%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP682+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 : n004.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 07:24:28 AM UTC 2026
% Result : Theorem 77.14s 17.75s
% Output : CNFRefutation 77.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 8
% Syntax : Number of formulae : 210 ( 203 unt; 0 def)
% Number of atoms : 217 ( 216 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 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 : 479 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0 ).
fof(f02,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0 ).
fof(f03,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)) ).
fof(f04,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0) ).
fof(f05,axiom,
! [X0,X1,X2,X3] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0) ).
fof(f06,axiom,
! [X0,X1,X2,X3] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)) ).
fof(f07,axiom,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
ld(X0,mult(X0,X0)) = X0,
inference(clausification,[status(esa)],[f01]) ).
cnf(c1,plain,
rd(mult(X0,X0),X0) = X0,
inference(clausification,[status(esa)],[f02]) ).
cnf(c2,plain,
mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(clausification,[status(esa)],[f03]) ).
cnf(c3,plain,
mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(clausification,[status(esa)],[f04]) ).
cnf(c4,plain,
ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(clausification,[status(esa)],[f05]) ).
cnf(c5,plain,
rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(clausification,[status(esa)],[f06]) ).
cnf(c6,plain,
ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(clausification,[status(esa)],[f07]) ).
cnf(c7,plain,
( ld(rd(sK16,sK17),mult(rd(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18))
| ld(ld(sK16,sK17),mult(ld(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ld(rd(sK16,sK17),mult(rd(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18))
| mult(ld(sK16,sK17),ld(ld(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18)) ),
inference(demodulation,[status(thm)],[c7,c2]) ).
cnf(d1,plain,
( ld(rd(sK16,sK17),mult(rd(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18))
| mult(ld(sK16,sK17),ld(ld(sK16,sK17),sK18)) != mult(sK16,ld(sK16,sK18)) ),
inference(demodulation,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( mult(rd(sK16,sK17),ld(rd(sK16,sK17),sK18)) != ld(sK16,mult(sK16,sK18))
| mult(ld(sK16,sK17),ld(ld(sK16,sK17),sK18)) != mult(sK16,ld(sK16,sK18)) ),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( mult(rd(sK16,sK17),ld(rd(sK16,sK17),sK18)) != mult(sK16,ld(sK16,sK18))
| mult(ld(sK16,sK17),ld(ld(sK16,sK17),sK18)) != mult(sK16,ld(sK16,sK18)) ),
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
mult(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d5,plain,
mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(demodulation,[status(thm)],[c4,c2]) ).
cnf(d6,plain,
mult(ld(X0,X2),ld(ld(X0,X2),mult(X1,X3))) = mult(mult(X0,ld(X0,X1)),X3),
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(superposition,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
mult(X0,ld(mult(X0,ld(X0,X0)),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(superposition,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
mult(X0,ld(X0,mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,X0)),ld(X0,X0)),
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d12,plain,
mult(ld(X0,X3),ld(ld(X0,X3),X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d13,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d4,d11]) ).
cnf(d14,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(demodulation,[status(thm)],[d13,d4]) ).
cnf(d15,plain,
X0 = mult(ld(X0,X2),ld(ld(X0,X2),X0)),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
mult(ld(X0,X1),ld(ld(X0,X1),mult(X0,X2))) = mult(X0,X2),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X0)) = X0,
inference(superposition,[status(thm)],[c2,d14]) ).
cnf(d18,plain,
mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X0)) = X0,
inference(demodulation,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
mult(X0,ld(mult(ld(X0,X1),ld(ld(X0,X1),X0)),ld(X0,X1))) = ld(X0,X1),
inference(superposition,[status(thm)],[d14,d18]) ).
cnf(d20,plain,
mult(X0,ld(X0,ld(X0,X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
mult(ld(X0,X3),ld(ld(X0,X3),ld(ld(X0,X1),X2))) = ld(ld(X0,X1),X2),
inference(superposition,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
mult(ld(X0,X1),ld(ld(X0,X1),ld(ld(X0,X1),X2))) = ld(ld(X0,X1),mult(mult(X0,ld(X0,X2)),ld(X2,X2))),
inference(superposition,[status(thm)],[d11,c2]) ).
cnf(d23,plain,
ld(ld(X0,X1),X2) = ld(ld(X0,X1),mult(mult(X0,ld(X0,X2)),ld(X2,X2))),
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
ld(ld(X0,X2),X1) = ld(ld(X0,X2),mult(X0,ld(X0,mult(X1,ld(X1,X1))))),
inference(demodulation,[status(thm)],[d23,d10]) ).
cnf(d25,plain,
ld(ld(X1,X2),X0) = ld(ld(X1,X2),mult(X1,ld(X1,X0))),
inference(demodulation,[status(thm)],[d24,d4]) ).
cnf(d26,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[d25,d16]) ).
cnf(d27,plain,
mult(rd(sK16,sK17),ld(rd(sK16,sK17),sK18)) != mult(sK16,ld(sK16,sK18)),
inference(resolution,[status(thm)],[d26,d3]) ).
cnf(d28,plain,
mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
inference(superposition,[status(thm)],[d4,d10]) ).
cnf(d29,plain,
mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(demodulation,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(superposition,[status(thm)],[c2,d11]) ).
cnf(d31,plain,
mult(X0,ld(X0,mult(X1,ld(ld(X0,mult(X0,X1)),X2)))) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(demodulation,[status(thm)],[d30,d10]) ).
cnf(d32,plain,
mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(demodulation,[status(thm)],[d31,c2]) ).
cnf(d33,plain,
mult(X0,ld(X0,mult(X2,ld(mult(X0,ld(X0,X2)),X1)))) = mult(X0,ld(X0,mult(X1,ld(X1,X1)))),
inference(demodulation,[status(thm)],[d32,d10]) ).
cnf(d34,plain,
mult(X1,ld(X1,mult(X2,ld(mult(X1,ld(X1,X2)),X0)))) = mult(X1,ld(X1,X0)),
inference(demodulation,[status(thm)],[d33,d4]) ).
cnf(d35,plain,
mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,mult(X0,ld(X0,X1))),X2),
inference(superposition,[status(thm)],[c2,d10]) ).
cnf(d36,plain,
mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,X1),X2),
inference(demodulation,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
mult(mult(X0,X1),ld(mult(X0,ld(X0,mult(X0,X1))),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
mult(mult(X0,X1),ld(mult(X0,mult(X0,ld(X0,X1))),X2)) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
mult(mult(X0,X1),ld(mult(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[d38,d29]) ).
cnf(d40,plain,
mult(X0,X2) = mult(ld(X0,X3),ld(ld(X0,X3),mult(X0,X2))),
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d41,plain,
mult(X0,X2) = mult(X0,ld(X0,mult(X0,X2))),
inference(demodulation,[status(thm)],[d40,d26]) ).
cnf(d42,plain,
mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(demodulation,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
mult(ld(X0,X1),X2) = mult(ld(X0,X1),mult(X0,ld(X0,X2))),
inference(superposition,[status(thm)],[d26,d42]) ).
cnf(d44,plain,
X0 = mult(mult(X0,ld(X0,X0)),ld(X0,X0)),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d45,plain,
X0 = mult(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d44,d4]) ).
cnf(d46,plain,
ld(X0,X1) = mult(ld(X0,X2),ld(ld(X0,X2),ld(X0,X1))),
inference(superposition,[status(thm)],[d12,d45]) ).
cnf(d47,plain,
mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[d4,c2]) ).
cnf(d48,plain,
mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[c6,c2]) ).
cnf(d49,plain,
mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d51,plain,
mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[d50,c3]) ).
cnf(d52,plain,
mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d51,d49]) ).
cnf(d53,plain,
ld(X0,X0) = rd(X0,X0),
inference(demodulation,[status(thm)],[d52,d47]) ).
cnf(d54,plain,
mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[d49,d53]) ).
cnf(d55,plain,
mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(demodulation,[status(thm)],[c5,c3]) ).
cnf(d56,plain,
mult(rd(mult(X2,X0),rd(X3,X1)),rd(X3,X1)) = mult(X2,mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d55,c3]) ).
cnf(d57,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[d4,d56]) ).
cnf(d58,plain,
mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(demodulation,[status(thm)],[d57,d54]) ).
cnf(d59,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d47,d58]) ).
cnf(d60,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d59,d4]) ).
cnf(d61,plain,
mult(rd(X0,ld(X0,X0)),rd(X0,X0)) = X0,
inference(superposition,[status(thm)],[d53,d60]) ).
cnf(d62,plain,
mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d61,d53]) ).
cnf(d63,plain,
mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d4,c3]) ).
cnf(d64,plain,
X0 = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
mult(rd(rd(X0,ld(X0,X0)),rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,ld(X0,X0)),mult(rd(ld(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[d63,d56]) ).
cnf(d66,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,ld(X0,X0)),mult(rd(ld(X0,X0),X2),X2)),
inference(demodulation,[status(thm)],[d65,d64]) ).
cnf(d67,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(demodulation,[status(thm)],[d66,d64]) ).
cnf(d68,plain,
mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(demodulation,[status(thm)],[d67,d54]) ).
cnf(d69,plain,
mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,ld(X1,X1)),
inference(demodulation,[status(thm)],[d68,d29]) ).
cnf(d70,plain,
mult(mult(X0,X1),ld(X3,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[d56,d69]) ).
cnf(d71,plain,
mult(ld(ld(X0,X1),X3),ld(ld(ld(X0,X1),X3),X2)) = mult(mult(mult(X0,ld(X0,X2)),ld(X2,X2)),ld(X2,X2)),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d72,plain,
mult(ld(ld(X0,X2),X3),ld(ld(ld(X0,X2),X3),X1)) = mult(mult(X0,ld(X0,X1)),mult(rd(ld(X1,X1),X1),X1)),
inference(demodulation,[status(thm)],[d71,d70]) ).
cnf(d73,plain,
mult(ld(ld(X0,X2),X3),ld(ld(ld(X0,X2),X3),X1)) = mult(X0,ld(X0,mult(X1,mult(rd(ld(X1,X1),X1),X1)))),
inference(demodulation,[status(thm)],[d72,d10]) ).
cnf(d74,plain,
mult(ld(ld(X1,X2),X3),ld(ld(ld(X1,X2),X3),X0)) = mult(X1,ld(X1,mult(X0,mult(X0,ld(X0,ld(X0,X0)))))),
inference(demodulation,[status(thm)],[d73,d54]) ).
cnf(d75,plain,
mult(ld(ld(X1,X2),X3),ld(ld(ld(X1,X2),X3),X0)) = mult(X1,ld(X1,mult(X0,ld(X0,X0)))),
inference(demodulation,[status(thm)],[d74,d29]) ).
cnf(d76,plain,
mult(ld(ld(X1,X2),X3),ld(ld(ld(X1,X2),X3),X0)) = mult(X1,ld(X1,X0)),
inference(demodulation,[status(thm)],[d75,d4]) ).
cnf(d77,plain,
ld(ld(X0,X1),X3) = mult(X0,ld(X0,ld(ld(X0,X1),X3))),
inference(superposition,[status(thm)],[d76,d46]) ).
cnf(d78,plain,
mult(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[d50,d53]) ).
cnf(d79,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d50,c2]) ).
cnf(d80,plain,
mult(ld(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d79,d53]) ).
cnf(d81,plain,
mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d80,d53]) ).
cnf(d82,plain,
mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(ld(X0,X0),X0),
inference(demodulation,[status(thm)],[d81,d53]) ).
cnf(d83,plain,
X0 = ld(ld(X0,X0),X0),
inference(demodulation,[status(thm)],[d82,d14]) ).
cnf(d84,plain,
ld(ld(X0,X0),X1) = mult(X0,ld(ld(ld(X0,X0),X0),ld(ld(X0,X0),X1))),
inference(superposition,[status(thm)],[d83,d46]) ).
cnf(d85,plain,
ld(ld(X0,X0),X1) = mult(X0,ld(X0,ld(ld(X0,X0),X1))),
inference(demodulation,[status(thm)],[d84,d83]) ).
cnf(d86,plain,
mult(X0,ld(X0,ld(rd(X0,X0),rd(X0,X0)))) = rd(X0,X0),
inference(superposition,[status(thm)],[d49,d50]) ).
cnf(d87,plain,
mult(X0,ld(X0,ld(ld(X0,X0),rd(X0,X0)))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d86,d53]) ).
cnf(d88,plain,
mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d87,d53]) ).
cnf(d89,plain,
mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(X0,X0),
inference(demodulation,[status(thm)],[d88,d53]) ).
cnf(d90,plain,
mult(X0,ld(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0))))) = ld(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d89,c2]) ).
cnf(d91,plain,
ld(X0,ld(ld(X0,X0),ld(X0,X0))) = ld(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d90,d20]) ).
cnf(d92,plain,
ld(ld(X0,X0),ld(X0,X0)) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[status(thm)],[d91,d85]) ).
cnf(d93,plain,
ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(demodulation,[status(thm)],[d92,d20]) ).
cnf(d94,plain,
mult(rd(X0,rd(X3,X1)),rd(X3,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[d58,d58]) ).
cnf(d95,plain,
X0 = mult(rd(X0,rd(X2,X0)),rd(X2,X0)),
inference(superposition,[status(thm)],[d60,d94]) ).
cnf(d96,plain,
X1 = mult(rd(X1,mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)),
inference(superposition,[status(thm)],[c3,d95]) ).
cnf(d97,plain,
X1 = mult(rd(X1,mult(rd(X0,X1),X1)),mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d96,c3]) ).
cnf(d98,plain,
rd(X1,X0) = mult(rd(rd(X1,X0),X0),mult(rd(X0,rd(X1,X0)),rd(X1,X0))),
inference(superposition,[status(thm)],[d95,d97]) ).
cnf(d99,plain,
rd(X1,X0) = mult(rd(rd(X1,X0),X0),X0),
inference(demodulation,[status(thm)],[d98,d95]) ).
cnf(d100,plain,
rd(X0,rd(X1,X2)) = mult(rd(X0,rd(X1,X2)),ld(X2,X2)),
inference(superposition,[status(thm)],[d69,d99]) ).
cnf(d101,plain,
mult(rd(X1,rd(X0,X0)),ld(X0,X0)) = mult(X1,ld(X0,X0)),
inference(superposition,[status(thm)],[d53,d69]) ).
cnf(d102,plain,
rd(X0,rd(X1,X1)) = mult(X0,ld(X1,X1)),
inference(demodulation,[status(thm)],[d101,d100]) ).
cnf(d103,plain,
rd(X1,ld(X0,X0)) = mult(X1,ld(X0,X0)),
inference(demodulation,[status(thm)],[d102,d53]) ).
cnf(d104,plain,
mult(rd(X1,X0),rd(X0,ld(X0,X0))) = mult(X1,ld(ld(X0,X0),ld(X0,X0))),
inference(superposition,[status(thm)],[d64,d69]) ).
cnf(d105,plain,
mult(rd(X1,X0),mult(X0,ld(X0,X0))) = mult(X1,ld(ld(X0,X0),ld(X0,X0))),
inference(demodulation,[status(thm)],[d104,d103]) ).
cnf(d106,plain,
mult(rd(X1,X0),X0) = mult(X1,ld(ld(X0,X0),ld(X0,X0))),
inference(demodulation,[status(thm)],[d105,d4]) ).
cnf(d107,plain,
mult(rd(X1,X0),X0) = mult(X1,ld(X0,X0)),
inference(demodulation,[status(thm)],[d106,d93]) ).
cnf(d108,plain,
mult(mult(X2,X0),ld(X1,X1)) = mult(X2,mult(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[d70,d107]) ).
cnf(d109,plain,
mult(X0,ld(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c3,d107]) ).
cnf(d110,plain,
mult(mult(X0,ld(X1,X1)),X1) = mult(mult(X0,X1),ld(X1,X1)),
inference(superposition,[status(thm)],[d109,d107]) ).
cnf(d111,plain,
mult(mult(X0,ld(X1,X1)),X1) = mult(X0,mult(X1,ld(X1,X1))),
inference(demodulation,[status(thm)],[d110,d108]) ).
cnf(d112,plain,
mult(mult(X1,ld(X0,X0)),X0) = mult(X1,X0),
inference(demodulation,[status(thm)],[d111,d4]) ).
cnf(d113,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,ld(X0,X0))),X0),
inference(superposition,[status(thm)],[d78,d6]) ).
cnf(d114,plain,
mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = mult(ld(X0,X0),ld(X0,X0)),
inference(superposition,[status(thm)],[d89,d113]) ).
cnf(d115,plain,
ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
inference(demodulation,[status(thm)],[d114,d46]) ).
cnf(d116,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)) = X1,
inference(superposition,[status(thm)],[c3,d60]) ).
cnf(d117,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),mult(rd(X0,X1),X1)) = X1,
inference(demodulation,[status(thm)],[d116,c3]) ).
cnf(d118,plain,
mult(rd(rd(X1,X0),X0),mult(rd(X0,rd(X1,X0)),rd(X1,X0))) = rd(X1,X0),
inference(superposition,[status(thm)],[d60,d117]) ).
cnf(d119,plain,
mult(rd(rd(X1,X0),X0),X0) = rd(X1,X0),
inference(demodulation,[status(thm)],[d118,d95]) ).
cnf(d120,plain,
mult(rd(rd(rd(X0,X0),X1),X1),X1) = rd(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(superposition,[status(thm)],[d49,c3]) ).
cnf(d121,plain,
mult(rd(rd(ld(X0,X0),X1),X1),X1) = rd(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(demodulation,[status(thm)],[d120,d53]) ).
cnf(d122,plain,
rd(ld(X0,X0),X1) = rd(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(demodulation,[status(thm)],[d121,d119]) ).
cnf(d123,plain,
rd(ld(X1,X1),ld(X0,X0)) = rd(mult(X1,ld(X1,ld(X0,X0))),ld(X0,X0)),
inference(superposition,[status(thm)],[d93,d122]) ).
cnf(d124,plain,
mult(ld(X0,X0),ld(X1,X1)) = rd(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(demodulation,[status(thm)],[d123,d103]) ).
cnf(d125,plain,
mult(ld(X0,X0),ld(X1,X1)) = mult(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(demodulation,[status(thm)],[d124,d103]) ).
cnf(d126,plain,
mult(ld(X0,X0),ld(X1,X1)) = mult(X0,ld(X0,mult(ld(X1,X1),ld(X1,X1)))),
inference(demodulation,[status(thm)],[d125,d10]) ).
cnf(d127,plain,
mult(ld(X1,X1),ld(X0,X0)) = mult(X1,ld(X1,ld(X0,X0))),
inference(demodulation,[status(thm)],[d126,d115]) ).
cnf(d128,plain,
mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X0),X1),
inference(superposition,[status(thm)],[d127,d112]) ).
cnf(d129,plain,
mult(X0,ld(X0,mult(ld(X1,X1),X1))) = mult(ld(X0,X0),X1),
inference(demodulation,[status(thm)],[d128,d10]) ).
cnf(d130,plain,
mult(X1,ld(X1,X0)) = mult(ld(X1,X1),X0),
inference(demodulation,[status(thm)],[d129,d78]) ).
cnf(d131,plain,
mult(X0,ld(X0,ld(ld(X0,X0),X1))) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[d130,d26]) ).
cnf(d132,plain,
ld(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[d131,d77]) ).
cnf(d133,plain,
mult(ld(X0,X0),mult(X0,ld(X0,X1))) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[d132,d26]) ).
cnf(d134,plain,
mult(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[d133,d43]) ).
cnf(d135,plain,
mult(rd(ld(X0,X0),rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,ld(ld(X0,X0),ld(X0,X0))),X2),X2)),
inference(superposition,[status(thm)],[d89,d56]) ).
cnf(d136,plain,
mult(X0,ld(X0,ld(rd(X1,X2),rd(X1,X2)))) = mult(X0,mult(rd(ld(X0,ld(ld(X0,X0),ld(X0,X0))),X2),X2)),
inference(demodulation,[status(thm)],[d135,d54]) ).
cnf(d137,plain,
mult(X0,ld(X0,ld(rd(X1,X2),rd(X1,X2)))) = mult(X0,mult(rd(ld(X0,ld(X0,X0)),X2),X2)),
inference(demodulation,[status(thm)],[d136,d93]) ).
cnf(d138,plain,
mult(rd(ld(X0,X0),rd(X1,X0)),rd(X1,X0)) = mult(ld(X0,X0),ld(X0,X0)),
inference(superposition,[status(thm)],[d4,d58]) ).
cnf(d139,plain,
mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))) = mult(ld(X0,X0),ld(X0,X0)),
inference(demodulation,[status(thm)],[d138,d54]) ).
cnf(d140,plain,
mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))) = ld(X0,X0),
inference(demodulation,[status(thm)],[d139,d115]) ).
cnf(d141,plain,
ld(X0,X0) = mult(X0,mult(rd(ld(X0,ld(X0,X0)),X0),X0)),
inference(superposition,[status(thm)],[d140,d137]) ).
cnf(d142,plain,
ld(X0,X0) = mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))),
inference(superposition,[status(thm)],[d137,d141]) ).
cnf(d143,plain,
mult(mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))),ld(ld(X0,X0),X0)) = X0,
inference(superposition,[status(thm)],[d142,d18]) ).
cnf(d144,plain,
mult(X0,ld(X0,mult(ld(rd(X1,X0),rd(X1,X0)),ld(ld(X0,X0),X0)))) = X0,
inference(demodulation,[status(thm)],[d143,d10]) ).
cnf(d145,plain,
mult(X0,ld(X0,mult(ld(rd(X1,X0),rd(X1,X0)),X0))) = X0,
inference(demodulation,[status(thm)],[d144,d83]) ).
cnf(d146,plain,
mult(X1,ld(X1,mult(ld(mult(rd(X0,X1),X1),rd(mult(X0,X1),X1)),X1))) = X1,
inference(superposition,[status(thm)],[c3,d145]) ).
cnf(d147,plain,
mult(X1,ld(X1,mult(ld(mult(X0,ld(X1,X1)),rd(mult(X0,X1),X1)),X1))) = X1,
inference(demodulation,[status(thm)],[d146,d107]) ).
cnf(d148,plain,
mult(X1,ld(X1,mult(ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1))),X1))) = X1,
inference(demodulation,[status(thm)],[d147,d109]) ).
cnf(d149,plain,
mult(X1,ld(X1,mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),X1)))) = X1,
inference(demodulation,[status(thm)],[d148,d134]) ).
cnf(d150,plain,
mult(X1,ld(X1,mult(X0,ld(X0,X1)))) = X1,
inference(demodulation,[status(thm)],[d149,d39]) ).
cnf(d151,plain,
mult(X0,X1) = mult(X0,ld(X0,mult(X2,ld(X2,mult(X0,X1))))),
inference(superposition,[status(thm)],[d150,d39]) ).
cnf(d152,plain,
mult(X0,ld(X0,mult(mult(X1,ld(X1,X0)),X2))) = mult(X0,X2),
inference(superposition,[status(thm)],[d150,d10]) ).
cnf(d153,plain,
mult(X1,ld(X1,mult(X0,ld(X0,mult(X1,X2))))) = mult(X1,X2),
inference(demodulation,[status(thm)],[d152,d10]) ).
cnf(d154,plain,
X0 = mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X0)),
inference(superposition,[status(thm)],[c2,d15]) ).
cnf(d155,plain,
X0 = mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X0)),
inference(demodulation,[status(thm)],[d154,c2]) ).
cnf(d156,plain,
X0 = mult(mult(X0,mult(X0,ld(X0,X1))),ld(mult(X0,ld(X0,mult(X0,X1))),X0)),
inference(superposition,[status(thm)],[c2,d155]) ).
cnf(d157,plain,
X0 = mult(mult(X0,mult(X0,ld(X0,X1))),ld(mult(X0,mult(X0,ld(X0,X1))),X0)),
inference(demodulation,[status(thm)],[d156,c2]) ).
cnf(d158,plain,
X0 = mult(mult(X0,X1),ld(mult(X0,mult(X0,ld(X0,X1))),X0)),
inference(demodulation,[status(thm)],[d157,d29]) ).
cnf(d159,plain,
X0 = mult(mult(X0,X1),ld(mult(X0,X1),X0)),
inference(demodulation,[status(thm)],[d158,d29]) ).
cnf(d160,plain,
rd(X0,X1) = mult(mult(rd(X0,X1),X1),ld(mult(X0,ld(X1,X1)),rd(X0,X1))),
inference(superposition,[status(thm)],[d107,d159]) ).
cnf(d161,plain,
rd(X0,X1) = mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),rd(X0,X1))),
inference(demodulation,[status(thm)],[d160,d107]) ).
cnf(d162,plain,
rd(X0,X1) = mult(X0,ld(X0,rd(X0,X1))),
inference(demodulation,[status(thm)],[d161,d39]) ).
cnf(d163,plain,
mult(X0,ld(X0,mult(rd(X0,X1),X2))) = mult(rd(X0,X1),X2),
inference(superposition,[status(thm)],[d162,d10]) ).
cnf(d164,plain,
mult(rd(X0,X1),ld(rd(X0,X1),mult(X0,X2))) = mult(X0,X2),
inference(superposition,[status(thm)],[d163,d153]) ).
cnf(d165,plain,
mult(rd(X0,X1),X2) = mult(X0,ld(X0,mult(rd(X0,X1),X2))),
inference(superposition,[status(thm)],[d164,d151]) ).
cnf(d166,plain,
mult(X0,ld(X0,mult(X0,X1))) = mult(mult(X0,ld(X1,X1)),X1),
inference(superposition,[status(thm)],[d112,d36]) ).
cnf(d167,plain,
mult(X0,mult(X0,ld(X0,X1))) = mult(mult(X0,ld(X1,X1)),X1),
inference(demodulation,[status(thm)],[d166,c2]) ).
cnf(d168,plain,
mult(X0,X1) = mult(mult(X0,ld(X1,X1)),X1),
inference(demodulation,[status(thm)],[d167,d29]) ).
cnf(d169,plain,
mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,ld(X2,X2))),X2),
inference(superposition,[status(thm)],[d108,d168]) ).
cnf(d170,plain,
mult(X0,mult(X0,ld(X0,ld(X2,X2)))) = mult(rd(X0,rd(X3,X2)),rd(X3,X2)),
inference(superposition,[status(thm)],[d58,d94]) ).
cnf(d171,plain,
mult(X0,ld(X1,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(demodulation,[status(thm)],[d170,d29]) ).
cnf(d172,plain,
mult(ld(X0,X0),ld(X2,X2)) = mult(X0,ld(X0,ld(rd(X1,X2),rd(X1,X2)))),
inference(superposition,[status(thm)],[d54,d171]) ).
cnf(d173,plain,
mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(X0,ld(rd(X2,X1),rd(X2,X1)))),
inference(demodulation,[status(thm)],[d172,d134]) ).
cnf(d174,plain,
mult(X0,ld(X0,X2)) = mult(ld(X0,X1),ld(ld(X0,X1),X2)),
inference(superposition,[status(thm)],[d25,d40]) ).
cnf(d175,plain,
mult(X0,ld(X0,mult(X2,ld(X2,ld(X0,X1))))) = ld(X0,X1),
inference(superposition,[status(thm)],[d150,d174]) ).
cnf(d176,plain,
mult(X0,ld(X0,ld(rd(X0,X1),X2))) = ld(rd(X0,X1),X2),
inference(superposition,[status(thm)],[d164,d175]) ).
cnf(d177,plain,
mult(X0,ld(X0,ld(X1,X1))) = ld(rd(X0,X1),rd(X0,X1)),
inference(superposition,[status(thm)],[d176,d173]) ).
cnf(d178,plain,
mult(X0,ld(X2,X2)) = mult(X0,ld(rd(X1,X2),rd(X1,X2))),
inference(demodulation,[status(thm)],[d171,d107]) ).
cnf(d179,plain,
mult(X2,ld(X1,X1)) = mult(X2,mult(X0,ld(X0,ld(X1,X1)))),
inference(demodulation,[status(thm)],[d178,d177]) ).
cnf(d180,plain,
mult(mult(X0,ld(X1,X1)),ld(X2,X2)) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(superposition,[status(thm)],[d107,d108]) ).
cnf(d181,plain,
mult(X0,mult(ld(X1,X1),ld(X2,X2))) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(demodulation,[status(thm)],[d180,d108]) ).
cnf(d182,plain,
mult(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(rd(X2,X0),mult(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[d181,d134]) ).
cnf(d183,plain,
mult(X0,ld(X2,X2)) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(demodulation,[status(thm)],[d182,d179]) ).
cnf(d184,plain,
mult(mult(rd(X0,X1),X1),X2) = mult(mult(X0,ld(X2,X2)),X2),
inference(superposition,[status(thm)],[d183,d169]) ).
cnf(d185,plain,
mult(mult(X0,ld(X1,X1)),X2) = mult(mult(X0,ld(X2,X2)),X2),
inference(demodulation,[status(thm)],[d184,d107]) ).
cnf(d186,plain,
mult(mult(X0,ld(X2,X2)),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[d185,d168]) ).
cnf(d187,plain,
mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(ld(X0,X0),X2),
inference(superposition,[status(thm)],[d134,d186]) ).
cnf(d188,plain,
mult(X0,ld(X0,mult(ld(X1,X1),X2))) = mult(ld(X0,X0),X2),
inference(demodulation,[status(thm)],[d187,d10]) ).
cnf(d189,plain,
mult(X2,ld(X2,mult(X0,ld(X0,X1)))) = mult(ld(X2,X2),X1),
inference(demodulation,[status(thm)],[d188,d134]) ).
cnf(d190,plain,
mult(X0,ld(X0,mult(X2,ld(X2,X1)))) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[d189,d134]) ).
cnf(d191,plain,
mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[d190,d165]) ).
cnf(d192,plain,
$false,
inference(resolution,[status(thm)],[d191,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP682+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
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 15:36:37 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.14/17.75 % SZS status Theorem for theBenchmark.p
% 77.14/17.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------