%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP710+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 : n007.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 07:24:33 AM UTC 2026
% Result : Theorem 74.23s 22.37s
% Output : CNFRefutation 74.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 30 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 10 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 21 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X0] : mult(X0,unit) = X0 ).
fof(f02,axiom,
! [X0] : mult(unit,X0) = X0 ).
fof(f03,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0) ).
fof(f04,axiom,
! [X0] : mult(X0,i(X0)) = unit ).
fof(f05,axiom,
! [X0] : mult(i(X0),X0) = unit ).
fof(goals,conjecture,
( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
mult(X0,unit) = X0,
inference(clausification,[status(esa)],[f01]) ).
cnf(c1,plain,
mult(unit,X0) = X0,
inference(clausification,[status(esa)],[f02]) ).
cnf(c2,plain,
mult(X0,mult(X1,mult(X1,X2))) = mult(mult(mult(X0,X1),X1),X2),
inference(clausification,[status(esa)],[f03]) ).
cnf(c3,plain,
mult(X0,i(X0)) = unit,
inference(clausification,[status(esa)],[f04]) ).
cnf(c4,plain,
mult(i(X0),X0) = unit,
inference(clausification,[status(esa)],[f05]) ).
cnf(c5,plain,
( mult(X1,sK11) != sK10
| mult(sK7,X0) != sK8 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
unit = i(unit),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(mult(unit,i(X0)),X1),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d2,plain,
mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(i(X0),X1),
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d4,plain,
mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
mult(X0,mult(X0,mult(i(mult(X0,X0)),mult(i(mult(X0,X0)),X1)))) = mult(i(mult(X0,X0)),X1),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( mult(X1,sK11) != sK10
| mult(i(mult(sK7,sK7)),X0) != sK8 ),
inference(superposition,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
mult(mult(mult(X0,X1),X1),mult(X2,mult(X2,X3))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
inference(superposition,[status(thm)],[c2,c2]) ).
cnf(d8,plain,
mult(X0,mult(X1,mult(X1,mult(X2,mult(X2,X3))))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
mult(X0,mult(X1,mult(X1,unit))) = mult(mult(X0,X1),X1),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d10,plain,
mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(demodulation,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
mult(X0,mult(X1,mult(X1,i(mult(mult(X0,X1),X1))))) = unit,
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d12,plain,
mult(X0,mult(X1,mult(X1,i(mult(X0,mult(X1,X1)))))) = unit,
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
mult(X0,mult(X1,mult(X1,mult(i(mult(X0,mult(X1,X1))),mult(i(mult(X0,mult(X1,X1))),X2))))) = mult(mult(unit,i(mult(X0,mult(X1,X1)))),X2),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
mult(X0,mult(X1,mult(X1,mult(i(mult(X0,mult(X1,X1))),mult(i(mult(X0,mult(X1,X1))),X2))))) = mult(i(mult(X0,mult(X1,X1))),X2),
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
( mult(X2,sK11) != sK10
| mult(i(mult(i(mult(sK7,sK7)),mult(X0,X0))),X1) != sK8 ),
inference(superposition,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
( mult(X1,sK11) != sK10
| mult(i(unit),X0) != sK8 ),
inference(superposition,[status(thm)],[c4,d15]) ).
cnf(d17,plain,
( mult(unit,X1) != sK8
| mult(X0,sK11) != sK10 ),
inference(demodulation,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
( X0 != sK8
| mult(X1,sK11) != sK10 ),
inference(demodulation,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
mult(X0,mult(X1,mult(X1,mult(X2,mult(X2,unit))))) = mult(mult(X0,mult(X1,mult(X1,X2))),X2),
inference(superposition,[status(thm)],[d8,c0]) ).
cnf(d20,plain,
mult(X1,mult(X2,mult(X2,mult(X0,X0)))) = mult(mult(X1,mult(X2,mult(X2,X0))),X0),
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
( X2 != sK8
| mult(X0,mult(X1,mult(X1,mult(sK11,sK11)))) != sK10 ),
inference(superposition,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
mult(i(X0),mult(X0,X0)) = mult(unit,X0),
inference(superposition,[status(thm)],[c4,d10]) ).
cnf(d23,plain,
mult(i(X0),mult(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
( X1 != sK8
| mult(X0,mult(i(sK11),sK11)) != sK10 ),
inference(superposition,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( mult(X1,unit) != sK10
| X0 != sK8 ),
inference(demodulation,[status(thm)],[d24,c4]) ).
cnf(d26,plain,
( X0 != sK10
| X1 != sK8 ),
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
X0 != sK8,
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
$false,
inference(equality_resolution,[status(thm)],[d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.62 % Computer : n007.cluster.edu
% 0.14/5.62 % Model : x86_64 x86_64
% 0.14/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.62 % Memory : 8046.5625MB
% 0.14/5.62 % OS : Linux 6.8.0-71-generic
% 0.14/5.62 % CPULimit : 300
% 0.14/5.62 % WCLimit : 300
% 0.14/5.62 % DateTime : Fri Sep 25 15:37:29 UTC 2026
% 0.14/5.63 % CPUTime :
% 0.14/5.63 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 74.23/22.37 % SZS status Theorem for theBenchmark.p
% 74.23/22.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------