%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE103+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 : n019.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 57.85s 15.46s
% Output : CNFRefutation 57.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 52
% Syntax : Number of formulae : 407 ( 403 unt; 28 def)
% Number of atoms : 1351 ( 410 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 : 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 : 277 ( 0 sgn 274 !; 3 ?; 183 :)
% 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(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(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain2) ).
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(forward_box(X0,domain(X1)),domain(X2)) = one
=> addition(domain(X1),backward_box(X0,domain(X2))) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_box(X0,domain(X1)),domain(X2)) = one
=> addition(domain(X1),backward_box(X0,domain(X2))) = one ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( addition(forward_box(X0,domain(X1)),domain(X2)) = one
& one != addition(domain(X1),backward_box(X0,domain(X2))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( one = addition(forward_box(sK0,domain(sK1)),domain(sK2))
& one != addition(domain(sK1),backward_box(sK0,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(forward_box(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
one != addition(domain(sK1),backward_box(sK0,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(f46,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f18]) ).
fof(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(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(sK1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))),sK0))))))),
inference(definition_unfolding,[],[f32,f42,f59,f42]) ).
fof(f63,plain,
one = addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1))))))))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f31,f61,f42,f42]) ).
tcf(c_49,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,[],[f62]) ).
tcf(c_50,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,[],[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_61,plain,
! [X0: $i,X1: $i] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[],[f46]) ).
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_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_50,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_49,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_161,c_160]) ).
tcf(c_296,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_84,c_160]) ).
tcf(c_300,plain,
addition(iPr_def_32,coantidomain(iPr_def_32)) = iPr_def_25,
inference(superposition,[status(thm)],[c_154,c_296]) ).
tcf(c_301,plain,
addition(iPr_def_32,iPr_def_33) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_300,c_155]) ).
tcf(c_302,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_85,c_160]) ).
tcf(c_320,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = iPr_def_25,
inference(superposition,[status(thm)],[c_134,c_302]) ).
tcf(c_321,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = iPr_def_25,
inference(superposition,[status(thm)],[c_132,c_302]) ).
tcf(c_322,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = iPr_def_25,
inference(superposition,[status(thm)],[c_133,c_302]) ).
tcf(c_323,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = iPr_def_25,
inference(superposition,[status(thm)],[c_135,c_302]) ).
tcf(c_329,plain,
addition(iPr_def_20,antidomain(iPr_def_20)) = iPr_def_25,
inference(superposition,[status(thm)],[c_142,c_302]) ).
tcf(c_330,plain,
addition(iPr_def_21,antidomain(iPr_def_21)) = iPr_def_25,
inference(superposition,[status(thm)],[c_143,c_302]) ).
tcf(c_334,plain,
addition(iPr_def_26,antidomain(iPr_def_26)) = iPr_def_25,
inference(superposition,[status(thm)],[c_148,c_302]) ).
tcf(c_338,plain,
addition(iPr_def_26,iPr_def_27) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_334,c_149]) ).
tcf(c_341,plain,
addition(iPr_def_21,iPr_def_22) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_330,c_144]) ).
tcf(c_342,plain,
addition(iPr_def_20,iPr_def_21) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_329,c_143]) ).
tcf(c_347,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_323,c_136]) ).
tcf(c_348,plain,
addition(iPr_def_11,iPr_def_26) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_322,c_148]) ).
tcf(c_349,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_321,c_133]) ).
tcf(c_350,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_320,c_135]) ).
tcf(c_351,plain,
addition(iPr_def_33,coantidomain(iPr_def_33)) = iPr_def_25,
inference(superposition,[status(thm)],[c_155,c_296]) ).
tcf(c_352,plain,
addition(iPr_def_34,antidomain(iPr_def_34)) = iPr_def_25,
inference(superposition,[status(thm)],[c_156,c_302]) ).
tcf(c_353,plain,
addition(iPr_def_34,iPr_def_35) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_352,c_157]) ).
tcf(c_354,plain,
addition(iPr_def_35,antidomain(iPr_def_35)) = iPr_def_25,
inference(superposition,[status(thm)],[c_157,c_302]) ).
tcf(c_355,plain,
addition(iPr_def_35,iPr_def_36) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_354,c_158]) ).
tcf(c_357,plain,
! [X0: $i] : multiplication(iPr_def_25,X0) = X0,
inference(light_normalisation,[status(thm)],[c_58,c_160]) ).
tcf(c_358,plain,
! [X0: $i] : multiplication(X0,iPr_def_25) = X0,
inference(light_normalisation,[status(thm)],[c_59,c_160]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i] : addition(coantidomain(X0),addition(X1,coantidomain(coantidomain(X0)))) = addition(X1,iPr_def_25),
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_25),
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_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_25) = zero,
inference(superposition,[status(thm)],[c_62,c_357]) ).
tcf(c_427,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = multiplication(iPr_def_28,iPr_def_29),
inference(demodulation,[status(thm)],[c_62,c_422]) ).
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_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_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_442,plain,
multiplication(iPr_def_20,iPr_def_19) = multiplication(iPr_def_28,iPr_def_29),
inference(superposition,[status(thm)],[c_142,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_25),
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_458,plain,
! [X0: $i,X1: $i] : addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(iPr_def_25,X1),
inference(superposition,[status(thm)],[c_302,c_54]) ).
tcf(c_459,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_24,X0)) = addition(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_147,c_54]) ).
tcf(c_463,plain,
! [X0: $i] : addition(iPr_def_32,addition(iPr_def_33,X0)) = addition(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_301,c_54]) ).
tcf(c_483,plain,
multiplication(iPr_def_11,iPr_def_10) = coantidomain(iPr_def_25),
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_25,
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_25,X0),
inference(superposition,[status(thm)],[c_350,c_54]) ).
tcf(c_496,plain,
multiplication(iPr_def_11,iPr_def_10) = antidomain(iPr_def_25),
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_25,
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_25),
inference(superposition,[status(thm)],[c_53,c_391]) ).
tcf(c_530,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(iPr_def_25,coantidomain(coantidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_515,c_54,c_55]) ).
tcf(c_531,plain,
! [X0: $i] : addition(iPr_def_25,coantidomain(coantidomain(X0))) = iPr_def_25,
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_25,
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_25,
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_25,
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_25),
inference(superposition,[status(thm)],[c_53,c_392]) ).
tcf(c_617,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_25,antidomain(antidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_572,c_54,c_55]) ).
tcf(c_618,plain,
! [X0: $i] : addition(iPr_def_25,antidomain(antidomain(X0))) = iPr_def_25,
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_25,
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_25,
inference(superposition,[status(thm)],[c_133,c_622]) ).
tcf(c_640,plain,
addition(iPr_def_12,addition(iPr_def_13,antidomain(iPr_def_34))) = iPr_def_25,
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_25,
inference(light_normalisation,[status(thm)],[c_640,c_157]) ).
tcf(c_660,plain,
addition(iPr_def_12,addition(iPr_def_13,iPr_def_26)) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_625,c_148]) ).
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_724,plain,
! [X0: $i] : addition(multiplication(iPr_def_32,X0),multiplication(iPr_def_33,X0)) = multiplication(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_301,c_51]) ).
tcf(c_729,plain,
! [X0: $i] : addition(multiplication(iPr_def_26,X0),multiplication(iPr_def_27,X0)) = multiplication(iPr_def_25,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_25,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_25,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_25,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_25,X0),
inference(superposition,[status(thm)],[c_349,c_51]) ).
tcf(c_743,plain,
! [X0: $i] : addition(multiplication(iPr_def_34,X0),multiplication(iPr_def_35,X0)) = multiplication(iPr_def_25,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_25,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_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_772,plain,
! [X0: $i] : addition(multiplication(iPr_def_32,X0),multiplication(iPr_def_33,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_724,c_357]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_296,c_52]) ).
tcf(c_795,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_24)) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_147,c_52]) ).
tcf(c_800,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_33)) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_301,c_52]) ).
tcf(c_809,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_20),multiplication(X0,iPr_def_21)) = multiplication(X0,iPr_def_25),
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_25),
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_25),
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_25),
inference(superposition,[status(thm)],[c_350,c_52]) ).
tcf(c_818,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_33),multiplication(X0,coantidomain(iPr_def_33))) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_351,c_52]) ).
tcf(c_819,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_34),multiplication(X0,iPr_def_35)) = multiplication(X0,iPr_def_25),
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_850,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_33)) = X0,
inference(light_normalisation,[status(thm)],[c_800,c_358]) ).
tcf(c_852,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_24)) = X0,
inference(light_normalisation,[status(thm)],[c_795,c_358]) ).
tcf(c_854,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_33),multiplication(X0,coantidomain(iPr_def_33))) = X0,
inference(light_normalisation,[status(thm)],[c_818,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_882,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(coantidomain(multiplication(X0,X1)),X2),multiplication(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),X2)) = multiplication(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),X2),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,coantidomain(multiplication(X1,X2))),multiplication(X0,coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)))) = multiplication(X0,coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))),
inference(superposition,[status(thm)],[c_61,c_52]) ).
tcf(c_893,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(light_normalisation,[status(thm)],[c_422,c_435]) ).
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_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_1101,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(light_normalisation,[status(thm)],[c_428,c_435]) ).
tcf(c_1112,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_1101,c_55]) ).
tcf(c_1116,plain,
coantidomain(multiplication(iPr_def_11,iPr_def_10)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_484,c_1112]) ).
tcf(c_1117,plain,
antidomain(multiplication(iPr_def_11,iPr_def_10)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_497,c_1112]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),addition(multiplication(iPr_def_11,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_759,c_54]) ).
tcf(c_1255,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_1259,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_14,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_1255,c_761]) ).
tcf(c_1282,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_20,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_442,c_435]) ).
tcf(c_1429,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_1438,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_1462,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_1471,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_1481,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_22,iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_1429,c_767]) ).
tcf(c_1533,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_27,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1462,c_770]) ).
tcf(c_1577,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_1585,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_1590,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_36,iPr_def_34)) = iPr_def_34,
inference(superposition,[status(thm)],[c_1585,c_756]) ).
tcf(c_1600,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_1612,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,addition(iPr_def_13,iPr_def_33))) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_544,c_52]) ).
tcf(c_1616,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_1612,c_358]) ).
tcf(c_1830,plain,
addition(multiplication(iPr_def_36,iPr_def_34),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_36,
inference(superposition,[status(thm)],[c_1600,c_835]) ).
tcf(c_1837,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_1830,c_54,c_55]) ).
tcf(c_1838,plain,
iPr_def_34 = iPr_def_36,
inference(light_normalisation,[status(thm)],[c_1837,c_1590]) ).
tcf(c_1847,plain,
addition(iPr_def_13,iPr_def_34) = iPr_def_37,
inference(demodulation,[status(thm)],[c_159,c_1838]) ).
tcf(c_1861,plain,
addition(multiplication(iPr_def_14,iPr_def_12),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_14,
inference(superposition,[status(thm)],[c_1282,c_836]) ).
tcf(c_1862,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_1868,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_1861,c_54,c_55]) ).
tcf(c_1869,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1868,c_1259]) ).
tcf(c_1879,plain,
antidomain(iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_137,c_1869]) ).
tcf(c_1880,plain,
antidomain(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_136,c_1869]) ).
tcf(c_1881,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_1879,c_135]) ).
tcf(c_1885,plain,
antidomain(iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_138,c_1881]) ).
tcf(c_1948,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,iPr_def_10),addition(multiplication(X0,iPr_def_11),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_837,c_54]) ).
tcf(c_1966,plain,
addition(multiplication(iPr_def_27,iPr_def_11),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_27,
inference(superposition,[status(thm)],[c_1471,c_838]) ).
tcf(c_1973,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_1966,c_54,c_55]) ).
tcf(c_1974,plain,
iPr_def_11 = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_1973,c_1533]) ).
tcf(c_1985,plain,
antidomain(iPr_def_11) = iPr_def_28,
inference(demodulation,[status(thm)],[c_150,c_1974]) ).
tcf(c_1987,plain,
iPr_def_26 = iPr_def_28,
inference(light_normalisation,[status(thm)],[c_1985,c_148]) ).
tcf(c_1989,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_26,iPr_def_29),
inference(demodulation,[status(thm)],[c_435,c_1987]) ).
tcf(c_1991,plain,
coantidomain(iPr_def_26) = iPr_def_29,
inference(demodulation,[status(thm)],[c_151,c_1987]) ).
tcf(c_2053,plain,
iPr_def_12 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1885,c_1880]) ).
tcf(c_2058,plain,
antidomain(iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_139,c_2053]) ).
tcf(c_2059,plain,
iPr_def_13 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_2058,c_135]) ).
tcf(c_2064,plain,
antidomain(iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_140,c_2059]) ).
tcf(c_2065,plain,
iPr_def_12 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_2064,c_1880]) ).
tcf(c_2068,plain,
multiplication(sK0,iPr_def_12) = iPr_def_19,
inference(demodulation,[status(thm)],[c_141,c_2065]) ).
tcf(c_2084,plain,
addition(multiplication(iPr_def_22,iPr_def_20),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_22,
inference(superposition,[status(thm)],[c_1438,c_844]) ).
tcf(c_2091,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_2084,c_54,c_55]) ).
tcf(c_2092,plain,
iPr_def_20 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_2091,c_1481]) ).
tcf(c_2103,plain,
antidomain(iPr_def_20) = iPr_def_23,
inference(demodulation,[status(thm)],[c_145,c_2092]) ).
tcf(c_2104,plain,
antidomain(iPr_def_21) = iPr_def_20,
inference(demodulation,[status(thm)],[c_144,c_2092]) ).
tcf(c_2105,plain,
iPr_def_21 = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_2103,c_143]) ).
tcf(c_2110,plain,
antidomain(iPr_def_21) = iPr_def_24,
inference(demodulation,[status(thm)],[c_146,c_2105]) ).
tcf(c_2181,plain,
multiplication(iPr_def_26,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_1112,c_760]) ).
tcf(c_2258,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_26,iPr_def_24)) = iPr_def_26,
inference(superposition,[status(thm)],[c_1462,c_852]) ).
tcf(c_2293,plain,
iPr_def_20 = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_2110,c_2104]) ).
tcf(c_2301,plain,
addition(iPr_def_11,iPr_def_20) = iPr_def_25,
inference(demodulation,[status(thm)],[c_147,c_2293]) ).
tcf(c_2354,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_32,coantidomain(iPr_def_33))) = iPr_def_32,
inference(superposition,[status(thm)],[c_903,c_854]) ).
tcf(c_2493,plain,
addition(iPr_def_10,multiplication(iPr_def_26,iPr_def_11)) = iPr_def_26,
inference(superposition,[status(thm)],[c_2181,c_837]) ).
tcf(c_2494,plain,
addition(iPr_def_10,multiplication(iPr_def_11,iPr_def_10)) = iPr_def_26,
inference(light_normalisation,[status(thm)],[c_2493,c_1462]) ).
tcf(c_2513,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_33)) = X0,
inference(demodulation,[status(thm)],[c_1616,c_52,c_1862]) ).
tcf(c_2648,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_20,X0)) = addition(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_2301,c_54]) ).
tcf(c_2653,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_20,X0)) = addition(iPr_def_12,addition(iPr_def_13,X0)),
inference(light_normalisation,[status(thm)],[c_2648,c_485]) ).
tcf(c_3231,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = multiplication(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_427,c_1987,c_1989]) ).
tcf(c_3261,plain,
addition(multiplication(iPr_def_32,coantidomain(iPr_def_33)),multiplication(iPr_def_11,iPr_def_10)) = coantidomain(iPr_def_33),
inference(superposition,[status(thm)],[c_3231,c_772]) ).
tcf(c_3294,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_32,coantidomain(iPr_def_33))) = coantidomain(iPr_def_33),
inference(theory_normalisation,[status(thm)],[c_3261,c_54,c_55]) ).
tcf(c_3295,plain,
coantidomain(iPr_def_33) = iPr_def_32,
inference(light_normalisation,[status(thm)],[c_3294,c_2354]) ).
tcf(c_3463,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_33,iPr_def_32),
inference(superposition,[status(thm)],[c_3295,c_3231]) ).
tcf(c_3860,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_3908,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_132,c_3860]) ).
tcf(c_3941,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_3908,c_133]) ).
tcf(c_3981,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_26)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_660,c_3941]) ).
tcf(c_3986,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_35)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_648,c_3941]) ).
tcf(c_4007,plain,
addition(iPr_def_10,iPr_def_25) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_3981,c_348]) ).
tcf(c_4084,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_25,X0)) = multiplication(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_4007,c_51]) ).
tcf(c_4091,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4084,c_357]) ).
tcf(c_4092,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_4091,c_54,c_55]) ).
tcf(c_4120,plain,
iPr_def_10 = iPr_def_26,
inference(demodulation,[status(thm)],[c_2494,c_1101]) ).
tcf(c_4122,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_1989,c_4120]) ).
tcf(c_4126,plain,
coantidomain(iPr_def_10) = iPr_def_29,
inference(demodulation,[status(thm)],[c_1991,c_4120]) ).
tcf(c_4128,plain,
iPr_def_10 = iPr_def_28,
inference(demodulation,[status(thm)],[c_1987,c_4120]) ).
tcf(c_4130,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_1462,c_4120]) ).
tcf(c_4138,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_454,c_4122]) ).
tcf(c_4139,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_3231,c_4122]) ).
tcf(c_4144,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_34,iPr_def_33),
inference(demodulation,[status(thm)],[c_1577,c_4122]) ).
tcf(c_4146,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_20,iPr_def_19),
inference(demodulation,[status(thm)],[c_1421,c_4122]) ).
tcf(c_4150,plain,
antidomain(multiplication(iPr_def_10,iPr_def_29)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_1117,c_4122]) ).
tcf(c_4151,plain,
coantidomain(multiplication(iPr_def_10,iPr_def_29)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_1116,c_4122]) ).
tcf(c_4153,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_32,iPr_def_33),
inference(demodulation,[status(thm)],[c_903,c_4122]) ).
tcf(c_4158,plain,
multiplication(iPr_def_10,iPr_def_29) = coantidomain(iPr_def_25),
inference(demodulation,[status(thm)],[c_483,c_4122]) ).
tcf(c_4856,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_4128]) ).
tcf(c_4937,plain,
! [X0: $i] : addition(coantidomain(X0),iPr_def_25) = iPr_def_25,
inference(superposition,[status(thm)],[c_296,c_456]) ).
tcf(c_4938,plain,
! [X0: $i] : addition(antidomain(X0),iPr_def_25) = iPr_def_25,
inference(superposition,[status(thm)],[c_302,c_456]) ).
tcf(c_5029,plain,
! [X0: $i] : addition(iPr_def_25,antidomain(X0)) = iPr_def_25,
inference(theory_normalisation,[status(thm)],[c_4938,c_54,c_55]) ).
tcf(c_5030,plain,
! [X0: $i] : addition(iPr_def_25,coantidomain(X0)) = iPr_def_25,
inference(theory_normalisation,[status(thm)],[c_4937,c_54,c_55]) ).
tcf(c_5276,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,antidomain(X0))) = iPr_def_25,
inference(demodulation,[status(thm)],[c_5029,c_485,c_3941]) ).
tcf(c_5281,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_13)) = iPr_def_25,
inference(superposition,[status(thm)],[c_135,c_5276]) ).
tcf(c_5294,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),multiplication(addition(iPr_def_11,antidomain(X1)),X0)) = multiplication(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_5276,c_51]) ).
tcf(c_5300,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),multiplication(addition(iPr_def_11,antidomain(X1)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5294,c_357]) ).
tcf(c_5307,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,coantidomain(X0))) = iPr_def_25,
inference(demodulation,[status(thm)],[c_5030,c_485,c_3941]) ).
tcf(c_5317,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),multiplication(addition(iPr_def_11,coantidomain(X1)),X0)) = multiplication(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_5307,c_51]) ).
tcf(c_5323,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_10,X0),multiplication(addition(iPr_def_11,coantidomain(X1)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5317,c_357]) ).
tcf(c_5325,plain,
! [X0: $i] : addition(iPr_def_10,addition(addition(iPr_def_11,iPr_def_13),X0)) = addition(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_5281,c_54]) ).
tcf(c_5328,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,iPr_def_13))) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_5281,c_52]) ).
tcf(c_5330,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,addition(iPr_def_13,X0))) = addition(iPr_def_25,X0),
inference(theory_normalisation,[status(thm)],[c_5325,c_54,c_55]) ).
tcf(c_5331,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,iPr_def_13))) = X0,
inference(light_normalisation,[status(thm)],[c_5328,c_358]) ).
tcf(c_5343,plain,
multiplication(iPr_def_10,iPr_def_29) = multiplication(iPr_def_33,iPr_def_32),
inference(light_normalisation,[status(thm)],[c_3463,c_4122]) ).
tcf(c_5371,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_13)) = X0,
inference(demodulation,[status(thm)],[c_5331,c_52,c_1948]) ).
tcf(c_5377,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(X0,iPr_def_13),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_5371,c_54]) ).
tcf(c_5470,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,addition(iPr_def_13,X0))) = addition(iPr_def_10,addition(iPr_def_11,X0)),
inference(light_normalisation,[status(thm)],[c_459,c_2293,c_2653,c_3941,c_5330]) ).
tcf(c_5626,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_10,iPr_def_29),
inference(demodulation,[status(thm)],[c_4122,c_4130]) ).
tcf(c_5628,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_33,iPr_def_32),
inference(demodulation,[status(thm)],[c_5343,c_5626]) ).
tcf(c_5629,plain,
multiplication(iPr_def_10,iPr_def_11) = coantidomain(iPr_def_25),
inference(demodulation,[status(thm)],[c_4158,c_5626]) ).
tcf(c_5631,plain,
coantidomain(multiplication(iPr_def_10,iPr_def_11)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_4151,c_5626]) ).
tcf(c_5633,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_4856,c_5626]) ).
tcf(c_5634,plain,
antidomain(multiplication(iPr_def_10,iPr_def_11)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_4150,c_5626]) ).
tcf(c_5673,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),X0) = X0,
inference(superposition,[status(thm)],[c_860,c_456]) ).
tcf(c_5679,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,coantidomain(X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_5673,c_54,c_55]) ).
tcf(c_5689,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_463,c_5330,c_5470]) ).
tcf(c_5776,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_5629,c_860]) ).
tcf(c_5779,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_11),X0) = X0,
inference(light_normalisation,[status(thm)],[c_5776,c_358,c_5631,c_5633]) ).
tcf(c_5837,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_25),multiplication(X0,coantidomain(iPr_def_25))) = X0,
inference(superposition,[status(thm)],[c_5631,c_860]) ).
tcf(c_5838,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,iPr_def_11)) = X0,
inference(light_normalisation,[status(thm)],[c_5837,c_358,c_5629,c_5633]) ).
tcf(c_5935,plain,
multiplication(iPr_def_10,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_5779,c_4092]) ).
tcf(c_6060,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(antidomain(X1),X0)) = X0,
inference(demodulation,[status(thm)],[c_5300,c_51,c_1153]) ).
tcf(c_6166,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(coantidomain(X1),X0)) = X0,
inference(demodulation,[status(thm)],[c_5323,c_51,c_1153]) ).
tcf(c_6264,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_34,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_4144,c_5626]) ).
tcf(c_6268,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_35,iPr_def_33)) = iPr_def_33,
inference(superposition,[status(thm)],[c_6264,c_757]) ).
tcf(c_6457,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_20,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_4146,c_5626]) ).
tcf(c_6637,plain,
multiplication(iPr_def_30,iPr_def_19) = multiplication(iPr_def_31,iPr_def_12),
inference(superposition,[status(thm)],[c_2068,c_707]) ).
tcf(c_6705,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_32,iPr_def_33),
inference(light_normalisation,[status(thm)],[c_4153,c_5626]) ).
tcf(c_8940,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_4138,c_5626]) ).
tcf(c_8979,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(antidomain(iPr_def_32),iPr_def_33)) = antidomain(iPr_def_32),
inference(superposition,[status(thm)],[c_8940,c_850]) ).
tcf(c_9074,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = multiplication(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_4139,c_5626]) ).
tcf(c_13651,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_10,iPr_def_20)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2258,c_2293,c_4120]) ).
tcf(c_13652,plain,
multiplication(iPr_def_10,iPr_def_20) = iPr_def_10,
inference(demodulation,[status(thm)],[c_13651,c_55,c_4130,c_5838]) ).
tcf(c_13655,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(iPr_def_20,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_13652,c_60]) ).
tcf(c_14106,plain,
multiplication(iPr_def_10,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_19),
inference(superposition,[status(thm)],[c_6457,c_13655]) ).
tcf(c_14121,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_10,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_14106,c_5935]) ).
tcf(c_15253,plain,
multiplication(iPr_def_35,iPr_def_33) = iPr_def_33,
inference(demodulation,[status(thm)],[c_6268,c_5779]) ).
tcf(c_15261,plain,
addition(iPr_def_35,iPr_def_33) = iPr_def_35,
inference(superposition,[status(thm)],[c_15253,c_2513]) ).
tcf(c_15263,plain,
addition(iPr_def_33,iPr_def_35) = iPr_def_35,
inference(theory_normalisation,[status(thm)],[c_15261,c_54,c_55]) ).
tcf(c_15360,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_35)) = addition(iPr_def_32,iPr_def_35),
inference(superposition,[status(thm)],[c_15263,c_5689]) ).
tcf(c_15364,plain,
addition(iPr_def_32,iPr_def_35) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_15360,c_3986]) ).
tcf(c_15398,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_35)) = multiplication(X0,iPr_def_25),
inference(superposition,[status(thm)],[c_15364,c_52]) ).
tcf(c_15404,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_32),multiplication(X0,iPr_def_35)) = X0,
inference(light_normalisation,[status(thm)],[c_15398,c_358]) ).
tcf(c_15415,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(antidomain(iPr_def_32),iPr_def_35)) = antidomain(iPr_def_32),
inference(superposition,[status(thm)],[c_8940,c_15404]) ).
tcf(c_15418,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_33,iPr_def_35)) = iPr_def_33,
inference(superposition,[status(thm)],[c_5628,c_15404]) ).
tcf(c_15984,plain,
multiplication(iPr_def_33,iPr_def_35) = iPr_def_33,
inference(demodulation,[status(thm)],[c_15418,c_5779]) ).
tcf(c_15995,plain,
addition(multiplication(iPr_def_32,iPr_def_35),iPr_def_33) = iPr_def_35,
inference(superposition,[status(thm)],[c_15984,c_772]) ).
tcf(c_16003,plain,
addition(iPr_def_33,multiplication(iPr_def_32,iPr_def_35)) = iPr_def_35,
inference(theory_normalisation,[status(thm)],[c_15995,c_54,c_55]) ).
tcf(c_16387,plain,
! [X0: $i] : addition(iPr_def_33,addition(multiplication(iPr_def_32,iPr_def_35),X0)) = addition(iPr_def_35,X0),
inference(superposition,[status(thm)],[c_16003,c_54]) ).
tcf(c_17234,plain,
multiplication(antidomain(iPr_def_32),iPr_def_33) = antidomain(iPr_def_32),
inference(demodulation,[status(thm)],[c_8979,c_5779]) ).
tcf(c_17241,plain,
addition(iPr_def_33,antidomain(iPr_def_32)) = iPr_def_33,
inference(superposition,[status(thm)],[c_17234,c_6060]) ).
tcf(c_17820,plain,
multiplication(antidomain(iPr_def_32),iPr_def_35) = antidomain(iPr_def_32),
inference(demodulation,[status(thm)],[c_15415,c_5779]) ).
tcf(c_17828,plain,
addition(iPr_def_35,antidomain(iPr_def_32)) = iPr_def_35,
inference(superposition,[status(thm)],[c_17820,c_6060]) ).
tcf(c_42481,plain,
! [X0: $i] : addition(multiplication(coantidomain(multiplication(iPr_def_10,iPr_def_11)),X0),multiplication(coantidomain(multiplication(coantidomain(coantidomain(iPr_def_10)),iPr_def_19)),X0)) = multiplication(coantidomain(multiplication(coantidomain(coantidomain(iPr_def_10)),iPr_def_19)),X0),
inference(superposition,[status(thm)],[c_14121,c_882]) ).
tcf(c_42585,plain,
! [X0: $i] : addition(X0,multiplication(coantidomain(multiplication(iPr_def_30,iPr_def_19)),X0)) = multiplication(coantidomain(multiplication(iPr_def_30,iPr_def_19)),X0),
inference(light_normalisation,[status(thm)],[c_42481,c_152,c_357,c_4126,c_5631]) ).
tcf(c_43029,plain,
! [X0: $i] : multiplication(coantidomain(multiplication(iPr_def_30,iPr_def_19)),X0) = X0,
inference(demodulation,[status(thm)],[c_42585,c_6166]) ).
tcf(c_43049,plain,
coantidomain(multiplication(iPr_def_30,iPr_def_19)) = iPr_def_25,
inference(superposition,[status(thm)],[c_43029,c_358]) ).
tcf(c_44138,plain,
! [X0: $i] : addition(multiplication(X0,coantidomain(multiplication(iPr_def_30,iPr_def_19))),multiplication(X0,coantidomain(multiplication(coantidomain(coantidomain(iPr_def_31)),iPr_def_12)))) = multiplication(X0,coantidomain(multiplication(coantidomain(coantidomain(iPr_def_31)),iPr_def_12))),
inference(superposition,[status(thm)],[c_6637,c_884]) ).
tcf(c_44283,plain,
! [X0: $i] : addition(X0,multiplication(X0,coantidomain(multiplication(iPr_def_33,iPr_def_12)))) = multiplication(X0,coantidomain(multiplication(iPr_def_33,iPr_def_12))),
inference(light_normalisation,[status(thm)],[c_44138,c_154,c_155,c_358,c_43049]) ).
tcf(c_44867,plain,
addition(iPr_def_34,multiplication(iPr_def_35,iPr_def_13)) = addition(iPr_def_34,iPr_def_13),
inference(superposition,[status(thm)],[c_757,c_5377]) ).
tcf(c_45103,plain,
addition(iPr_def_34,multiplication(iPr_def_35,iPr_def_13)) = addition(iPr_def_13,iPr_def_34),
inference(theory_normalisation,[status(thm)],[c_44867,c_54,c_55]) ).
tcf(c_45104,plain,
addition(iPr_def_34,multiplication(iPr_def_35,iPr_def_13)) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_45103,c_1847]) ).
tcf(c_45401,plain,
! [X0: $i] : multiplication(X0,coantidomain(multiplication(iPr_def_33,iPr_def_12))) = X0,
inference(demodulation,[status(thm)],[c_44283,c_5679]) ).
tcf(c_45425,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_33,iPr_def_12),
inference(superposition,[status(thm)],[c_45401,c_9074]) ).
tcf(c_61838,plain,
addition(multiplication(iPr_def_10,iPr_def_11),multiplication(iPr_def_33,iPr_def_13)) = iPr_def_33,
inference(superposition,[status(thm)],[c_45425,c_836]) ).
tcf(c_95715,plain,
multiplication(iPr_def_33,iPr_def_13) = iPr_def_33,
inference(demodulation,[status(thm)],[c_61838,c_5779]) ).
tcf(c_121981,plain,
! [X0: $i] : addition(multiplication(antidomain(multiplication(iPr_def_10,iPr_def_11)),X0),multiplication(antidomain(multiplication(iPr_def_32,antidomain(antidomain(iPr_def_33)))),X0)) = multiplication(antidomain(multiplication(iPr_def_32,antidomain(antidomain(iPr_def_33)))),X0),
inference(superposition,[status(thm)],[c_6705,c_1055]) ).
tcf(c_122247,plain,
! [X0: $i] : addition(X0,multiplication(antidomain(multiplication(iPr_def_32,iPr_def_35)),X0)) = multiplication(antidomain(multiplication(iPr_def_32,iPr_def_35)),X0),
inference(light_normalisation,[status(thm)],[c_121981,c_156,c_157,c_357,c_5634]) ).
tcf(c_122916,plain,
! [X0: $i] : multiplication(antidomain(multiplication(iPr_def_32,iPr_def_35)),X0) = X0,
inference(demodulation,[status(thm)],[c_122247,c_6060]) ).
tcf(c_122956,plain,
multiplication(iPr_def_10,iPr_def_11) = multiplication(iPr_def_32,iPr_def_35),
inference(superposition,[status(thm)],[c_122916,c_8940]) ).
tcf(c_123212,plain,
! [X0: $i] : addition(iPr_def_33,addition(multiplication(iPr_def_10,iPr_def_11),X0)) = addition(iPr_def_35,X0),
inference(demodulation,[status(thm)],[c_16387,c_122956]) ).
tcf(c_123214,plain,
! [X0: $i] : addition(iPr_def_33,X0) = addition(iPr_def_35,X0),
inference(light_normalisation,[status(thm)],[c_123212,c_5779]) ).
tcf(c_123223,plain,
addition(iPr_def_33,antidomain(iPr_def_32)) = iPr_def_35,
inference(demodulation,[status(thm)],[c_17828,c_123214]) ).
tcf(c_123235,plain,
iPr_def_33 = iPr_def_35,
inference(light_normalisation,[status(thm)],[c_123223,c_17241]) ).
tcf(c_123271,plain,
addition(iPr_def_34,multiplication(iPr_def_33,iPr_def_13)) = iPr_def_37,
inference(demodulation,[status(thm)],[c_45104,c_123235]) ).
tcf(c_123324,plain,
addition(iPr_def_34,iPr_def_33) = iPr_def_25,
inference(demodulation,[status(thm)],[c_353,c_123235]) ).
tcf(c_123326,plain,
addition(iPr_def_33,iPr_def_34) = iPr_def_25,
inference(theory_normalisation,[status(thm)],[c_123324,c_54,c_55]) ).
tcf(c_123335,plain,
addition(iPr_def_34,iPr_def_33) = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_123271,c_95715]) ).
tcf(c_123336,plain,
addition(iPr_def_33,iPr_def_34) = iPr_def_37,
inference(theory_normalisation,[status(thm)],[c_123335,c_54,c_55]) ).
tcf(c_125595,plain,
iPr_def_25 = iPr_def_37,
inference(light_normalisation,[status(thm)],[c_123336,c_123326]) ).
tcf(c_125596,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_125595,c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.58 % Computer : n019.cluster.edu
% 0.08/5.58 % Model : x86_64 x86_64
% 0.08/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.58 % Memory : 8046.5625MB
% 0.08/5.58 % OS : Linux 6.8.0-71-generic
% 0.08/5.58 % CPULimit : 300
% 0.08/5.58 % WCLimit : 300
% 0.08/5.58 % DateTime : Wed Sep 23 18:56:55 UTC 2026
% 0.08/5.58 % CPUTime :
% 0.08/5.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.62 Running first-order theorem proving
% 0.14/5.62 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
% 0.14/5.63
% 0.14/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.63
% 0.14/5.63 % Detected problem language: tptp
% 0.14/5.64 % Proving...
% 57.85/15.46 % SZS status Started for theBenchmark.p
% 57.85/15.46 % SZS status Theorem for theBenchmark.p
% 57.85/15.46
% 57.85/15.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.85/15.46
% 57.85/15.46 % ------ iProver source info
% 57.85/15.46
% 57.85/15.46 % git: date: 2026-07-19 20:42:38 +0200
% 57.85/15.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.85/15.46 % git: non_committed_changes: false
% 57.85/15.46
% 57.85/15.46 % ------ Parsing...
% 57.85/15.46 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 57.85/15.46 %
% 57.85/15.46
% 57.85/15.46 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 57.85/15.46
% 57.85/15.46 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 57.85/15.46 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.85/15.46
% 57.85/15.46 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 57.85/15.46 % ------ Proving...
% 57.85/15.46 % ------ Problem Properties
% 57.85/15.46
% 57.85/15.46 %
% 57.85/15.46 % clauses 47
% 57.85/15.46 % conjectures 2
% 57.85/15.46 % EPR 2
% 57.85/15.46 % Horn 47
% 57.85/15.46 % unary 47
% 57.85/15.46 % binary 0
% 57.85/15.46 % lits 47
% 57.85/15.46 % lits eq 47
% 57.85/15.46 % fd_pure 0
% 57.85/15.46 % fd_pseudo 0
% 57.85/15.46 % fd_cond 0
% 57.85/15.46 % fd_pseudo_cond 0
% 57.85/15.46 % AC symbols 1
% 57.85/15.46
% 57.85/15.46 % ------ Schedule UEQ
% 57.85/15.46
% 57.85/15.46 % ------ Option_UEQ Time Limit: 10.
% 57.85/15.46
% 57.85/15.46
% 57.85/15.46 % ------
% 57.85/15.46 % Current options:
% 57.85/15.46 % ------
% 57.85/15.46
% 57.85/15.46
% 57.85/15.46 %
% 57.85/15.46
% 57.85/15.46 % ------ Proving...
% 57.85/15.46 %
% 57.85/15.46
% 57.85/15.46 % SZS status Theorem for theBenchmark.p
% 57.85/15.46
% 57.85/15.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.85/15.47
% 57.85/15.47
%------------------------------------------------------------------------------