836,c_54]) ).
tcf(c_1914,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_14,iPr_def_12)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_1907,c_54,c_55]) ).
tcf(c_1915,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1914,c_1250]) ).
tcf(c_1925,plain,
antidomain(iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_137,c_1915]) ).
tcf(c_1926,plain,
antidomain(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_136,c_1915]) ).
tcf(c_1927,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_1925,c_135]) ).
tcf(c_1931,plain,
antidomain(iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_138,c_1927]) ).
tcf(c_1980,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,iPr_def_26),X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_660,c_51]) ).
tcf(c_1987,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,iPr_def_26),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1980,c_357]) ).
tcf(c_2021,plain,
addition(multiplication(iPr_def_27,iPr_def_11),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_27,
inference(superposition,[status(thm)],[c_1463,c_838]) ).
tcf(c_2028,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_27,iPr_def_11)) = iPr_def_27,
inference(theory_normalisation,[status(thm)],[c_2021,c_54,c_55]) ).
tcf(c_2029,plain,
iPr_def_11 = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_2028,c_1532]) ).
tcf(c_2040,plain,
antidomain(iPr_def_11) = iPr_def_28,
inference(demodulation,[status(thm)],[c_150,c_2029]) ).
tcf(c_2041,plain,
antidomain(iPr_def_26) = iPr_def_11,
inference(demodulation,[status(thm)],[c_149,c_2029]) ).
tcf(c_2042,plain,
iPr_def_26 = iPr_def_28,
inference(light_normalisation,[status(thm)],[c_2040,c_148]) ).
tcf(c_2044,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_26,iPr_def_29),
inference(demodulation,[status(thm)],[c_435,c_2042]) ).
tcf(c_2119,plain,
multiplication(iPr_def_26,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_1104,c_760]) ).
tcf(c_2141,plain,
iPr_def_12 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1931,c_1926]) ).
tcf(c_2146,plain,
antidomain(iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_139,c_2141]) ).
tcf(c_2147,plain,
iPr_def_13 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_2146,c_135]) ).
tcf(c_2152,plain,
antidomain(iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_140,c_2147]) ).
tcf(c_2153,plain,
iPr_def_12 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_2152,c_1926]) ).
tcf(c_2156,plain,
multiplication(sK0,iPr_def_12) = iPr_def_19,
inference(demodulation,[status(thm)],[c_141,c_2153]) ).
tcf(c_2172,plain,
addition(multiplication(iPr_def_22,iPr_def_20),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_22,
inference(superposition,[status(thm)],[c_1430,c_844]) ).
tcf(c_2179,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_22,iPr_def_20)) = iPr_def_22,
inference(theory_normalisation,[status(thm)],[c_2172,c_54,c_55]) ).
tcf(c_2180,plain,
iPr_def_20 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_2179,c_1480]) ).
tcf(c_2191,plain,
antidomain(iPr_def_20) = iPr_def_23,
inference(demodulation,[status(thm)],[c_145,c_2180]) ).
tcf(c_2192,plain,
antidomain(iPr_def_21) = iPr_def_20,
inference(demodulation,[status(thm)],[c_144,c_2180]) ).
tcf(c_2193,plain,
iPr_def_21 = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_2191,c_143]) ).
tcf(c_2198,plain,
antidomain(iPr_def_21) = iPr_def_24,
inference(demodulation,[status(thm)],[c_146,c_2193]) ).
tcf(c_2363,plain,
iPr_def_20 = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_2198,c_2192]) ).
tcf(c_2368,plain,
addition(iPr_def_11,iPr_def_20) = iPr_def_25,
inference(demodulation,[status(thm)],[c_147,c_2363]) ).
tcf(c_2446,plain,
addition(iPr_def_10,multiplication(iPr_def_26,iPr_def_11)) = iPr_def_26,
inference(superposition,[status(thm)],[c_2119,c_837]) ).
tcf(c_2447,plain,
addition(iPr_def_10,multiplication(iPr_def_11,iPr_def_10)) = iPr_def_26,
inference(light_normalisation,[status(thm)],[c_2446,c_1454]) ).
tcf(c_2547,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_33)) = X0,
inference(demodulation,[status(thm)],[c_1628,c_52,c_1908]) ).
tcf(c_2723,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,iPr_def_11),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1669,c_2029]) ).
tcf(c_2724,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_2723,c_51,c_55,c_944]) ).
tcf(c_2730,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(iPr_def_11,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_2724,c_54]) ).
tcf(c_2799,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_34,multiplication(iPr_def_35,X0)),
inference(superposition,[status(thm)],[c_1877,c_60]) ).
tcf(c_2804,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_34,multiplication(iPr_def_35,X0)),
inference(light_normalisation,[status(thm)],[c_2799,c_1249]) ).
tcf(c_2935,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_26,iPr_def_30)) = iPr_def_26,
inference(superposition,[status(thm)],[c_2044,c_851]) ).
tcf(c_2964,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_26,X0)) = X0,
inference(demodulation,[status(thm)],[c_1987,c_51,c_940]) ).
tcf(c_3656,plain,
iPr_def_10 = iPr_def_26,
inference(demodulation,[status(thm)],[c_2447,c_1093]) ).
tcf(c_3658,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = X0,
inference(demodulation,[status(thm)],[c_2964,c_3656]) ).
tcf(c_3660,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_2044,c_3656]) ).
tcf(c_3664,plain,
antidomain(iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2041,c_3656]) ).
tcf(c_3665,plain,
iPr_def_10 = iPr_def_28,
inference(demodulation,[status(thm)],[c_2042,c_3656]) ).
tcf(c_3668,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_1454,c_3656]) ).
tcf(c_3672,plain,
antidomain(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_148,c_3656]) ).
tcf(c_3682,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_454,c_3660]) ).
tcf(c_3685,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_34,iPr_def_35),
inference(demodulation,[status(thm)],[c_1877,c_3660]) ).
tcf(c_3688,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_34,iPr_def_33),
inference(demodulation,[status(thm)],[c_1589,c_3660]) ).
tcf(c_3692,plain,
multiplication(iPr_def_10,sK2) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_1139,c_3660]) ).
tcf(c_3694,plain,
antidomain(multiplication(iPr_def_10,iPr_def_29)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_1109,c_3660]) ).
tcf(c_3695,plain,
coantidomain(multiplication(iPr_def_10,iPr_def_29)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_1108,c_3660]) ).
tcf(c_3697,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_32,iPr_def_33),
inference(demodulation,[status(thm)],[c_903,c_3660]) ).
tcf(c_3698,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_31,iPr_def_32),
inference(demodulation,[status(thm)],[c_898,c_3660]) ).
tcf(c_3702,plain,
multiplication(iPr_def_10,iPr_def_29) = coantidomain(iPr_def_37),
inference(demodulation,[status(thm)],[c_483,c_3660]) ).
tcf(c_3817,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_10,iPr_def_29)) = multiplication(iPr_def_10,iPr_def_29),
inference(light_normalisation,[status(thm)],[c_429,c_3665]) ).
tcf(c_4068,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_29),X0) = multiplication(iPr_def_10,iPr_def_29),
inference(light_normalisation,[status(thm)],[c_430,c_3665]) ).
tcf(c_4069,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_29,X0)) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_4068,c_60]) ).
tcf(c_4089,plain,
! [X0: $i] : addition(antidomain(X0),iPr_def_37) = iPr_def_37,
inference(superposition,[status(thm)],[c_302,c_456]) ).
tcf(c_4187,plain,
! [X0: $i] : addition(iPr_def_37,antidomain(X0)) = iPr_def_37,
inference(theory_normalisation,[status(thm)],[c_4089,c_54,c_55]) ).
tcf(c_4224,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,antidomain(X0))) = iPr_def_37,
inference(demodulation,[status(thm)],[c_4187,c_485]) ).
tcf(c_4242,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,antidomain(X1)),X0)) = multiplication(iPr_def_37,X0),
inference(superposition,[status(thm)],[c_4224,c_51]) ).
tcf(c_4258,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_12,X0),multiplication(addition(iPr_def_13,antidomain(X1)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4242,c_357]) ).
tcf(c_4317,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(iPr_def_12,addition(iPr_def_13,X1)),
inference(demodulation,[status(thm)],[c_458,c_485]) ).
tcf(c_4372,plain,
! [X0: $i] : addition(iPr_def_10,addition(antidomain(iPr_def_10),X0)) = addition(iPr_def_12,addition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_3672,c_4317]) ).
tcf(c_4389,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,X0)) = addition(iPr_def_12,addition(iPr_def_13,X0)),
inference(light_normalisation,[status(thm)],[c_4372,c_3664]) ).
tcf(c_4442,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_35)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_648,c_4389]) ).
tcf(c_5086,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(iPr_def_10,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_3658,c_54]) ).
tcf(c_5406,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_3660,c_3668]) ).
tcf(c_5409,plain,
multiplication(iPr_def_10,iPr_def_11) = coantidomain(iPr_def_37),
inference(demodulation,[status(thm)],[c_3702,c_5406]) ).
tcf(c_5411,plain,
coantidomain(multiplication(iPr_def_10,iPr_def_11)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_3695,c_5406]) ).
tcf(c_5412,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_29,X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_4069,c_5406]) ).
tcf(c_5413,plain,
antidomain(multiplication(iPr_def_10,iPr_def_11)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_3694,c_5406]) ).
tcf(c_5415,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_3817,c_5406]) ).
tcf(c_5418,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_11),X0) = multiplication(iPr_def_10,multiplication(iPr_def_29,X0)),
inference(superposition,[status(thm)],[c_5406,c_60]) ).
tcf(c_5423,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_11),X0) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_5418,c_5412]) ).
tcf(c_5517,plain,
! [X0: $i] : addition(multiplication(X0,multiplication(iPr_def_10,iPr_def_11)),multiplication(X0,coantidomain(multiplication(iPr_def_10,iPr_def_11)))) = X0,
inference(superposition,[status(thm)],[c_5409,c_860]) ).
tcf(c_5528,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_11),X0) = X0,
inference(light_normalisation,[status(thm)],[c_5517,c_358,c_5411,c_5415]) ).
tcf(c_5566,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,iPr_def_11)) = X0,
inference(superposition,[status(thm)],[c_5528,c_55]) ).
tcf(c_5810,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(antidomain(X1),X0)) = X0,
inference(demodulation,[status(thm)],[c_4258,c_51,c_940]) ).
tcf(c_6014,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_34,iPr_def_35),
inference(light_normalisation,[status(thm)],[c_3685,c_5406]) ).
tcf(c_6017,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_11),X0) = multiplication(iPr_def_34,multiplication(iPr_def_35,X0)),
inference(superposition,[status(thm)],[c_6014,c_60]) ).
tcf(c_6024,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_6017,c_2804,c_5423]) ).
tcf(c_6143,plain,
multiplication(iPr_def_30,iPr_def_19) = multiplication(iPr_def_31,iPr_def_12),
inference(superposition,[status(thm)],[c_2156,c_707]) ).
tcf(c_6207,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_34,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_3688,c_5406]) ).
tcf(c_6213,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_35,iPr_def_33)) = iPr_def_33,
inference(superposition,[status(thm)],[c_6207,c_757]) ).
tcf(c_6437,plain,
multiplication(iPr_def_10,sK2) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3692,c_5406]) ).
tcf(c_6440,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_11),X0) = multiplication(iPr_def_10,multiplication(sK2,X0)),
inference(superposition,[status(thm)],[c_6437,c_60]) ).
tcf(c_6445,plain,
! [X0: $i] : multiplication(iPr_def_29,multiplication(iPr_def_30,X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_6440,c_1143,c_5423]) ).
tcf(c_6726,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_32,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_3697,c_5406]) ).
tcf(c_6738,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_31,iPr_def_32),
inference(light_normalisation,[status(thm)],[c_3698,c_5406]) ).
tcf(c_9690,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3682,c_5406]) ).
tcf(c_10346,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,X0)) = addition(iPr_def_32,addition(iPr_def_33,X0)),
inference(light_normalisation,[status(thm)],[c_692,c_4389]) ).
tcf(c_11102,plain,
! [X0: $i] : multiplication(iPr_def_31,multiplication(iPr_def_32,X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_901,c_6445]) ).
tcf(c_11106,plain,
multiplication(iPr_def_31,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_6726,c_11102]) ).
tcf(c_12973,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_34,iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1733,c_1871]) ).
tcf(c_12974,plain,
multiplication(iPr_def_34,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_12973,c_3668,c_5528]) ).
tcf(c_13266,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_10,iPr_def_30)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2935,c_3656]) ).
tcf(c_13267,plain,
multiplication(iPr_def_10,iPr_def_30) = iPr_def_10,
inference(demodulation,[status(thm)],[c_13266,c_55,c_3668,c_5566]) ).
tcf(c_13270,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_30,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_13267,c_60]) ).
tcf(c_14482,plain,
multiplication(iPr_def_35,iPr_def_33) = iPr_def_33,
inference(demodulation,[status(thm)],[c_6213,c_5528]) ).
tcf(c_14490,plain,
addition(iPr_def_35,iPr_def_33) = iPr_def_35,
inference(superposition,[status(thm)],[c_14482,c_2547]) ).
tcf(c_14492,plain,
addition(iPr_def_33,iPr_def_35) = iPr_def_35,
inference(theory_normalisation,[status(thm)],[c_14490,c_54,c_55]) ).
tcf(c_14642,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_35)) = addition(iPr_def_32,iPr_def_35),
inference(superposition,[status(thm)],[c_14492,c_10346]) ).
tcf(c_14645,plain,
addition(iPr_def_32,iPr_def_35) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_14642,c_4442]) ).
tcf(c_14650,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_35)) = multiplication(X0,iPr_def_37),
inference(superposition,[status(thm)],[c_14645,c_52]) ).
tcf(c_14654,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_35)) = X0,
inference(light_normalisation,[status(thm)],[c_14650,c_358]) ).
tcf(c_14673,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_31,iPr_def_35)) = iPr_def_31,
inference(superposition,[status(thm)],[c_6738,c_14654]) ).
tcf(c_14871,plain,
multiplication(iPr_def_31,iPr_def_35) = iPr_def_31,
inference(demodulation,[status(thm)],[c_14673,c_5528]) ).
tcf(c_14874,plain,
! [X0: $i] : multiplication(iPr_def_31,multiplication(iPr_def_35,X0)) = multiplication(iPr_def_31,X0),
inference(superposition,[status(thm)],[c_14871,c_60]) ).
tcf(c_15380,plain,
! [X0: $i] : multiplication(iPr_def_35,multiplication(iPr_def_34,X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_1609,c_6024]) ).
tcf(c_15387,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_35,iPr_def_12),
inference(superposition,[status(thm)],[c_12974,c_15380]) ).
tcf(c_15416,plain,
multiplication(iPr_def_31,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_31,iPr_def_12),
inference(superposition,[status(thm)],[c_15387,c_14874]) ).
tcf(c_15428,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_30,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_15416,c_6143,c_11106]) ).
tcf(c_15442,plain,
multiplication(iPr_def_10,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_19),
inference(superposition,[status(thm)],[c_15428,c_13270]) ).
tcf(c_22486,plain,
addition(iPr_def_20,multiplication(iPr_def_11,iPr_def_21)) = addition(iPr_def_20,iPr_def_11),
inference(superposition,[status(thm)],[c_844,c_2730]) ).
tcf(c_22671,plain,
addition(iPr_def_20,multiplication(iPr_def_11,iPr_def_21)) = addition(iPr_def_11,iPr_def_20),
inference(theory_normalisation,[status(thm)],[c_22486,c_54,c_55]) ).
tcf(c_22672,plain,
addition(iPr_def_20,multiplication(iPr_def_11,iPr_def_21)) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_22671,c_2368]) ).
tcf(c_29009,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,multiplication(iPr_def_10,iPr_def_11)),X0) = addition(multiplication(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_5086,c_5528]) ).
tcf(c_29040,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_19),X0) = X0,
inference(light_normalisation,[status(thm)],[c_29009,c_5528,c_15442]) ).
tcf(c_36184,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_10,iPr_def_19),
inference(superposition,[status(thm)],[c_29040,c_5566]) ).
tcf(c_130079,plain,
! [X0: $i] : addition(multiplication(antidomain(multiplication(iPr_def_10,iPr_def_11)),X0),multiplication(antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_19)))),X0)) = multiplication(antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_19)))),X0),
inference(superposition,[status(thm)],[c_36184,c_1055]) ).
tcf(c_130184,plain,
! [X0: $i] : addition(X0,multiplication(antidomain(multiplication(iPr_def_10,iPr_def_21)),X0)) = multiplication(antidomain(multiplication(iPr_def_10,iPr_def_21)),X0),
inference(light_normalisation,[status(thm)],[c_130079,c_142,c_143,c_357,c_5413]) ).
tcf(c_131775,plain,
! [X0: $i] : multiplication(antidomain(multiplication(iPr_def_10,iPr_def_21)),X0) = X0,
inference(demodulation,[status(thm)],[c_130184,c_5810]) ).
tcf(c_131812,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_10,iPr_def_21),
inference(superposition,[status(thm)],[c_131775,c_9690]) ).
tcf(c_135674,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_11,iPr_def_21)) = iPr_def_21,
inference(superposition,[status(thm)],[c_131812,c_759]) ).
tcf(c_142091,plain,
multiplication(iPr_def_11,iPr_def_21) = iPr_def_21,
inference(demodulation,[status(thm)],[c_135674,c_5528]) ).
tcf(c_142094,plain,
addition(iPr_def_20,iPr_def_21) = iPr_def_25,
inference(demodulation,[status(thm)],[c_22672,c_142091]) ).
tcf(c_142096,plain,
iPr_def_25 = iPr_def_37,
inference(demodulation,[status(thm)],[c_342,c_142094]) ).
tcf(c_142097,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_142096,c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE104+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n009.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 18:57:00 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 69.25/10.36 % SZS status Started for theBenchmark.p
% 69.25/10.36 % SZS status Theorem for theBenchmark.p
% 69.25/10.36
% 69.25/10.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 69.25/10.36
% 69.25/10.36 % ------ iProver source info
% 69.25/10.36
% 69.25/10.36 % git: date: 2026-07-19 20:42:38 +0200
% 69.25/10.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 69.25/10.36 % git: non_committed_changes: false
% 69.25/10.36
% 69.25/10.36 % ------ Parsing...
% 69.25/10.36 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 69.25/10.36 %
% 69.25/10.36
% 69.25/10.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 69.25/10.36
% 69.25/10.36 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 69.25/10.36 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 69.25/10.36
% 69.25/10.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 69.25/10.36 % ------ Proving...
% 69.25/10.36 % ------ Problem Properties
% 69.25/10.36
% 69.25/10.36 %
% 69.25/10.36 % clauses 47
% 69.25/10.36 % conjectures 2
% 69.25/10.36 % EPR 2
% 69.25/10.36 % Horn 47
% 69.25/10.36 % unary 47
% 69.25/10.36 % binary 0
% 69.25/10.36 % lits 47
% 69.25/10.36 % lits eq 47
% 69.25/10.36 % fd_pure 0
% 69.25/10.36 % fd_pseudo 0
% 69.25/10.36 % fd_cond 0
% 69.25/10.36 % fd_pseudo_cond 0
% 69.25/10.36 % AC symbols 1
% 69.25/10.36
% 69.25/10.36 % ------ Schedule UEQ
% 69.25/10.36
% 69.25/10.36 % ------ Option_UEQ Time Limit: 10.
% 69.25/10.36
% 69.25/10.36
% 69.25/10.36 % ------
% 69.25/10.36 % Current options:
% 69.25/10.36 % ------
% 69.25/10.36
% 69.25/10.36
% 69.25/10.36 %
% 69.25/10.36
% 69.25/10.36 % ------ Proving...
% 69.25/10.36 %
% 69.25/10.36
% 69.25/10.36 % SZS status Theorem for theBenchmark.p
% 69.25/10.36
% 69.25/10.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.25/10.37
% 69.25/10.37
%------------------------------------------------------------------------------