%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:43:37 AM UTC 2026
% Result : Theorem 25.49s 8.82s
% Output : CNFRefutation 25.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(right_annihilation,axiom,
! [X0] : multiplication(X0,zero) = zero ).
fof(codomain1,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero ).
fof(codomain3,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one ).
fof(codomain4,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)) ).
fof(backward_diamond,axiom,
! [X0,X1] : 'backward$udiamond'(X0,X1) = codomain(multiplication(codomain(X1),X0)) ).
fof(goals,conjecture,
! [X0,X1] : addition('backward$udiamond'(zero,domain(X0)),domain(X1)) = domain(X1) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : addition('backward$udiamond'(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(clausification,[status(esa)],[right_annihilation]) ).
cnf(c17,plain,
multiplication(X0,coantidomain(X0)) = zero,
inference(clausification,[status(esa)],[codomain1]) ).
cnf(c19,plain,
addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(clausification,[status(esa)],[codomain3]) ).
cnf(c20,plain,
codomain(X0) = coantidomain(coantidomain(X0)),
inference(clausification,[status(esa)],[codomain4]) ).
cnf(c24,plain,
'backward$udiamond'(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(clausification,[status(esa)],[backward_diamond]) ).
cnf(c27,plain,
addition('backward$udiamond'(zero,domain(sK43)),domain(sK44)) != domain(sK44),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
zero = coantidomain(one),
inference(superposition,[status(thm)],[c17,c6]) ).
cnf(d1,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(demodulation,[status(thm)],[c19,c0]) ).
cnf(d3,plain,
addition(zero,coantidomain(coantidomain(one))) = one,
inference(superposition,[status(thm)],[d0,d2]) ).
cnf(d4,plain,
coantidomain(coantidomain(one)) = one,
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
codomain(one) = one,
inference(demodulation,[status(thm)],[d4,c20]) ).
cnf(d6,plain,
codomain(one) = coantidomain(zero),
inference(superposition,[status(thm)],[d0,c20]) ).
cnf(d7,plain,
one = coantidomain(zero),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
codomain(zero) = coantidomain(one),
inference(superposition,[status(thm)],[d7,c20]) ).
cnf(d9,plain,
codomain(zero) = zero,
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
'backward$udiamond'(zero,X0) = codomain(zero),
inference(superposition,[status(thm)],[c9,c24]) ).
cnf(d11,plain,
addition(domain(sK44),'backward$udiamond'(zero,domain(sK43))) != domain(sK44),
inference(demodulation,[status(thm)],[c27,c0]) ).
cnf(d12,plain,
addition(domain(sK44),codomain(zero)) != domain(sK44),
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
addition(domain(sK44),zero) != domain(sK44),
inference(demodulation,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
domain(sK44) != domain(sK44),
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
$false,
inference(equality_resolution,[status(thm)],[d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.56 % Computer : n017.cluster.edu
% 0.12/5.56 % Model : x86_64 x86_64
% 0.12/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.56 % Memory : 8046.5625MB
% 0.12/5.56 % OS : Linux 6.8.0-71-generic
% 0.12/5.56 % CPULimit : 300
% 0.12/5.56 % WCLimit : 300
% 0.12/5.56 % DateTime : Fri Sep 25 19:19:40 UTC 2026
% 0.12/5.56 % CPUTime :
% 0.12/5.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.49/8.82 % SZS status Theorem for theBenchmark.p
% 25.49/8.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------