%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE132+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:28 PM UTC 2026
% Result : Theorem 94.75s 13.82s
% Output : CNFRefutation 94.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of formulae : 172 ( 159 unt; 9 def)
% Number of atoms : 415 ( 197 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 50 ( 24 ~; 16 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 164 ( 0 sgn 160 !; 4 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] : addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> ! [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
=> domain(X2) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> ! [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
=> domain(X2) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
? [X0] :
( ! [X1] : addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
& ? [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& zero != domain(X2) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
? [X0] :
( ! [X2] : forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2)))) = addition(forward_diamond(X0,domain(X2)),forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2)))))
& ? [X1] :
( forward_diamond(X0,domain(X1)) = addition(domain(X1),forward_diamond(X0,domain(X1)))
& zero != domain(X1) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
( ! [X2] : forward_diamond(star(sK0),domain_difference(domain(X2),forward_diamond(sK0,domain(X2)))) = addition(forward_diamond(sK0,domain(X2)),forward_diamond(star(sK0),domain_difference(domain(X2),forward_diamond(sK0,domain(X2)))))
& forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1)))
& zero != domain(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f42,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f44,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f46,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f47,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(f48,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f55,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f62,plain,
! [X2] : forward_diamond(star(sK0),domain_difference(domain(X2),forward_diamond(sK0,domain(X2)))) = addition(forward_diamond(sK0,domain(X2)),forward_diamond(star(sK0),domain_difference(domain(X2),forward_diamond(sK0,domain(X2))))),
inference(cnf_transformation,[],[f34]) ).
fof(f63,plain,
forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1))),
inference(cnf_transformation,[],[f34]) ).
fof(f64,plain,
zero != domain(sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f68,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
inference(definition_unfolding,[],[f55,f49]) ).
fof(f69,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f56,f49,f49]) ).
fof(f73,plain,
zero != antidomain(antidomain(sK1)),
inference(definition_unfolding,[],[f64,f49]) ).
fof(f74,plain,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))) = addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))),
inference(definition_unfolding,[],[f63,f69,f49,f49,f69,f49]) ).
fof(f75,plain,
! [X2] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X2)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X2)))))))))))))) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X2))))))),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X2)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X2))))))))))))))),
inference(definition_unfolding,[],[f62,f69,f68,f49,f69,f49,f69,f49,f69,f68,f49,f69,f49]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f44]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f45]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f47]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f48]) ).
tcf(c_68,negated_conjecture,
antidomain(antidomain(sK1)) != zero,
inference(cnf_transformation,[],[f73]) ).
tcf(c_69,negated_conjecture,
addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) = antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),
inference(cnf_transformation,[],[f74]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] : addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))))))))),
inference(cnf_transformation,[],[f75]) ).
tcf(c_89,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_148,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_149,definition,
iPr_def_11 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_150,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_151,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_152,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_153,definition,
iPr_def_15 = multiplication(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_154,definition,
iPr_def_16 = antidomain(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_155,definition,
iPr_def_17 = antidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_156,definition,
iPr_def_18 = addition(iPr_def_12,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_157,negated_conjecture,
! [X0: $i] : addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))))))))) = antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))))))))),
inference(demodulation,[status(thm)],[c_70,c_148]) ).
tcf(c_158,negated_conjecture,
iPr_def_18 = iPr_def_17,
inference(demodulation,[status(thm)],[c_69,c_151,c_152,c_153,c_154,c_155,c_149,c_150,c_156]) ).
tcf(c_159,negated_conjecture,
iPr_def_12 != zero,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_160,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_171,plain,
zero = zero,
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_278,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_149,c_89]) ).
tcf(c_279,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_150,c_89]) ).
tcf(c_280,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_279,c_151]) ).
tcf(c_281,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_278,c_150]) ).
tcf(c_282,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_89,c_280]) ).
tcf(c_300,plain,
addition(iPr_def_12,iPr_def_17) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_156,c_158]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_356,plain,
! [X0: $i] :
( ( iPr_def_12 = zero )
| ( iPr_def_12 != X0 )
| ( zero != X0 ) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_361,plain,
addition(iPr_def_11,iPr_def_12) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_280,c_281]) ).
tcf(c_404,plain,
iPr_def_12 = iPr_def_12,
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_12 = X0 )
| ( iPr_def_12 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_596,plain,
! [X0: $i] :
( ( iPr_def_12 = X0 )
| ( iPr_def_12 != iPr_def_12 )
| ( X0 != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_937,plain,
( ( iPr_def_12 = addition(iPr_def_12,zero) )
| ( iPr_def_12 != iPr_def_12 )
| ( addition(iPr_def_12,zero) != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_596]) ).
tcf(c_938,plain,
addition(iPr_def_12,zero) = iPr_def_12,
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1148,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_11,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_282,c_361]) ).
tcf(c_1163,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = addition(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_155,c_1148]) ).
tcf(c_1919,plain,
( ( iPr_def_12 = zero )
| ( iPr_def_12 != addition(iPr_def_12,zero) )
| ( zero != addition(iPr_def_12,zero) ) ),
inference(instantiation,[status(thm)],[c_356]) ).
tcf(c_3340,plain,
addition(iPr_def_17,addition(iPr_def_11,iPr_def_12)) = addition(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_1163,c_329]) ).
tcf(c_3367,plain,
addition(iPr_def_11,addition(iPr_def_12,iPr_def_17)) = addition(iPr_def_11,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_3340,c_50,c_49]) ).
tcf(c_3368,plain,
addition(iPr_def_11,iPr_def_12) = addition(iPr_def_11,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_3367,c_300]) ).
tcf(c_3527,plain,
! [X0: $i] : addition(X0,addition(iPr_def_11,iPr_def_12)) = addition(iPr_def_11,addition(X0,iPr_def_17)),
inference(superposition,[status(thm)],[c_3368,c_269]) ).
tcf(c_3954,plain,
! [X0: $i] : addition(iPr_def_11,addition(X0,iPr_def_12)) = addition(iPr_def_11,addition(X0,iPr_def_17)),
inference(superposition,[status(thm)],[c_3527,c_269]) ).
tcf(c_4613,plain,
! [X0: $i] :
( ( zero = addition(iPr_def_12,zero) )
| ( zero != X0 )
| ( addition(iPr_def_12,zero) != X0 ) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_4614,plain,
( ( zero = addition(iPr_def_12,zero) )
| ( zero != zero )
| ( addition(iPr_def_12,zero) != zero ) ),
inference(instantiation,[status(thm)],[c_4613]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_11631,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_149,c_89]) ).
tcf(c_11632,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_150,c_89]) ).
tcf(c_11664,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_11632,c_151]) ).
tcf(c_11665,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_11631,c_150]) ).
tcf(c_11709,plain,
addition(iPr_def_11,iPr_def_12) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_11664,c_11665]) ).
tcf(c_11711,plain,
addition(iPr_def_12,addition(iPr_def_11,iPr_def_12)) = addition(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_11709,c_11187]) ).
tcf(c_11713,plain,
addition(iPr_def_11,addition(iPr_def_12,iPr_def_12)) = addition(iPr_def_11,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_11711,c_50,c_49]) ).
tcf(c_197985,plain,
addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(iPr_def_11)))))),antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(iPr_def_11))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(iPr_def_11)))))))))))))) = antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(iPr_def_11))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(iPr_def_11))))))))))))),
inference(superposition,[status(thm)],[c_149,c_157]) ).
tcf(c_197986,plain,
addition(iPr_def_17,antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_14,antidomain(iPr_def_17)))))))) = antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_14,antidomain(iPr_def_17))))))),
inference(light_normalisation,[status(thm)],[c_197985,c_150,c_151,c_152,c_153,c_154,c_155]) ).
tcf(c_197991,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_149,c_89]) ).
tcf(c_197992,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_150,c_89]) ).
tcf(c_197993,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_197992,c_151]) ).
tcf(c_197994,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_197991,c_150]) ).
tcf(c_198010,plain,
addition(iPr_def_12,iPr_def_17) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_156,c_158]) ).
tcf(c_198011,plain,
addition(iPr_def_11,addition(iPr_def_12,iPr_def_12)) = addition(iPr_def_11,iPr_def_17),
inference(superposition,[status(thm)],[c_198010,c_3954]) ).
tcf(c_198012,plain,
addition(iPr_def_11,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_198011,c_197994,c_11713]) ).
tcf(c_198020,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_60,c_54]) ).
tcf(c_198027,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_198030,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_198020,c_89]) ).
tcf(c_198065,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_198068,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_17,X0)) = addition(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_198010,c_50]) ).
tcf(c_198125,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_60,c_53]) ).
tcf(c_198191,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_60,c_56]) ).
tcf(c_198198,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,zero)),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_198212,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(X1,zero)),
inference(theory_normalisation,[status(thm)],[c_198198,c_50,c_49]) ).
tcf(c_198374,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_198377,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_60,c_57]) ).
tcf(c_198477,plain,
! [X0: $i] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_199190,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_198030,c_198027]) ).
tcf(c_200027,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_89,c_198065]) ).
tcf(c_200061,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_200027,c_50,c_49]) ).
tcf(c_204245,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_198125,c_59]) ).
tcf(c_210588,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_198191,c_51,c_198212]) ).
tcf(c_210594,plain,
! [X0: $i] : multiplication(iPr_def_14,addition(iPr_def_13,X0)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_152,c_210588]) ).
tcf(c_210611,plain,
multiplication(antidomain(iPr_def_11),one) = multiplication(antidomain(iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_197994,c_210588]) ).
tcf(c_210638,plain,
multiplication(antidomain(iPr_def_11),one) = multiplication(antidomain(iPr_def_11),iPr_def_17),
inference(superposition,[status(thm)],[c_198012,c_210588]) ).
tcf(c_210713,plain,
multiplication(iPr_def_12,one) = multiplication(iPr_def_12,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_210638,c_150]) ).
tcf(c_210716,plain,
multiplication(iPr_def_12,one) = multiplication(iPr_def_12,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_210611,c_150]) ).
tcf(c_211314,plain,
multiplication(iPr_def_12,iPr_def_12) = multiplication(iPr_def_12,iPr_def_17),
inference(demodulation,[status(thm)],[c_210713,c_210716]) ).
tcf(c_213550,plain,
! [X0: $i] : multiplication(iPr_def_14,addition(X0,iPr_def_13)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_49,c_210594]) ).
tcf(c_214217,plain,
multiplication(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_210716,c_54]) ).
tcf(c_214218,plain,
multiplication(iPr_def_12,iPr_def_17) = iPr_def_12,
inference(demodulation,[status(thm)],[c_211314,c_214217]) ).
tcf(c_214279,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(iPr_def_17,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_214218,c_53]) ).
tcf(c_214580,plain,
multiplication(iPr_def_14,one) = multiplication(iPr_def_14,iPr_def_12),
inference(superposition,[status(thm)],[c_197993,c_213550]) ).
tcf(c_218052,plain,
multiplication(iPr_def_14,iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_214580,c_54]) ).
tcf(c_225013,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_204245,c_198374]) ).
tcf(c_225295,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_225013,c_50,c_49]) ).
tcf(c_225296,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(one,multiplication(X0,X1)),
inference(light_normalisation,[status(thm)],[c_225295,c_200061]) ).
tcf(c_226961,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_198377,c_55,c_225296]) ).
tcf(c_226968,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_89,c_226961]) ).
tcf(c_227045,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_226968,c_55]) ).
tcf(c_227347,plain,
multiplication(antidomain(iPr_def_13),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_151,c_227045]) ).
tcf(c_227378,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_227347,c_152,c_218052]) ).
tcf(c_227513,plain,
addition(iPr_def_17,antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_12,antidomain(iPr_def_17)))))))) = antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_12,antidomain(iPr_def_17))))))),
inference(demodulation,[status(thm)],[c_197986,c_227378]) ).
tcf(c_240729,plain,
! [X0: $i] : addition(one,antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(light_normalisation,[status(thm)],[c_198477,c_199190]) ).
tcf(c_240730,plain,
! [X0: $i] : antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))) = one,
inference(demodulation,[status(thm)],[c_240729,c_200061]) ).
tcf(c_240748,plain,
antidomain(multiplication(iPr_def_17,antidomain(iPr_def_17))) = one,
inference(superposition,[status(thm)],[c_155,c_240730]) ).
tcf(c_241033,plain,
multiplication(one,multiplication(iPr_def_17,antidomain(iPr_def_17))) = zero,
inference(superposition,[status(thm)],[c_240748,c_60]) ).
tcf(c_242105,plain,
multiplication(iPr_def_17,antidomain(iPr_def_17)) = zero,
inference(demodulation,[status(thm)],[c_241033,c_55]) ).
tcf(c_242130,plain,
multiplication(iPr_def_12,antidomain(iPr_def_17)) = multiplication(iPr_def_12,zero),
inference(superposition,[status(thm)],[c_242105,c_214279]) ).
tcf(c_242157,plain,
addition(iPr_def_17,antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_12,zero))))))) = antidomain(antidomain(multiplication(iPr_def_10,antidomain(antidomain(multiplication(iPr_def_12,zero)))))),
inference(demodulation,[status(thm)],[c_227513,c_242130]) ).
tcf(c_242962,plain,
zero = iPr_def_17,
inference(demodulation,[status(thm)],[c_242157,c_51,c_58,c_198020,c_199190]) ).
tcf(c_243014,plain,
! [X0: $i] : addition(iPr_def_17,X0) = X0,
inference(demodulation,[status(thm)],[c_198027,c_242962]) ).
tcf(c_243066,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(demodulation,[status(thm)],[c_198068,c_243014]) ).
tcf(c_243228,plain,
addition(iPr_def_12,zero) = zero,
inference(instantiation,[status(thm)],[c_243066]) ).
tcf(c_243229,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_243228,c_4614,c_1919,c_938,c_937,c_404,c_159,c_171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE132+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 19:04:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 94.75/13.82 % SZS status Started for theBenchmark.p
% 94.75/13.82 % SZS status Theorem for theBenchmark.p
% 94.75/13.82
% 94.75/13.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 94.75/13.82
% 94.75/13.82 % ------ iProver source info
% 94.75/13.82
% 94.75/13.82 % git: date: 2026-07-19 20:42:38 +0200
% 94.75/13.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 94.75/13.82 % git: non_committed_changes: false
% 94.75/13.82
% 94.75/13.82 % ------ Parsing...
% 94.75/13.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 94.75/13.82
% 94.75/13.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 94.75/13.82
% 94.75/13.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 94.75/13.82
% 94.75/13.82 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 94.75/13.82 % ------ Proving...
% 94.75/13.82 % ------ Problem Properties
% 94.75/13.82
% 94.75/13.82 %
% 94.75/13.82 % clauses 31
% 94.75/13.82 % conjectures 3
% 94.75/13.82 % EPR 2
% 94.75/13.82 % Horn 31
% 94.75/13.82 % unary 30
% 94.75/13.82 % binary 1
% 94.75/13.82 % lits 32
% 94.75/13.82 % lits eq 32
% 94.75/13.82 % fd_pure 0
% 94.75/13.82 % fd_pseudo 0
% 94.75/13.82 % fd_cond 0
% 94.75/13.82 % fd_pseudo_cond 0
% 94.75/13.82 % AC symbols 1
% 94.75/13.82
% 94.75/13.82 % ------ Schedule dynamic 5 is on
% 94.75/13.82
% 94.75/13.82 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 94.75/13.82
% 94.75/13.82
% 94.75/13.82 % ------
% 94.75/13.82 % Current options:
% 94.75/13.82 % ------
% 94.75/13.82
% 94.75/13.82
% 94.75/13.82 %
% 94.75/13.82
% 94.75/13.82 % ------ Proving...
% 94.75/13.82 % Proof_search_loop: time out after: 5603 full_loop iterations
% 94.75/13.82
% 94.75/13.82 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 94.75/13.82
% 94.75/13.82
% 94.75/13.82 % ------
% 94.75/13.82 % Current options:
% 94.75/13.82 % ------
% 94.75/13.82
% 94.75/13.82
% 94.75/13.82 %
% 94.75/13.82
% 94.75/13.82 % ------ Proving...
% 94.75/13.82 %
% 94.75/13.82
% 94.75/13.82 % SZS status Theorem for theBenchmark.p
% 94.75/13.82
% 94.75/13.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 94.75/13.82
% 94.75/13.82
%------------------------------------------------------------------------------