%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP665+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 : n015.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 07:24:25 AM UTC 2026
% Result : Theorem 26.02s 6.57s
% Output : CNFRefutation 26.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 23 ~; 13 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0 ).
fof(f04,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1 ).
fof(f07,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)) ).
fof(f08,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))) ).
fof(f09,axiom,
! [X0] : mult('op$uc',X0) = mult(X0,'op$uc') ).
fof(goals,conjecture,
! [X0,X1] :
( mult(mult(X0,X1),'op$uc') = mult(X0,mult(X1,'op$uc'))
& mult(mult(X0,'op$uc'),X1) = mult(X0,mult('op$uc',X1))
& mult('op$uc',mult(X0,X1)) = mult(mult('op$uc',X0),X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( mult(mult(X0,X1),'op$uc') = mult(X0,mult(X1,'op$uc'))
& mult(mult(X0,'op$uc'),X1) = mult(X0,mult('op$uc',X1))
& mult('op$uc',mult(X0,X1)) = mult(mult('op$uc',X0),X1) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c1,plain,
ld(X0,mult(X0,X1)) = X1,
inference(clausification,[status(esa)],[f02]) ).
cnf(c3,plain,
rd(mult(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[f04]) ).
cnf(c6,plain,
mult(X0,mult(X1,X2)) = mult(rd(mult(X0,X1),X0),mult(X0,X2)),
inference(clausification,[status(esa)],[f07]) ).
cnf(c7,plain,
mult(mult(X0,X1),X2) = mult(mult(X0,X2),ld(X2,mult(X1,X2))),
inference(clausification,[status(esa)],[f08]) ).
cnf(c8,plain,
mult('op$uc',X0) = mult(X0,'op$uc'),
inference(clausification,[status(esa)],[f09]) ).
cnf(c9,plain,
( mult(mult(sK17,sK18),'op$uc') != mult(sK17,mult(sK18,'op$uc'))
| mult(mult(sK17,'op$uc'),sK18) != mult(sK17,mult('op$uc',sK18))
| mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
ld('op$uc',mult(X0,'op$uc')) = X0,
inference(superposition,[status(thm)],[c8,c1]) ).
cnf(d1,plain,
mult(mult(X1,X0),'op$uc') = mult(mult(X1,'op$uc'),X0),
inference(superposition,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
mult('op$uc',mult(X0,X1)) = mult(mult(X0,'op$uc'),X1),
inference(demodulation,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
mult('op$uc',mult(X0,X1)) = mult(mult('op$uc',X0),X1),
inference(superposition,[status(thm)],[c8,d2]) ).
cnf(d4,plain,
rd(mult(X0,'op$uc'),X0) = 'op$uc',
inference(superposition,[status(thm)],[c8,c3]) ).
cnf(d5,plain,
mult(X0,mult('op$uc',X1)) = mult('op$uc',mult(X0,X1)),
inference(superposition,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult(mult(sK17,sK18),'op$uc') != mult(sK17,mult(sK18,'op$uc'))
| mult(mult('op$uc',sK17),sK18) != mult(sK17,mult('op$uc',sK18)) ),
inference(demodulation,[status(thm)],[c9,c8]) ).
cnf(d7,plain,
( mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult('op$uc',mult(sK17,sK18)) != mult(sK17,mult(sK18,'op$uc'))
| mult(mult('op$uc',sK17),sK18) != mult(sK17,mult('op$uc',sK18)) ),
inference(demodulation,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult('op$uc',mult(sK17,sK18)) != mult(sK17,mult('op$uc',sK18))
| mult(mult('op$uc',sK17),sK18) != mult(sK17,mult('op$uc',sK18)) ),
inference(demodulation,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
( mult('op$uc',mult(sK17,sK18)) != mult(sK17,mult('op$uc',sK18))
| mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult(mult('op$uc',sK17),sK18) != mult('op$uc',mult(sK17,sK18)) ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( mult('op$uc',mult(sK17,sK18)) != mult('op$uc',mult(sK17,sK18))
| mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult(mult('op$uc',sK17),sK18) != mult('op$uc',mult(sK17,sK18)) ),
inference(demodulation,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
ld('op$uc',mult('op$uc',X0)) = X0,
inference(superposition,[status(thm)],[c8,d0]) ).
cnf(d12,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
( mult('op$uc',mult(sK17,sK18)) != mult(mult('op$uc',sK17),sK18)
| mult(mult('op$uc',sK17),sK18) != mult('op$uc',mult(sK17,sK18)) ),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
mult(mult('op$uc',sK17),sK18) != mult('op$uc',mult(sK17,sK18)),
inference(resolution,[status(thm)],[d3,d13]) ).
cnf(d15,plain,
mult('op$uc',mult(sK17,sK18)) != mult('op$uc',mult(sK17,sK18)),
inference(demodulation,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d12,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP665+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 : n015.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 15:36:42 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.02/6.57 % SZS status Theorem for theBenchmark.p
% 26.02/6.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------