%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP656+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 : n002.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 07:24:23 AM UTC 2026
% Result : Theorem 13.72s 3.44s
% Output : CNFRefutation 13.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 26 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 60 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0 ).
fof(f02,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0 ).
fof(f03,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1 ).
fof(f04,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1 ).
fof(f05,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),mult(X0,X2)) = mult(mult(X2,mult(X1,X0)),X2) ).
fof(goals,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
mult(X0,ld(X0,X1)) = X1,
inference(clausification,[status(esa)],[f01]) ).
cnf(c1,plain,
ld(X0,mult(X0,X1)) = X1,
inference(clausification,[status(esa)],[f02]) ).
cnf(c2,plain,
mult(rd(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[f03]) ).
cnf(c3,plain,
rd(mult(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[f04]) ).
cnf(c4,plain,
mult(mult(X0,X1),mult(X2,X0)) = mult(mult(X0,mult(X1,X2)),X0),
inference(clausification,[status(esa)],[f05]) ).
cnf(c5,plain,
( mult(X0,sK12(X0)) != sK12(X0)
| mult(sK12(X0),X0) != sK12(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
rd(mult(mult(X0,X1),mult(X2,X0)),X0) = mult(X0,mult(X1,X2)),
inference(superposition,[status(thm)],[c4,c3]) ).
cnf(d1,plain,
rd(mult(mult(X1,X2),X0),X1) = mult(X1,mult(X2,rd(X0,X1))),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
mult(X0,mult(X1,rd(X0,X0))) = mult(X0,X1),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
ld(X0,mult(X0,X1)) = mult(X1,rd(X0,X0)),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
X1 = mult(X1,rd(X0,X0)),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0))
| sK12(rd(X0,X0)) != sK12(rd(X0,X0)) ),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
mult(mult(X2,X0),mult(ld(X0,X1),X2)) = mult(mult(X2,X1),X2),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d7,plain,
ld(mult(X0,mult(X1,X2)),mult(mult(X0,X1),mult(X2,X0))) = X0,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d8,plain,
ld(mult(X2,X1),mult(mult(X2,X0),mult(ld(X0,X1),X2))) = X2,
inference(superposition,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
ld(mult(X0,X2),mult(mult(X0,X2),X0)) = X0,
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0)),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
ld(X0,X0) = rd(X1,X1),
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d13,plain,
mult(ld(X1,X1),sK12(rd(X0,X0))) != sK12(rd(X0,X0)),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
mult(rd(X1,X1),sK12(rd(X2,X2))) != sK12(rd(X2,X2)),
inference(superposition,[status(thm)],[d12,d13]) ).
cnf(d15,plain,
sK12(rd(X0,X0)) != sK12(rd(X0,X0)),
inference(superposition,[status(thm)],[c2,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d10,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:33:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.72/3.44 % SZS status Theorem for theBenchmark.p
% 13.72/3.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------