%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 74.43s 11.28s
% Output : CNFRefutation 74.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 6
% Syntax : Number of formulae : 87 ( 80 unt; 0 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 14 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 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 : 174 ( 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,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)) ).
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,mult(X1,X2)),X1) = mult(mult(X0,X1),mult(X2,X1)),
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(X1,ld(X0,X1)) = X0,
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d1,plain,
ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d2,plain,
mult(X0,X1) = mult(mult(rd(X0,mult(X1,X2)),X1),mult(X2,X1)),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d3,plain,
rd(mult(X0,X1),mult(X2,X1)) = mult(rd(X0,mult(X1,X2)),X1),
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
rd(mult(mult(X0,X1),mult(X2,X1)),X1) = mult(X0,mult(X1,X2)),
inference(superposition,[status(thm)],[c4,c3]) ).
cnf(d5,plain,
rd(mult(mult(X2,X1),X0),X1) = mult(X2,mult(X1,rd(X0,X1))),
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
mult(X0,mult(X1,rd(X1,X1))) = mult(X0,X1),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
ld(X0,mult(X0,X1)) = mult(X1,rd(X1,X1)),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
X1 = mult(X1,rd(X1,X1)),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
ld(X0,X0) = rd(X0,X0),
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
mult(ld(X0,X0),X0) = X0,
inference(superposition,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
rd(X0,X0) = ld(X0,X0),
inference(superposition,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
mult(rd(X0,mult(X1,X0)),X1) = ld(mult(X0,X1),mult(X0,X1)),
inference(superposition,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
rd(mult(X0,X1),mult(rd(X0,mult(X1,X0)),X1)) = mult(X0,X1),
inference(superposition,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
mult(rd(X0,mult(X1,rd(X0,mult(X1,X0)))),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
rd(mult(X0,X1),X1) = rd(X0,mult(X1,rd(X0,mult(X1,X0)))),
inference(superposition,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
X0 = rd(X0,mult(X1,rd(X0,mult(X1,X0)))),
inference(demodulation,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
ld(X0,X0) = mult(X1,rd(X0,mult(X1,X0))),
inference(superposition,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
ld(X0,ld(X1,X1)) = rd(X1,mult(X0,X1)),
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
ld(ld(X1,ld(X0,X0)),X0) = mult(X1,X0),
inference(superposition,[status(thm)],[d18,d1]) ).
cnf(d20,plain,
ld(X1,X0) = mult(rd(ld(X0,X0),X1),X0),
inference(superposition,[status(thm)],[d1,d19]) ).
cnf(d21,plain,
ld(mult(rd(X0,mult(X1,X2)),X1),mult(X0,X1)) = mult(X2,X1),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d22,plain,
X0 = mult(rd(X0,mult(X1,rd(X1,X1))),X1),
inference(superposition,[status(thm)],[c2,d6]) ).
cnf(d23,plain,
X1 = mult(rd(X1,mult(X0,ld(X0,X0))),X0),
inference(demodulation,[status(thm)],[d22,d9]) ).
cnf(d24,plain,
X1 = mult(rd(X1,X0),X0),
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
X0 = mult(X1,ld(X1,X0)),
inference(superposition,[status(thm)],[d0,d24]) ).
cnf(d26,plain,
ld(mult(rd(X2,X1),X0),mult(X2,X0)) = mult(ld(X0,X1),X0),
inference(superposition,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
X0 = mult(ld(X0,X0),X0),
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d28,plain,
ld(mult(rd(ld(X0,X0),X1),X0),X0) = mult(ld(X0,X1),X0),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
ld(ld(X1,X0),X0) = mult(ld(X0,X1),X0),
inference(demodulation,[status(thm)],[d28,d20]) ).
cnf(d30,plain,
rd(X1,mult(ld(X1,X0),X1)) = ld(X0,X1),
inference(superposition,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
ld(ld(X0,X1),ld(X0,X0)) = ld(X1,X0),
inference(demodulation,[status(thm)],[d30,d18]) ).
cnf(d32,plain,
ld(X1,ld(X0,X0)) = ld(mult(X0,X1),X0),
inference(superposition,[status(thm)],[c1,d31]) ).
cnf(d33,plain,
rd(X0,ld(X1,ld(X0,X0))) = mult(X0,X1),
inference(superposition,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
ld(X1,X0) = mult(ld(X0,rd(X0,X1)),X0),
inference(superposition,[status(thm)],[d1,d29]) ).
cnf(d35,plain,
rd(ld(X1,X0),X0) = ld(X0,rd(X0,X1)),
inference(superposition,[status(thm)],[d34,c3]) ).
cnf(d36,plain,
rd(ld(X1,X0),X0) = rd(ld(X0,X0),X1),
inference(superposition,[status(thm)],[d20,c3]) ).
cnf(d37,plain,
rd(X1,X0) = rd(ld(X0,X0),rd(X0,X1)),
inference(superposition,[status(thm)],[d1,d36]) ).
cnf(d38,plain,
rd(ld(X1,X0),X0) = rd(ld(X0,X0),X1),
inference(superposition,[status(thm)],[d0,d37]) ).
cnf(d39,plain,
ld(X1,rd(X1,X0)) = rd(ld(X1,X1),X0),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
rd(ld(X0,X0),ld(X1,X0)) = ld(X0,X1),
inference(superposition,[status(thm)],[d31,d0]) ).
cnf(d41,plain,
rd(ld(X0,X0),ld(X1,ld(X0,X0))) = ld(ld(X0,X0),X1),
inference(superposition,[status(thm)],[d31,d40]) ).
cnf(d42,plain,
ld(X0,rd(X0,ld(X1,ld(X0,X0)))) = ld(ld(X0,X0),X1),
inference(demodulation,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
ld(X0,mult(X0,X1)) = ld(ld(X0,X0),X1),
inference(demodulation,[status(thm)],[d42,d33]) ).
cnf(d44,plain,
X1 = ld(ld(X0,X0),X1),
inference(demodulation,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
mult(ld(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
mult(mult(X2,X1),X0) = mult(mult(X2,X0),mult(ld(X0,X1),X0)),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d47,plain,
mult(mult(X2,rd(X0,X1)),X0) = mult(mult(X2,X0),ld(X1,X0)),
inference(superposition,[status(thm)],[d34,d46]) ).
cnf(d48,plain,
mult(X0,rd(X1,X1)) = mult(mult(rd(X0,mult(rd(X1,X1),X1)),rd(X1,X1)),X1),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d49,plain,
mult(X0,rd(X1,X1)) = mult(mult(rd(X0,mult(rd(X1,X1),X1)),X1),ld(X1,X1)),
inference(demodulation,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
mult(X1,rd(X0,X0)) = mult(mult(rd(X1,X0),X0),ld(X0,X0)),
inference(demodulation,[status(thm)],[d49,c2]) ).
cnf(d51,plain,
mult(X0,rd(X1,X1)) = mult(X0,ld(X1,X1)),
inference(demodulation,[status(thm)],[d50,c2]) ).
cnf(d52,plain,
( mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0))
| mult(sK12(rd(X0,X0)),ld(X0,X0)) != sK12(rd(X0,X0)) ),
inference(superposition,[status(thm)],[d51,c5]) ).
cnf(d53,plain,
ld(rd(X0,X1),ld(X1,X1)) = rd(X1,X0),
inference(superposition,[status(thm)],[d24,d18]) ).
cnf(d54,plain,
rd(ld(X1,X1),rd(X1,mult(X0,X1))) = X0,
inference(superposition,[status(thm)],[d17,c3]) ).
cnf(d55,plain,
rd(ld(X1,X1),rd(X1,X0)) = rd(X0,X1),
inference(superposition,[status(thm)],[d24,d54]) ).
cnf(d56,plain,
rd(ld(X0,X0),X1) = rd(ld(X1,X0),X0),
inference(superposition,[status(thm)],[d0,d55]) ).
cnf(d57,plain,
mult(rd(ld(X1,X1),X0),X1) = ld(X0,X1),
inference(superposition,[status(thm)],[d56,c2]) ).
cnf(d58,plain,
mult(rd(X1,X0),X0) = ld(rd(X0,X1),X0),
inference(superposition,[status(thm)],[d55,d57]) ).
cnf(d59,plain,
X0 = ld(rd(X1,X0),X1),
inference(demodulation,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
X1 = ld(rd(ld(X1,X0),X0),ld(X0,X0)),
inference(superposition,[status(thm)],[d36,d59]) ).
cnf(d61,plain,
X0 = rd(X1,ld(X0,X1)),
inference(demodulation,[status(thm)],[d60,d53]) ).
cnf(d62,plain,
ld(X0,X0) = rd(X1,X1),
inference(superposition,[status(thm)],[d44,d61]) ).
cnf(d63,plain,
( mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0))
| mult(sK12(rd(X0,X0)),rd(X1,X1)) != sK12(rd(X0,X0)) ),
inference(superposition,[status(thm)],[d62,d52]) ).
cnf(d64,plain,
( mult(sK12(rd(X0,X0)),ld(X1,X1)) != sK12(rd(X0,X0))
| mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0)) ),
inference(demodulation,[status(thm)],[d63,d51]) ).
cnf(d65,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)],[d25,d64]) ).
cnf(d66,plain,
ld(mult(X0,mult(X1,X2)),mult(mult(X0,X1),mult(X2,X1))) = X1,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d67,plain,
ld(mult(X2,X1),mult(mult(X2,X0),mult(ld(X0,X1),X0))) = X0,
inference(superposition,[status(thm)],[c0,d66]) ).
cnf(d68,plain,
ld(mult(X0,X2),mult(mult(X0,X2),X1)) = X1,
inference(demodulation,[status(thm)],[d67,d46]) ).
cnf(d69,plain,
X2 = X2,
inference(demodulation,[status(thm)],[d68,c1]) ).
cnf(d70,plain,
mult(rd(X0,X0),sK12(rd(X0,X0))) != sK12(rd(X0,X0)),
inference(resolution,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
mult(ld(X1,X1),sK12(rd(X0,X0))) != sK12(rd(X0,X0)),
inference(superposition,[status(thm)],[d62,d70]) ).
cnf(d72,plain,
sK12(rd(X1,X1)) != sK12(rd(X1,X1)),
inference(demodulation,[status(thm)],[d71,d45]) ).
cnf(d73,plain,
$false,
inference(resolution,[status(thm)],[d69,d72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:34:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 74.43/11.28 % SZS status Theorem for theBenchmark.p
% 74.43/11.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------