%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 09:15:39 AM UTC 2026
% Result : Theorem 10.57s 1.98s
% Output : CNFRefutation 10.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 23 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 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 : 32 ( 1 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_016,axiom,
pB != pE ).
fof(axiom_017,axiom,
! [X0,X1] : proj1C(c2(X0,X1)) = X0 ).
fof(axiom_019,axiom,
! [X0] : append(nil,X0) = X0 ).
fof(axiom_020,axiom,
! [X0,X1,X2] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)) ).
fof(axiom_024,axiom,
linP(pB) = cons(b,nil) ).
fof(axiom_025,axiom,
linP(pE) = nil ).
fof(axiom_026,axiom,
! [X0,X1] : linC(c2(X0,X1)) = append(linP(X0),linP(X1)) ).
fof(goal_027,conjecture,
? [X0,X1] :
~ ( linC(X0) = linC(X1)
=> X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
~ ( linC(X0) = linC(X1)
=> X0 = X1 ),
inference(negate_conjecture,[status(cth)],[goal_027]) ).
cnf(c15,plain,
pB != pE,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c16,plain,
proj1C(c2(X0,X1)) = X0,
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c18,plain,
append(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c19,plain,
append(cons(X0,X1),X2) = cons(X0,append(X1,X2)),
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c23,plain,
linP(pB) = cons(b,nil),
inference(clausification,[status(esa)],[axiom_024]) ).
cnf(c24,plain,
linP(pE) = nil,
inference(clausification,[status(esa)],[axiom_025]) ).
cnf(c25,plain,
linC(c2(X0,X1)) = append(linP(X0),linP(X1)),
inference(clausification,[status(esa)],[axiom_026]) ).
cnf(c26,plain,
( X0 = X1
| linC(X0) != linC(X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
linC(c2(X0,pE)) = append(linP(X0),nil),
inference(superposition,[status(thm)],[c24,c25]) ).
cnf(d1,plain,
( X1 = c2(X0,pE)
| linC(X1) != append(linP(X0),nil) ),
inference(superposition,[status(thm)],[d0,c26]) ).
cnf(d2,plain,
append(linP(pB),X0) = cons(b,append(nil,X0)),
inference(superposition,[status(thm)],[c23,c19]) ).
cnf(d3,plain,
append(linP(pB),X0) = cons(b,X0),
inference(demodulation,[status(thm)],[d2,c18]) ).
cnf(d4,plain,
( X0 = c2(pB,pE)
| linC(X0) != cons(b,nil) ),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( linC(X0) != linP(pB)
| X0 = c2(pB,pE) ),
inference(demodulation,[status(thm)],[d4,c23]) ).
cnf(d6,plain,
linC(c2(pE,X0)) = append(nil,linP(X0)),
inference(superposition,[status(thm)],[c24,c25]) ).
cnf(d7,plain,
linC(c2(pE,X0)) = linP(X0),
inference(demodulation,[status(thm)],[d6,c18]) ).
cnf(d8,plain,
( c2(pE,X0) = c2(pB,pE)
| linP(X0) != linP(pB) ),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
c2(pE,pB) = c2(pB,pE),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
proj1C(c2(pB,pE)) = pE,
inference(superposition,[status(thm)],[d9,c16]) ).
cnf(d11,plain,
pB = pE,
inference(demodulation,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c15,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.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 : Sat Sep 26 16:56:15 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.57/1.98 % SZS status Theorem for theBenchmark.p
% 10.57/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------