%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE133+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 : n007.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 228.55s 53.38s
% Output : CNFRefutation 228.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 20
% Syntax : Number of formulae : 152 ( 140 unt; 0 def)
% Number of atoms : 166 ( 139 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 9 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 212 ( 24 sgn 40 !; 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(left_annihilation,axiom,
! [X0] : multiplication(zero,X0) = 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(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$udiamond'(X0,divergence(X0)) = divergence(X0) ).
fof(goals,conjecture,
! [X0] :
( ( ! [X2] : 'forward$udiamond'(X0,'forward$udiamond'(X0,domain(X2))) = 'forward$udiamond'(X0,domain(X2))
& ! [X1] : addition(domain(X1),'forward$udiamond'(star(X0),'domain$udifference'(domain(X1),'forward$udiamond'(X0,domain(X1))))) = 'forward$udiamond'(star(X0),'domain$udifference'(domain(X1),'forward$udiamond'(X0,domain(X1)))) )
=> ! [X3] : addition('forward$udiamond'(X0,domain(X3)),'forward$udiamond'(star(X0),'domain$udifference'(domain(X3),'forward$udiamond'(X0,domain(X3))))) = 'forward$udiamond'(star(X0),'domain$udifference'(domain(X3),'forward$udiamond'(X0,domain(X3)))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( ! [X2] : 'forward$udiamond'(X0,'forward$udiamond'(X0,domain(X2))) = 'forward$udiamond'(X0,domain(X2))
& ! [X1] : addition(domain(X1),'forward$udiamond'(star(X0),'domain$udifference'(domain(X1),'forward$udiamond'(X0,domain(X1))))) = 'forward$udiamond'(star(X0),'domain$udifference'(domain(X1),'forward$udiamond'(X0,domain(X1)))) )
=> ! [X3] : addition('forward$udiamond'(X0,domain(X3)),'forward$udiamond'(star(X0),'domain$udifference'(domain(X3),'forward$udiamond'(X0,domain(X3))))) = 'forward$udiamond'(star(X0),'domain$udifference'(domain(X3),'forward$udiamond'(X0,domain(X3)))) ),
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(addition(X0,X1),X2) = addition(X0,addition(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(multiplication(X0,X1),X2) = multiplication(X0,multiplication(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,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c8,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(clausification,[status(esa)],[right_annihilation]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_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,
antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,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,
antidomain(antidomain(X0)) = domain(X0),
inference(clausification,[status(esa)],[domain4]) ).
cnf(c22,plain,
multiplication(domain(X0),antidomain(X1)) = 'domain$udifference'(X0,X1),
inference(clausification,[status(esa)],[domain_difference]) ).
cnf(c23,plain,
domain(multiplication(X0,domain(X1))) = 'forward$udiamond'(X0,X1),
inference(clausification,[status(esa)],[forward_diamond]) ).
cnf(c27,plain,
divergence(X0) = 'forward$udiamond'(X0,divergence(X0)),
inference(clausification,[status(esa)],[divergence1]) ).
cnf(c29,plain,
'forward$udiamond'(sK47,domain(X0)) = 'forward$udiamond'(sK47,'forward$udiamond'(sK47,domain(X0))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))) = addition(domain(X0),'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
'forward$udiamond'(star(sK47),'domain$udifference'(domain(sK50),'forward$udiamond'(sK47,domain(sK50)))) != addition('forward$udiamond'(sK47,domain(sK50)),'forward$udiamond'(star(sK47),'domain$udifference'(domain(sK50),'forward$udiamond'(sK47,domain(sK50))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d2,plain,
addition(X1,addition(X2,X0)) = addition(X2,addition(X1,X0)),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d4,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(demodulation,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d6,plain,
addition(antidomain(X0),domain(X0)) = addition(antidomain(X0),one),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
one = addition(antidomain(X0),one),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
one = addition(one,antidomain(X0)),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
addition(multiplication(antidomain(X0),X1),zero) = multiplication(antidomain(X0),addition(X1,X0)),
inference(superposition,[status(thm)],[c13,c7]) ).
cnf(d10,plain,
multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
multiplication(antidomain(addition(X0,X1)),X0) = multiplication(antidomain(addition(X0,X1)),addition(X0,X1)),
inference(superposition,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
multiplication(antidomain(addition(X0,X1)),X0) = zero,
inference(demodulation,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
zero = antidomain(one),
inference(superposition,[status(thm)],[c13,c5]) ).
cnf(d14,plain,
antidomain(zero) = domain(one),
inference(superposition,[status(thm)],[d13,c16]) ).
cnf(d15,plain,
addition(one,X1) = addition(antidomain(X0),addition(antidomain(antidomain(X0)),X1)),
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d16,plain,
addition(one,X1) = addition(antidomain(X0),addition(domain(X0),X1)),
inference(demodulation,[status(thm)],[d15,c16]) ).
cnf(d17,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d18,plain,
addition(one,X0) = addition(zero,addition(domain(one),X0)),
inference(superposition,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
addition(one,X0) = addition(domain(one),X0),
inference(demodulation,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
addition(one,X0) = addition(antidomain(zero),X0),
inference(demodulation,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
antidomain(multiplication(X0,antidomain(antidomain(one)))) = addition(antidomain(X0),antidomain(multiplication(X0,antidomain(antidomain(one))))),
inference(superposition,[status(thm)],[c5,c14]) ).
cnf(d22,plain,
antidomain(multiplication(X0,domain(one))) = addition(antidomain(X0),antidomain(multiplication(X0,antidomain(antidomain(one))))),
inference(demodulation,[status(thm)],[d21,c16]) ).
cnf(d23,plain,
antidomain(multiplication(X0,domain(one))) = addition(antidomain(X0),antidomain(multiplication(X0,domain(one)))),
inference(demodulation,[status(thm)],[d22,c16]) ).
cnf(d24,plain,
( leq(antidomain(X0),antidomain(multiplication(X0,domain(one))))
| antidomain(multiplication(X0,domain(one))) != antidomain(multiplication(X0,domain(one))) ),
inference(superposition,[status(thm)],[d23,c12]) ).
cnf(d25,plain,
( leq(antidomain(X0),antidomain(multiplication(X0,domain(one))))
| antidomain(multiplication(X0,antidomain(zero))) != antidomain(multiplication(X0,domain(one))) ),
inference(demodulation,[status(thm)],[d24,d14]) ).
cnf(d26,plain,
( leq(antidomain(X0),antidomain(multiplication(X0,domain(one))))
| antidomain(multiplication(X0,antidomain(zero))) != antidomain(multiplication(X0,antidomain(zero))) ),
inference(demodulation,[status(thm)],[d25,d14]) ).
cnf(d27,plain,
( leq(antidomain(X0),antidomain(multiplication(X0,antidomain(zero))))
| antidomain(multiplication(X0,antidomain(zero))) != antidomain(multiplication(X0,antidomain(zero))) ),
inference(demodulation,[status(thm)],[d26,d14]) ).
cnf(d28,plain,
addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c5,c7]) ).
cnf(d29,plain,
addition(antidomain(X0),zero) = multiplication(antidomain(X0),addition(one,X0)),
inference(superposition,[status(thm)],[c13,d28]) ).
cnf(d30,plain,
antidomain(X0) = multiplication(antidomain(X0),addition(one,X0)),
inference(demodulation,[status(thm)],[d29,c2]) ).
cnf(d31,plain,
antidomain(X0) = multiplication(antidomain(X0),one),
inference(demodulation,[status(thm)],[d30,d10]) ).
cnf(d32,plain,
antidomain(X0) = antidomain(X0),
inference(demodulation,[status(thm)],[d31,c5]) ).
cnf(d33,plain,
leq(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))),
inference(resolution,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
( leq(multiplication(X0,X1),multiplication(X2,X1))
| multiplication(addition(X0,X2),X1) != multiplication(X2,X1) ),
inference(superposition,[status(thm)],[c8,c12]) ).
cnf(d35,plain,
( leq(multiplication(X0,X2),multiplication(addition(X0,X1),X2))
| multiplication(addition(X0,X1),X2) != multiplication(addition(X0,X1),X2) ),
inference(superposition,[status(thm)],[d5,d34]) ).
cnf(d36,plain,
multiplication(X0,X1) = multiplication(X0,multiplication(one,X1)),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(d37,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d36,c6]) ).
cnf(d38,plain,
leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
addition(X0,X1) = addition(X0,addition(zero,X1)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d40,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d39,d0]) ).
cnf(d41,plain,
multiplication(domain(X0),antidomain(X0)) = zero,
inference(superposition,[status(thm)],[c16,c13]) ).
cnf(d42,plain,
'domain$udifference'(X0,X0) = zero,
inference(demodulation,[status(thm)],[d41,c22]) ).
cnf(d43,plain,
( leq(domain(X0),'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))))
| 'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))) != 'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))) ),
inference(superposition,[status(thm)],[c30,c12]) ).
cnf(d44,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),X1) = addition(domain(X0),addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),X1)),
inference(superposition,[status(thm)],[c30,c1]) ).
cnf(d45,plain,
addition(addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),X1),X2) = addition(domain(X0),addition(addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),X1),X2)),
inference(superposition,[status(thm)],[d44,c1]) ).
cnf(d46,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),addition(X1,X2)) = addition(domain(X0),addition(addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),X1),X2)),
inference(demodulation,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),addition(X1,X2)) = addition(domain(X0),addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),addition(X1,X2))),
inference(demodulation,[status(thm)],[d46,c1]) ).
cnf(d48,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),addition(X1,X2)) = addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),addition(X1,X2)),
inference(demodulation,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X1),'forward$udiamond'(sK47,domain(X1)))),X0) = addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X1),'forward$udiamond'(sK47,domain(X1)))),addition(X0,X0)),
inference(superposition,[status(thm)],[c3,d48]) ).
cnf(d50,plain,
addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X1),'forward$udiamond'(sK47,domain(X1)))),X0) = addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X1),'forward$udiamond'(sK47,domain(X1)))),X0),
inference(demodulation,[status(thm)],[d49,c3]) ).
cnf(d51,plain,
'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))) = addition('forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),zero),
inference(superposition,[status(thm)],[c2,d50]) ).
cnf(d52,plain,
'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))) = 'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0)))),
inference(demodulation,[status(thm)],[d51,c2]) ).
cnf(d53,plain,
leq(domain(X0),'forward$udiamond'(star(sK47),'domain$udifference'(domain(X0),'forward$udiamond'(sK47,domain(X0))))),
inference(resolution,[status(thm)],[d52,d43]) ).
cnf(d54,plain,
leq('forward$udiamond'(X0,X1),'forward$udiamond'(star(sK47),'domain$udifference'(domain(multiplication(X0,domain(X1))),'forward$udiamond'(sK47,domain(multiplication(X0,domain(X1))))))),
inference(superposition,[status(thm)],[c23,d53]) ).
cnf(d55,plain,
leq('forward$udiamond'(X0,X1),'forward$udiamond'(star(sK47),'domain$udifference'('forward$udiamond'(X0,X1),'forward$udiamond'(sK47,domain(multiplication(X0,domain(X1))))))),
inference(demodulation,[status(thm)],[d54,c23]) ).
cnf(d56,plain,
leq('forward$udiamond'(X0,X1),'forward$udiamond'(star(sK47),'domain$udifference'('forward$udiamond'(X0,X1),'forward$udiamond'(sK47,'forward$udiamond'(X0,X1))))),
inference(demodulation,[status(thm)],[d55,c23]) ).
cnf(d57,plain,
leq(divergence(X0),'forward$udiamond'(star(sK47),'domain$udifference'('forward$udiamond'(X0,divergence(X0)),'forward$udiamond'(sK47,'forward$udiamond'(X0,divergence(X0)))))),
inference(superposition,[status(thm)],[c27,d56]) ).
cnf(d58,plain,
leq(divergence(X0),'forward$udiamond'(star(sK47),'domain$udifference'(divergence(X0),'forward$udiamond'(sK47,'forward$udiamond'(X0,divergence(X0)))))),
inference(demodulation,[status(thm)],[d57,c27]) ).
cnf(d59,plain,
leq(divergence(X0),'forward$udiamond'(star(sK47),'domain$udifference'(divergence(X0),'forward$udiamond'(sK47,divergence(X0))))),
inference(demodulation,[status(thm)],[d58,c27]) ).
cnf(d60,plain,
leq(divergence(sK47),'forward$udiamond'(star(sK47),'domain$udifference'(divergence(sK47),divergence(sK47)))),
inference(superposition,[status(thm)],[c27,d59]) ).
cnf(d61,plain,
leq(divergence(sK47),'forward$udiamond'(star(sK47),zero)),
inference(demodulation,[status(thm)],[d60,d42]) ).
cnf(d62,plain,
addition(divergence(sK47),'forward$udiamond'(star(sK47),zero)) = 'forward$udiamond'(star(sK47),zero),
inference(resolution,[status(thm)],[d61,c11]) ).
cnf(d63,plain,
'forward$udiamond'(star(sK47),zero) = addition(divergence(sK47),'forward$udiamond'(star(sK47),zero)),
inference(superposition,[status(thm)],[d62,d40]) ).
cnf(d64,plain,
leq(multiplication(divergence(sK47),X0),multiplication('forward$udiamond'(star(sK47),zero),X0)),
inference(superposition,[status(thm)],[d63,d38]) ).
cnf(d65,plain,
multiplication('forward$udiamond'(X0,X1),antidomain(X2)) = 'domain$udifference'(multiplication(X0,domain(X1)),X2),
inference(superposition,[status(thm)],[c23,c22]) ).
cnf(d66,plain,
antidomain(multiplication(X0,antidomain(antidomain(zero)))) = addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(zero))))),
inference(superposition,[status(thm)],[c9,c14]) ).
cnf(d67,plain,
antidomain(multiplication(X0,domain(zero))) = addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(zero))))),
inference(demodulation,[status(thm)],[d66,c16]) ).
cnf(d68,plain,
antidomain(multiplication(X0,domain(zero))) = addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d67,c16]) ).
cnf(d69,plain,
multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(zero)) = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(multiplication(X0,domain(zero)))),
inference(superposition,[status(thm)],[d68,d10]) ).
cnf(d70,plain,
multiplication(domain(multiplication(X0,domain(zero))),antidomain(zero)) = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d69,c16]) ).
cnf(d71,plain,
'domain$udifference'(multiplication(X0,domain(zero)),zero) = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d70,c22]) ).
cnf(d72,plain,
multiplication('forward$udiamond'(X0,zero),antidomain(zero)) = multiplication(antidomain(antidomain(multiplication(X0,domain(zero)))),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d71,d65]) ).
cnf(d73,plain,
multiplication('forward$udiamond'(X0,zero),antidomain(zero)) = zero,
inference(demodulation,[status(thm)],[d72,c13]) ).
cnf(d74,plain,
leq(multiplication(divergence(sK47),antidomain(zero)),zero),
inference(superposition,[status(thm)],[d73,d64]) ).
cnf(d75,plain,
addition(multiplication(divergence(sK47),antidomain(zero)),zero) = zero,
inference(resolution,[status(thm)],[d74,c11]) ).
cnf(d76,plain,
multiplication(divergence(sK47),antidomain(zero)) = zero,
inference(demodulation,[status(thm)],[d75,c2]) ).
cnf(d77,plain,
leq(antidomain(divergence(sK47)),antidomain(zero)),
inference(superposition,[status(thm)],[d76,d33]) ).
cnf(d78,plain,
addition(antidomain(divergence(sK47)),antidomain(zero)) = antidomain(zero),
inference(resolution,[status(thm)],[d77,c11]) ).
cnf(d79,plain,
addition(antidomain(zero),antidomain(divergence(sK47))) = antidomain(zero),
inference(demodulation,[status(thm)],[d78,c0]) ).
cnf(d80,plain,
addition(one,antidomain(divergence(sK47))) = antidomain(zero),
inference(demodulation,[status(thm)],[d79,d20]) ).
cnf(d81,plain,
multiplication(antidomain(antidomain(zero)),one) = zero,
inference(superposition,[status(thm)],[d80,d12]) ).
cnf(d82,plain,
antidomain(antidomain(zero)) = zero,
inference(demodulation,[status(thm)],[d81,c5]) ).
cnf(d83,plain,
domain(zero) = zero,
inference(demodulation,[status(thm)],[d82,c16]) ).
cnf(d84,plain,
antidomain(multiplication(X1,domain(X0))) = addition(antidomain(multiplication(X1,X0)),antidomain(multiplication(X1,antidomain(antidomain(X0))))),
inference(demodulation,[status(thm)],[c14,c16]) ).
cnf(d85,plain,
antidomain(multiplication(X1,domain(X0))) = addition(antidomain(multiplication(X1,X0)),antidomain(multiplication(X1,domain(X0)))),
inference(demodulation,[status(thm)],[d84,c16]) ).
cnf(d86,plain,
multiplication(zero,X1) = multiplication(X0,multiplication(zero,X1)),
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(d87,plain,
zero = multiplication(X1,multiplication(zero,X0)),
inference(demodulation,[status(thm)],[d86,c10]) ).
cnf(d88,plain,
zero = multiplication(X1,zero),
inference(demodulation,[status(thm)],[d87,c10]) ).
cnf(d89,plain,
antidomain(multiplication(X0,domain(zero))) = addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))),
inference(superposition,[status(thm)],[d88,d85]) ).
cnf(d90,plain,
antidomain(multiplication(X0,zero)) = addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d89,d83]) ).
cnf(d91,plain,
antidomain(zero) = addition(antidomain(zero),antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d90,c9]) ).
cnf(d92,plain,
antidomain(zero) = addition(one,antidomain(multiplication(X0,domain(zero)))),
inference(demodulation,[status(thm)],[d91,d20]) ).
cnf(d93,plain,
antidomain(zero) = addition(one,antidomain(multiplication(X0,zero))),
inference(demodulation,[status(thm)],[d92,d83]) ).
cnf(d94,plain,
antidomain(zero) = addition(one,antidomain(zero)),
inference(demodulation,[status(thm)],[d93,c9]) ).
cnf(d95,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[d94,d8]) ).
cnf(d96,plain,
multiplication('forward$udiamond'(X0,zero),one) = zero,
inference(demodulation,[status(thm)],[d73,d95]) ).
cnf(d97,plain,
'forward$udiamond'(X0,zero) = zero,
inference(demodulation,[status(thm)],[d96,c5]) ).
cnf(d98,plain,
leq('forward$udiamond'(sK47,domain(X0)),'forward$udiamond'(star(sK47),'domain$udifference'('forward$udiamond'(sK47,domain(X0)),'forward$udiamond'(sK47,domain(X0))))),
inference(superposition,[status(thm)],[c29,d56]) ).
cnf(d99,plain,
leq('forward$udiamond'(sK47,domain(X0)),'forward$udiamond'(star(sK47),zero)),
inference(demodulation,[status(thm)],[d98,d42]) ).
cnf(d100,plain,
addition('forward$udiamond'(sK47,domain(X0)),'forward$udiamond'(star(sK47),zero)) = 'forward$udiamond'(star(sK47),zero),
inference(resolution,[status(thm)],[d99,c11]) ).
cnf(d101,plain,
addition(X1,'forward$udiamond'(star(sK47),zero)) = addition('forward$udiamond'(sK47,domain(X0)),addition('forward$udiamond'(star(sK47),zero),X1)),
inference(superposition,[status(thm)],[d100,d1]) ).
cnf(d102,plain,
addition(X0,zero) = addition('forward$udiamond'(sK47,domain(X1)),addition('forward$udiamond'(star(sK47),zero),X0)),
inference(demodulation,[status(thm)],[d101,d97]) ).
cnf(d103,plain,
X0 = addition('forward$udiamond'(sK47,domain(X1)),addition('forward$udiamond'(star(sK47),zero),X0)),
inference(demodulation,[status(thm)],[d102,c2]) ).
cnf(d104,plain,
X0 = addition('forward$udiamond'(sK47,domain(X1)),addition(zero,X0)),
inference(demodulation,[status(thm)],[d103,d97]) ).
cnf(d105,plain,
X1 = addition(zero,addition('forward$udiamond'(sK47,domain(X0)),X1)),
inference(demodulation,[status(thm)],[d104,d2]) ).
cnf(d106,plain,
X1 = addition('forward$udiamond'(sK47,domain(X0)),X1),
inference(demodulation,[status(thm)],[d105,d0]) ).
cnf(d107,plain,
$false,
inference(resolution,[status(thm)],[d106,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 19:23:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 228.55/53.38 % SZS status Theorem for theBenchmark.p
% 228.55/53.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------