%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:43:38 AM UTC 2026
% Result : Theorem 76.24s 29.39s
% Output : CNFRefutation 76.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 21
% Syntax : Number of formulae : 157 ( 140 unt; 0 def)
% Number of atoms : 176 ( 155 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 13 |; 0 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 230 ( 21 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_associativity,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ).
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(additive_idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
fof(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
fof(left_distributivity,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ).
fof(right_annihilation,axiom,
! [X0] : multiplication(X0,zero) = zero ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero ).
fof(domain2,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(complement,axiom,
! [X0] : c(X0) = antidomain(domain(X0)) ).
fof(domain_difference,axiom,
! [X0,X1] : 'domain$udifference'(X0,X1) = multiplication(domain(X0),antidomain(X1)) ).
fof(forward_diamond,axiom,
! [X0,X1] : 'forward$udiamond'(X0,X1) = domain(multiplication(X0,domain(X1))) ).
fof(divergence1,axiom,
! [X0] : 'forward$udiamond'(X0,divergence(X0)) = divergence(X0) ).
fof(divergence2,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition('forward$udiamond'(X1,domain(X0)),domain(X2))) = addition('forward$udiamond'(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),'forward$udiamond'(star(X1),domain(X2)))) = addition(divergence(X1),'forward$udiamond'(star(X1),domain(X2))) ) ).
fof(goals,conjecture,
! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),'forward$udiamond'(X0,domain(X1))) = 'forward$udiamond'(X0,domain(X1))
=> domain(X1) = zero ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),'forward$udiamond'(X0,domain(X1))) = 'forward$udiamond'(X0,domain(X1))
=> domain(X1) = zero ) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c1,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(clausification,[status(esa)],[right_annihilation]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c13,plain,
multiplication(antidomain(X0),X0) = zero,
inference(clausification,[status(esa)],[domain1]) ).
cnf(c14,plain,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(clausification,[status(esa)],[domain2]) ).
cnf(c15,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(clausification,[status(esa)],[domain3]) ).
cnf(c16,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(clausification,[status(esa)],[domain4]) ).
cnf(c21,plain,
c(X0) = antidomain(domain(X0)),
inference(clausification,[status(esa)],[complement]) ).
cnf(c22,plain,
'domain$udifference'(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(clausification,[status(esa)],[domain_difference]) ).
cnf(c23,plain,
'forward$udiamond'(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(clausification,[status(esa)],[forward_diamond]) ).
cnf(c27,plain,
'forward$udiamond'(X0,divergence(X0)) = divergence(X0),
inference(clausification,[status(esa)],[divergence1]) ).
cnf(c28,plain,
( addition(domain(X0),addition(divergence(X1),'forward$udiamond'(star(X1),domain(X2)))) = addition(divergence(X1),'forward$udiamond'(star(X1),domain(X2)))
| addition(domain(X0),addition('forward$udiamond'(X1,domain(X0)),domain(X2))) != addition('forward$udiamond'(X1,domain(X0)),domain(X2)) ),
inference(clausification,[status(esa)],[divergence2]) ).
cnf(c29,plain,
divergence(sK47) = zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
addition(domain(sK48),'forward$udiamond'(sK47,domain(sK48))) = 'forward$udiamond'(sK47,domain(sK48)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
domain(sK48) != zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d3,plain,
addition(X0,addition(zero,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d4,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
addition(domain(sK48),addition('forward$udiamond'(sK47,domain(sK48)),X0)) = addition('forward$udiamond'(sK47,domain(sK48)),X0),
inference(superposition,[status(thm)],[c30,c1]) ).
cnf(d7,plain,
addition(domain(sK48),addition(X0,'forward$udiamond'(sK47,domain(sK48)))) = addition('forward$udiamond'(sK47,domain(sK48)),X0),
inference(superposition,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
addition(domain(sK48),addition(addition(X0,'forward$udiamond'(sK47,domain(sK48))),X1)) = addition(addition('forward$udiamond'(sK47,domain(sK48)),X0),X1),
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
addition(domain(sK48),addition(X0,addition('forward$udiamond'(sK47,domain(sK48)),X1))) = addition(addition('forward$udiamond'(sK47,domain(sK48)),X0),X1),
inference(demodulation,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
addition(domain(sK48),addition(X0,addition('forward$udiamond'(sK47,domain(sK48)),X1))) = addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1)),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(superposition,[status(thm)],[c1,c1]) ).
cnf(d12,plain,
addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X1,X2)),X3),
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(addition(X1,X2),X3)),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
addition(X3,addition(X0,addition(X1,X2))) = addition(X3,addition(X0,addition(X1,X2))),
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d16,plain,
addition(X3,addition(X1,addition(X2,X0))) = addition(X3,addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d18,plain,
addition(addition(X0,addition('forward$udiamond'(sK47,domain(sK48)),X1)),addition(domain(sK48),X2)) = addition(addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1)),X2),
inference(superposition,[status(thm)],[d10,d17]) ).
cnf(d19,plain,
addition(X0,addition(addition('forward$udiamond'(sK47,domain(sK48)),X1),addition(domain(sK48),X2))) = addition(addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1)),X2),
inference(demodulation,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
addition(X0,addition(domain(sK48),addition(X2,addition('forward$udiamond'(sK47,domain(sK48)),X1)))) = addition(addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1)),X2),
inference(demodulation,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
addition(X2,addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1))) = addition(addition('forward$udiamond'(sK47,domain(sK48)),addition(X2,X1)),X0),
inference(demodulation,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
addition(X0,addition('forward$udiamond'(sK47,domain(sK48)),addition(X2,X1))) = addition('forward$udiamond'(sK47,domain(sK48)),addition(addition(X0,X1),X2)),
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
addition(X0,addition('forward$udiamond'(sK47,domain(sK48)),addition(X2,X1))) = addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,addition(X1,X2))),
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
leq(X0,addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,addition(X2,X1)))),
inference(superposition,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X0,X1),X2),
inference(superposition,[status(thm)],[d0,d17]) ).
cnf(d26,plain,
addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[d26,c1]) ).
cnf(d28,plain,
leq(X0,addition('forward$udiamond'(sK47,domain(sK48)),addition(X0,X1))),
inference(superposition,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d30,plain,
addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)) = addition(one,X1),
inference(superposition,[status(thm)],[d29,c1]) ).
cnf(d31,plain,
addition(antidomain(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(demodulation,[status(thm)],[d30,c16]) ).
cnf(d32,plain,
addition(domain(X0),addition(X1,antidomain(X0))) = addition(one,X1),
inference(demodulation,[status(thm)],[d31,d15]) ).
cnf(d33,plain,
addition('forward$udiamond'(X0,X1),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(one,X2),
inference(superposition,[status(thm)],[c23,d32]) ).
cnf(d34,plain,
leq(X0,addition(one,X0)),
inference(superposition,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(demodulation,[status(thm)],[d29,c16]) ).
cnf(d36,plain,
addition(domain(X0),antidomain(X0)) = one,
inference(demodulation,[status(thm)],[d35,c0]) ).
cnf(d37,plain,
addition(one,domain(X0)) = addition(domain(X0),antidomain(X0)),
inference(superposition,[status(thm)],[d32,d0]) ).
cnf(d38,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
leq(domain(X0),one),
inference(superposition,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
domain(antidomain(X0)) = antidomain(domain(X0)),
inference(superposition,[status(thm)],[c16,c16]) ).
cnf(d41,plain,
domain(antidomain(X0)) = c(X0),
inference(demodulation,[status(thm)],[d40,c21]) ).
cnf(d42,plain,
leq(c(X0),one),
inference(superposition,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
addition(c(X0),one) = one,
inference(resolution,[status(thm)],[d42,c11]) ).
cnf(d44,plain,
addition(one,c(X0)) = one,
inference(demodulation,[status(thm)],[d43,c0]) ).
cnf(d45,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d46,plain,
addition(domain(one),addition(X0,zero)) = addition(one,X0),
inference(superposition,[status(thm)],[d45,d32]) ).
cnf(d47,plain,
addition(zero,addition(domain(one),X0)) = addition(one,X0),
inference(demodulation,[status(thm)],[d46,d15]) ).
cnf(d48,plain,
addition(domain(one),X0) = addition(one,X0),
inference(demodulation,[status(thm)],[d47,d2]) ).
cnf(d49,plain,
zero = antidomain(one),
inference(superposition,[status(thm)],[c13,c5]) ).
cnf(d50,plain,
domain(one) = antidomain(zero),
inference(superposition,[status(thm)],[d49,c16]) ).
cnf(d51,plain,
'domain$udifference'(X1,antidomain(X0)) = multiplication(domain(X1),domain(X0)),
inference(superposition,[status(thm)],[c16,c22]) ).
cnf(d52,plain,
( leq(multiplication(X0,X1),multiplication(X2,X1))
| multiplication(addition(X0,X2),X1) != multiplication(X2,X1) ),
inference(superposition,[status(thm)],[c8,c12]) ).
cnf(d53,plain,
( leq(multiplication(X0,X2),multiplication(addition(X0,X1),X2))
| multiplication(addition(X0,X1),X2) != multiplication(addition(X0,X1),X2) ),
inference(superposition,[status(thm)],[d0,d52]) ).
cnf(d54,plain,
multiplication(X0,multiplication(one,X1)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(d55,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d54,c6]) ).
cnf(d56,plain,
leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(resolution,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
( addition(domain(sK48),addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0)))) = addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0)))
| addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) ),
inference(superposition,[status(thm)],[d6,c28]) ).
cnf(d58,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition(domain(sK48),addition(zero,'forward$udiamond'(star(sK47),domain(X0)))) = addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0))) ),
inference(demodulation,[status(thm)],[d57,c29]) ).
cnf(d59,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition(zero,addition('forward$udiamond'(star(sK47),domain(X0)),domain(sK48))) = addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0))) ),
inference(demodulation,[status(thm)],[d58,d15]) ).
cnf(d60,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition('forward$udiamond'(star(sK47),domain(X0)),domain(sK48)) = addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0))) ),
inference(demodulation,[status(thm)],[d59,d2]) ).
cnf(d61,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition(domain(sK48),'forward$udiamond'(star(sK47),domain(X0))) = addition(divergence(sK47),'forward$udiamond'(star(sK47),domain(X0))) ),
inference(demodulation,[status(thm)],[d60,c0]) ).
cnf(d62,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition(domain(sK48),'forward$udiamond'(star(sK47),domain(X0))) = addition(zero,'forward$udiamond'(star(sK47),domain(X0))) ),
inference(demodulation,[status(thm)],[d61,c29]) ).
cnf(d63,plain,
( addition('forward$udiamond'(sK47,domain(sK48)),domain(X0)) != addition('forward$udiamond'(sK47,domain(sK48)),domain(X0))
| addition(domain(sK48),'forward$udiamond'(star(sK47),domain(X0))) = 'forward$udiamond'(star(sK47),domain(X0)) ),
inference(demodulation,[status(thm)],[d62,d2]) ).
cnf(d64,plain,
addition(domain(sK48),'forward$udiamond'(star(sK47),domain(X0))) = 'forward$udiamond'(star(sK47),domain(X0)),
inference(resolution,[status(thm)],[d4,d63]) ).
cnf(d65,plain,
leq(domain(sK48),'forward$udiamond'(star(sK47),domain(X0))),
inference(superposition,[status(thm)],[d64,d5]) ).
cnf(d66,plain,
leq(domain(sK48),'forward$udiamond'(star(sK47),'forward$udiamond'(X0,X1))),
inference(superposition,[status(thm)],[c23,d65]) ).
cnf(d67,plain,
'forward$udiamond'(sK47,zero) = divergence(sK47),
inference(superposition,[status(thm)],[c29,c27]) ).
cnf(d68,plain,
'forward$udiamond'(sK47,zero) = zero,
inference(demodulation,[status(thm)],[d67,c29]) ).
cnf(d69,plain,
leq(domain(sK48),'forward$udiamond'(star(sK47),zero)),
inference(superposition,[status(thm)],[d68,d66]) ).
cnf(d70,plain,
addition(domain(sK48),'forward$udiamond'(star(sK47),zero)) = 'forward$udiamond'(star(sK47),zero),
inference(resolution,[status(thm)],[d69,c11]) ).
cnf(d71,plain,
leq(multiplication(domain(sK48),X0),multiplication('forward$udiamond'(star(sK47),zero),X0)),
inference(superposition,[status(thm)],[d70,d56]) ).
cnf(d72,plain,
'domain$udifference'(multiplication(X0,domain(X1)),X2) = multiplication('forward$udiamond'(X0,X1),antidomain(X2)),
inference(superposition,[status(thm)],[c23,c22]) ).
cnf(d73,plain,
multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[status(thm)],[c13,c7]) ).
cnf(d74,plain,
multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[d73,c2]) ).
cnf(d75,plain,
addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(zero))))) = antidomain(multiplication(X0,antidomain(antidomain(zero)))),
inference(superposition,[status(thm)],[c9,c14]) ).
cnf(d76,plain,
addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))) = antidomain(multiplication(X0,antidomain(antidomain(zero)))),
inference(demodulation,[status(thm)],[d75,c16]) ).
cnf(d77,plain,
addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))) = antidomain(multiplication(X0,domain(zero))),
inference(demodulation,[status(thm)],[d76,c16]) ).
cnf(d78,plain,
multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(multiplication(X0,domain(zero)))) = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(zero)),
inference(superposition,[status(thm)],[d77,d74]) ).
cnf(d79,plain,
zero = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(zero)),
inference(demodulation,[status(thm)],[d78,c13]) ).
cnf(d80,plain,
zero = multiplication(domain(multiplication(X0,domain(zero))),antidomain(zero)),
inference(demodulation,[status(thm)],[d79,c16]) ).
cnf(d81,plain,
zero = 'domain$udifference'(multiplication(X0,domain(zero)),zero),
inference(demodulation,[status(thm)],[d80,c22]) ).
cnf(d82,plain,
zero = multiplication('forward$udiamond'(X0,zero),antidomain(zero)),
inference(demodulation,[status(thm)],[d81,d72]) ).
cnf(d83,plain,
zero = multiplication('forward$udiamond'(X0,zero),domain(one)),
inference(demodulation,[status(thm)],[d82,d50]) ).
cnf(d84,plain,
leq(multiplication(domain(sK48),domain(one)),zero),
inference(superposition,[status(thm)],[d83,d71]) ).
cnf(d85,plain,
leq('domain$udifference'(sK48,antidomain(one)),zero),
inference(demodulation,[status(thm)],[d84,d51]) ).
cnf(d86,plain,
leq('domain$udifference'(sK48,zero),zero),
inference(demodulation,[status(thm)],[d85,d49]) ).
cnf(d87,plain,
addition('domain$udifference'(sK48,zero),zero) = zero,
inference(resolution,[status(thm)],[d86,c11]) ).
cnf(d88,plain,
'domain$udifference'(sK48,zero) = zero,
inference(demodulation,[status(thm)],[d87,c2]) ).
cnf(d89,plain,
addition(antidomain(X0),antidomain(multiplication(X0,antidomain(antidomain(one))))) = antidomain(multiplication(X0,antidomain(antidomain(one)))),
inference(superposition,[status(thm)],[c5,c14]) ).
cnf(d90,plain,
addition(antidomain(X0),antidomain(multiplication(X0,domain(one)))) = antidomain(multiplication(X0,antidomain(antidomain(one)))),
inference(demodulation,[status(thm)],[d89,c16]) ).
cnf(d91,plain,
addition(antidomain(X0),antidomain(multiplication(X0,domain(one)))) = antidomain(multiplication(X0,domain(one))),
inference(demodulation,[status(thm)],[d90,c16]) ).
cnf(d92,plain,
addition(c(X0),antidomain(multiplication(domain(X0),domain(one)))) = antidomain(multiplication(domain(X0),domain(one))),
inference(superposition,[status(thm)],[c21,d91]) ).
cnf(d93,plain,
addition(c(X0),antidomain('domain$udifference'(X0,antidomain(one)))) = antidomain(multiplication(domain(X0),domain(one))),
inference(demodulation,[status(thm)],[d92,d51]) ).
cnf(d94,plain,
addition(c(X0),antidomain('domain$udifference'(X0,zero))) = antidomain(multiplication(domain(X0),domain(one))),
inference(demodulation,[status(thm)],[d93,d49]) ).
cnf(d95,plain,
addition(c(X0),antidomain('domain$udifference'(X0,zero))) = antidomain('domain$udifference'(X0,antidomain(one))),
inference(demodulation,[status(thm)],[d94,d51]) ).
cnf(d96,plain,
addition(c(X0),antidomain('domain$udifference'(X0,zero))) = antidomain('domain$udifference'(X0,zero)),
inference(demodulation,[status(thm)],[d95,d49]) ).
cnf(d97,plain,
addition(c(sK48),antidomain(zero)) = antidomain('domain$udifference'(sK48,zero)),
inference(superposition,[status(thm)],[d88,d96]) ).
cnf(d98,plain,
addition(antidomain(zero),c(sK48)) = antidomain('domain$udifference'(sK48,zero)),
inference(demodulation,[status(thm)],[d97,c0]) ).
cnf(d99,plain,
addition(domain(one),c(sK48)) = antidomain('domain$udifference'(sK48,zero)),
inference(demodulation,[status(thm)],[d98,d50]) ).
cnf(d100,plain,
addition(domain(one),c(sK48)) = antidomain(zero),
inference(demodulation,[status(thm)],[d99,d88]) ).
cnf(d101,plain,
addition(domain(one),c(sK48)) = domain(one),
inference(demodulation,[status(thm)],[d100,d50]) ).
cnf(d102,plain,
domain(one) = addition(domain(one),c(sK48)),
inference(superposition,[status(thm)],[d101,d4]) ).
cnf(d103,plain,
domain(one) = addition(one,c(sK48)),
inference(demodulation,[status(thm)],[d102,d48]) ).
cnf(d104,plain,
domain(one) = one,
inference(demodulation,[status(thm)],[d103,d44]) ).
cnf(d105,plain,
zero = multiplication('forward$udiamond'(X0,zero),one),
inference(demodulation,[status(thm)],[d83,d104]) ).
cnf(d106,plain,
zero = 'forward$udiamond'(X0,zero),
inference(demodulation,[status(thm)],[d105,c5]) ).
cnf(d107,plain,
addition(domain(sK48),zero) = 'forward$udiamond'(star(sK47),zero),
inference(demodulation,[status(thm)],[d70,d106]) ).
cnf(d108,plain,
addition(domain(sK48),zero) = zero,
inference(demodulation,[status(thm)],[d107,d106]) ).
cnf(d109,plain,
domain(sK48) = zero,
inference(demodulation,[status(thm)],[d108,c2]) ).
cnf(d110,plain,
$false,
inference(resolution,[status(thm)],[c31,d109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n003.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Fri Sep 25 19:26:58 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.24/29.39 % SZS status Theorem for theBenchmark.p
% 76.24/29.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------