%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP703+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 : n005.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 07:24:31 AM UTC 2026
% Result : Theorem 25.81s 11.24s
% Output : CNFRefutation 25.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 38 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 37 ~; 23 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 23 !; 0 ?)
% 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] : mult(X0,unit) = X0 ).
fof(f06,axiom,
! [X0] : mult(unit,X0) = X0 ).
fof(f08,axiom,
! [X0,X1] : mult('op$uc',mult(X1,X0)) = mult(mult('op$uc',X1),X0) ).
fof(f09,axiom,
! [X0,X1] : mult(X1,mult(X0,'op$uc')) = mult(mult(X1,X0),'op$uc') ).
fof(f10,axiom,
! [X0,X1] : mult(X1,mult('op$uc',X0)) = mult(mult(X1,'op$uc'),X0) ).
fof(f11,axiom,
! [X0] : 'op$ud' = ld(X0,mult('op$uc',X0)) ).
fof(f12,axiom,
! [X0,X1] : 'op$ue' = mult(mult(rd('op$uc',mult(X1,X0)),X0),X1) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(X0,mult('op$ue',X1)) = mult(mult(X0,'op$ue'),X1)
& mult(X0,mult(X1,'op$ue')) = mult(mult(X0,X1),'op$ue')
& mult('op$ue',mult(X0,X1)) = mult(mult('op$ue',X0),X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,mult('op$ue',X1)) = mult(mult(X0,'op$ue'),X1)
& mult(X0,mult(X1,'op$ue')) = mult(mult(X0,X1),'op$ue')
& mult('op$ue',mult(X0,X1)) = mult(mult('op$ue',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(X0,unit) = X0,
inference(clausification,[status(esa)],[f05]) ).
cnf(c5,plain,
mult(unit,X0) = X0,
inference(clausification,[status(esa)],[f06]) ).
cnf(c7,plain,
mult('op$uc',mult(X0,X1)) = mult(mult('op$uc',X0),X1),
inference(clausification,[status(esa)],[f08]) ).
cnf(c8,plain,
mult(X0,mult(X1,'op$uc')) = mult(mult(X0,X1),'op$uc'),
inference(clausification,[status(esa)],[f09]) ).
cnf(c9,plain,
mult(X0,mult('op$uc',X1)) = mult(mult(X0,'op$uc'),X1),
inference(clausification,[status(esa)],[f10]) ).
cnf(c10,plain,
'op$ud' = ld(X0,mult('op$uc',X0)),
inference(clausification,[status(esa)],[f11]) ).
cnf(c11,plain,
'op$ue' = mult(mult(rd('op$uc',mult(X0,X1)),X1),X0),
inference(clausification,[status(esa)],[f12]) ).
cnf(c13,plain,
( mult(sK24,mult('op$ue',sK25)) != mult(mult(sK24,'op$ue'),sK25)
| mult(sK24,mult(sK25,'op$ue')) != mult(mult(sK24,sK25),'op$ue')
| mult('op$ue',mult(sK24,sK25)) != mult(mult('op$ue',sK24),sK25) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'op$ud' = 'op$uc',
inference(superposition,[status(thm)],[c10,c1]) ).
cnf(d1,plain,
mult(X0,'op$ud') = mult('op$uc',X0),
inference(superposition,[status(thm)],[c10,c0]) ).
cnf(d2,plain,
mult(X0,'op$uc') = mult('op$uc',X0),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
mult(X0,mult(X1,'op$uc')) = mult('op$uc',mult(X0,X1)),
inference(demodulation,[status(thm)],[c8,d2]) ).
cnf(d4,plain,
rd(X0,unit) = X0,
inference(superposition,[status(thm)],[c4,c2]) ).
cnf(d5,plain,
X0 = mult(X0,unit),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
mult(rd('op$uc',mult(unit,X0)),X0) = 'op$ue',
inference(superposition,[status(thm)],[c11,d5]) ).
cnf(d7,plain,
mult(rd('op$uc',X0),X0) = 'op$ue',
inference(demodulation,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
'op$uc' = 'op$ue',
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( mult(sK24,mult(sK25,'op$ue')) != mult(mult(sK24,sK25),'op$ue')
| mult(sK24,mult('op$ue',sK25)) != mult(mult(sK24,'op$ue'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$ue',sK24),sK25) ),
inference(demodulation,[status(thm)],[c13,d8]) ).
cnf(d10,plain,
( mult(sK24,mult(sK25,'op$ue')) != mult(mult(sK24,sK25),'op$ue')
| mult(sK24,mult('op$ue',sK25)) != mult(mult(sK24,'op$ue'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$uc',sK24),sK25) ),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( mult(sK24,mult(sK25,'op$ue')) != mult(mult(sK24,sK25),'op$ue')
| mult(sK24,mult('op$uc',sK25)) != mult(mult(sK24,'op$ue'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$uc',sK24),sK25) ),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( mult(sK24,mult(sK25,'op$ue')) != mult(mult(sK24,sK25),'op$ue')
| mult(sK24,mult('op$uc',sK25)) != mult(mult(sK24,'op$uc'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$uc',sK24),sK25) ),
inference(demodulation,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( mult(sK24,mult(sK25,'op$uc')) != mult(mult(sK24,sK25),'op$ue')
| mult(sK24,mult('op$uc',sK25)) != mult(mult(sK24,'op$uc'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$uc',sK24),sK25) ),
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( mult(sK24,mult(sK25,'op$uc')) != mult(mult(sK24,sK25),'op$uc')
| mult(sK24,mult('op$uc',sK25)) != mult(mult(sK24,'op$uc'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult(mult('op$uc',sK24),sK25) ),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( mult(sK24,mult(sK25,'op$uc')) != mult(mult(sK24,sK25),'op$uc')
| mult(sK24,mult('op$uc',sK25)) != mult(mult(sK24,'op$uc'),sK25)
| mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25)) ),
inference(demodulation,[status(thm)],[d14,c7]) ).
cnf(d16,plain,
( mult(sK24,mult(sK25,'op$uc')) != mult(mult(sK24,sK25),'op$uc')
| mult(sK24,mult('op$uc',sK25)) != mult(sK24,mult('op$uc',sK25))
| mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25)) ),
inference(demodulation,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( mult('op$uc',mult(sK24,sK25)) != mult(mult(sK24,sK25),'op$uc')
| mult(sK24,mult('op$uc',sK25)) != mult(sK24,mult('op$uc',sK25))
| mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25)) ),
inference(demodulation,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
( mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25))
| mult(sK24,mult('op$uc',sK25)) != mult(sK24,mult('op$uc',sK25))
| mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25)) ),
inference(demodulation,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
'op$ud' = ld(ld('op$uc',X0),X0),
inference(superposition,[status(thm)],[c0,c10]) ).
cnf(d20,plain,
'op$uc' = ld(ld('op$uc',X0),X0),
inference(demodulation,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
mult(ld('op$uc',X0),'op$uc') = X0,
inference(superposition,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
mult('op$uc',ld('op$uc',X0)) = X0,
inference(demodulation,[status(thm)],[d21,d2]) ).
cnf(d23,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
( mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25))
| mult(sK24,mult('op$uc',sK25)) != mult(sK24,mult('op$uc',sK25)) ),
inference(resolution,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
mult('op$uc',mult(sK24,sK25)) != mult('op$uc',mult(sK24,sK25)),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d23,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP703+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
% 0.16/5.44 % Computer : n005.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 15:38:54 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.81/11.24 % SZS status Theorem for theBenchmark.p
% 25.81/11.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------