%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE129+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 : n016.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 11.65s 3.32s
% Output : CNFRefutation 11.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
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] :
( ! [X1] :
( addition(domain(X1),'forward$udiamond'(X0,domain(X1))) = 'forward$udiamond'(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( addition(domain(X1),'forward$udiamond'(X0,domain(X1))) = 'forward$udiamond'(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
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(c29,plain,
( domain(X0) = zero
| addition(domain(X0),'forward$udiamond'(sK47,domain(X0))) != 'forward$udiamond'(sK47,domain(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
divergence(sK47) != zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( domain(multiplication(X0,domain(X1))) = zero
| addition(domain(multiplication(X0,domain(X1))),'forward$udiamond'(sK47,'forward$udiamond'(X0,X1))) != 'forward$udiamond'(sK47,domain(multiplication(X0,domain(X1)))) ),
inference(superposition,[status(thm)],[c23,c29]) ).
cnf(d1,plain,
( domain(multiplication(X0,domain(X1))) = zero
| addition('forward$udiamond'(X0,X1),'forward$udiamond'(sK47,'forward$udiamond'(X0,X1))) != 'forward$udiamond'(sK47,domain(multiplication(X0,domain(X1)))) ),
inference(demodulation,[status(thm)],[d0,c23]) ).
cnf(d2,plain,
( domain(multiplication(X0,domain(X1))) = zero
| addition('forward$udiamond'(X0,X1),'forward$udiamond'(sK47,'forward$udiamond'(X0,X1))) != 'forward$udiamond'(sK47,'forward$udiamond'(X0,X1)) ),
inference(demodulation,[status(thm)],[d1,c23]) ).
cnf(d3,plain,
( 'forward$udiamond'(X0,X1) = zero
| addition('forward$udiamond'(X0,X1),'forward$udiamond'(sK47,'forward$udiamond'(X0,X1))) != 'forward$udiamond'(sK47,'forward$udiamond'(X0,X1)) ),
inference(demodulation,[status(thm)],[d2,c23]) ).
cnf(d4,plain,
( 'forward$udiamond'(X0,divergence(X0)) = zero
| addition(divergence(X0),'forward$udiamond'(sK47,'forward$udiamond'(X0,divergence(X0)))) != 'forward$udiamond'(sK47,'forward$udiamond'(X0,divergence(X0))) ),
inference(superposition,[status(thm)],[c27,d3]) ).
cnf(d5,plain,
( 'forward$udiamond'(X0,divergence(X0)) = zero
| addition(divergence(X0),'forward$udiamond'(sK47,divergence(X0))) != 'forward$udiamond'(sK47,'forward$udiamond'(X0,divergence(X0))) ),
inference(demodulation,[status(thm)],[d4,c27]) ).
cnf(d6,plain,
( 'forward$udiamond'(X0,divergence(X0)) = zero
| addition(divergence(X0),'forward$udiamond'(sK47,divergence(X0))) != 'forward$udiamond'(sK47,divergence(X0)) ),
inference(demodulation,[status(thm)],[d5,c27]) ).
cnf(d7,plain,
( divergence(X0) = zero
| addition(divergence(X0),'forward$udiamond'(sK47,divergence(X0))) != 'forward$udiamond'(sK47,divergence(X0)) ),
inference(demodulation,[status(thm)],[d6,c27]) ).
cnf(d8,plain,
( divergence(sK47) = zero
| addition(divergence(sK47),divergence(sK47)) != 'forward$udiamond'(sK47,divergence(sK47)) ),
inference(superposition,[status(thm)],[c27,d7]) ).
cnf(d9,plain,
( divergence(sK47) = zero
| divergence(sK47) != 'forward$udiamond'(sK47,divergence(sK47)) ),
inference(demodulation,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( divergence(sK47) = zero
| divergence(sK47) != divergence(sK47) ),
inference(demodulation,[status(thm)],[d9,c27]) ).
cnf(d11,plain,
divergence(sK47) != divergence(sK47),
inference(resolution,[status(thm)],[c30,d10]) ).
cnf(d12,plain,
$false,
inference(equality_resolution,[status(thm)],[d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE129+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
% 0.16/0.43 % Computer : n016.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 19:29:45 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.65/3.32 % SZS status Theorem for theBenchmark.p
% 11.65/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------