%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP685+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 : n020.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 07:24:29 AM UTC 2026
% Result : Theorem 58.67s 9.01s
% Output : CNFRefutation 58.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 8
% Syntax : Number of formulae : 191 ( 182 unt; 0 def)
% Number of atoms : 200 ( 199 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 19 ~; 7 |; 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 : 389 ( 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] :
( rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2)
& rd(mult(X0,ld(X1,X2)),ld(X1,X2)) = rd(mult(X0,X2),X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2)
& rd(mult(X0,ld(X1,X2)),ld(X1,X2)) = rd(mult(X0,X2),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,
( rd(mult(sK16,rd(sK17,sK18)),rd(sK17,sK18)) != rd(mult(sK16,sK18),sK18)
| rd(mult(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != rd(mult(sK16,sK18),sK18) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[c6,c2]) ).
cnf(d1,plain,
mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d3,plain,
mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
mult(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d6,plain,
mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
rd(X0,X0) = ld(X0,X0),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
mult(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d5,d7]) ).
cnf(d9,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(d10,plain,
mult(ld(X0,X2),ld(ld(X0,X2),mult(X1,X3))) = mult(mult(X0,ld(X0,X1)),X3),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
mult(X0,ld(X0,rd(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d4,d7]) ).
cnf(d13,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(demodulation,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
mult(rd(X0,X0),ld(ld(X0,X0),X0)) = X0,
inference(superposition,[status(thm)],[d7,d14]) ).
cnf(d16,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X0)) = X0,
inference(demodulation,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d18,plain,
X0 = ld(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
mult(X1,ld(X1,rd(X0,X0))) = mult(rd(rd(X1,X1),X0),X0),
inference(demodulation,[status(thm)],[d1,d7]) ).
cnf(d20,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(d21,plain,
mult(rd(mult(X2,X0),rd(X3,X1)),rd(X3,X1)) = mult(X2,mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(rd(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[d8,d21]) ).
cnf(d23,plain,
mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,mult(X0,ld(X0,rd(X1,X1)))),
inference(demodulation,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,X0)),rd(X0,X0)),
inference(superposition,[status(thm)],[d8,d10]) ).
cnf(d25,plain,
mult(ld(X0,X3),ld(ld(X0,X3),X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[d24,d24]) ).
cnf(d26,plain,
X0 = mult(ld(X0,X2),ld(ld(X0,X2),X0)),
inference(superposition,[status(thm)],[d14,d25]) ).
cnf(d27,plain,
mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X0)) = X0,
inference(superposition,[status(thm)],[c2,d14]) ).
cnf(d28,plain,
mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X0)) = X0,
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
mult(X0,ld(mult(ld(X0,X1),ld(ld(X0,X1),X0)),ld(X0,X1))) = ld(X0,X1),
inference(superposition,[status(thm)],[d14,d28]) ).
cnf(d30,plain,
mult(X0,ld(X0,ld(X0,X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
mult(ld(X0,X1),mult(ld(X0,X1),ld(ld(X0,X1),X2))) = mult(mult(X0,ld(X0,ld(X0,X1))),X2),
inference(superposition,[status(thm)],[c2,d10]) ).
cnf(d32,plain,
mult(ld(X0,X1),mult(ld(X0,X1),ld(ld(X0,X1),X2))) = mult(ld(X0,X1),X2),
inference(demodulation,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
mult(rd(ld(X0,X1),rd(X3,X2)),rd(X3,X2)) = mult(ld(X0,X1),rd(X2,X2)),
inference(superposition,[status(thm)],[d32,d23]) ).
cnf(d34,plain,
mult(rd(ld(rd(X0,X0),X0),rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X0),mult(rd(ld(rd(X0,X0),X0),X2),X2)),
inference(superposition,[status(thm)],[d17,d21]) ).
cnf(d35,plain,
mult(ld(rd(X0,X0),X0),rd(X2,X2)) = mult(rd(X0,X0),mult(rd(ld(rd(X0,X0),X0),X2),X2)),
inference(demodulation,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
mult(X0,rd(X1,X1)) = mult(rd(X0,X0),mult(rd(ld(rd(X0,X0),X0),X1),X1)),
inference(demodulation,[status(thm)],[d35,d18]) ).
cnf(d37,plain,
mult(X0,rd(X1,X1)) = mult(rd(X0,X0),mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d36,d18]) ).
cnf(d38,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X0),mult(rd(X0,X2),X2)),
inference(superposition,[status(thm)],[d2,d21]) ).
cnf(d39,plain,
mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,rd(X1,X1)),
inference(demodulation,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
mult(rd(X0,rd(X3,X1)),rd(X3,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[d23,d23]) ).
cnf(d41,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(X0,rd(X0,X0)),
inference(superposition,[status(thm)],[d12,d23]) ).
cnf(d42,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d41,d8]) ).
cnf(d43,plain,
X0 = mult(rd(X0,rd(X2,X0)),rd(X2,X0)),
inference(superposition,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)) = X1,
inference(superposition,[status(thm)],[c3,d42]) ).
cnf(d45,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),mult(rd(X0,X1),X1)) = X1,
inference(demodulation,[status(thm)],[d44,c3]) ).
cnf(d46,plain,
mult(rd(rd(X1,X0),X0),mult(rd(X0,rd(X1,X0)),rd(X1,X0))) = rd(X1,X0),
inference(superposition,[status(thm)],[d42,d45]) ).
cnf(d47,plain,
mult(rd(rd(X1,X0),X0),X0) = rd(X1,X0),
inference(demodulation,[status(thm)],[d46,d43]) ).
cnf(d48,plain,
mult(rd(X0,X0),mult(rd(X0,X2),X2)) = mult(rd(X0,rd(X3,X2)),rd(X3,X2)),
inference(superposition,[status(thm)],[d38,d40]) ).
cnf(d49,plain,
mult(X0,rd(X1,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(demodulation,[status(thm)],[d48,d37]) ).
cnf(d50,plain,
mult(rd(X0,rd(X1,X2)),rd(X2,X2)) = rd(X0,rd(X1,X2)),
inference(superposition,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
rd(X0,rd(X1,X1)) = mult(X0,rd(X1,X1)),
inference(superposition,[status(thm)],[d50,d39]) ).
cnf(d52,plain,
mult(mult(X0,X1),rd(X3,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[d21,d49]) ).
cnf(d53,plain,
mult(rd(rd(rd(X0,X0),X1),X1),X1) = rd(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d54,plain,
mult(rd(rd(rd(X1,X1),X0),X0),X0) = rd(mult(X1,ld(X1,rd(X0,X0))),X0),
inference(demodulation,[status(thm)],[d53,d7]) ).
cnf(d55,plain,
rd(rd(X0,X0),X1) = rd(mult(X0,ld(X0,rd(X1,X1))),X1),
inference(demodulation,[status(thm)],[d54,d47]) ).
cnf(d56,plain,
mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d57,plain,
mult(rd(X0,rd(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d56,d7]) ).
cnf(d58,plain,
mult(rd(X0,rd(X0,X0)),rd(X0,X0)) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d57,d7]) ).
cnf(d59,plain,
mult(rd(X0,rd(X0,X0)),rd(X0,X0)) = rd(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d58,d7]) ).
cnf(d60,plain,
mult(X0,mult(X0,ld(X0,rd(X0,X0)))) = rd(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d59,d23]) ).
cnf(d61,plain,
mult(X0,rd(X0,X0)) = rd(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d60,d12]) ).
cnf(d62,plain,
X0 = rd(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d61,d8]) ).
cnf(d63,plain,
mult(rd(rd(X0,X1),rd(X2,X1)),rd(X2,X1)) = rd(X0,X1),
inference(superposition,[status(thm)],[d40,d2]) ).
cnf(d64,plain,
mult(rd(rd(X1,rd(X0,X0)),X0),rd(X0,rd(X0,X0))) = rd(X1,rd(X0,X0)),
inference(superposition,[status(thm)],[d62,d63]) ).
cnf(d65,plain,
mult(rd(rd(X1,rd(X0,X0)),X0),X0) = rd(X1,rd(X0,X0)),
inference(demodulation,[status(thm)],[d64,d62]) ).
cnf(d66,plain,
mult(rd(X0,X0),ld(ld(X0,X0),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(superposition,[status(thm)],[d7,d10]) ).
cnf(d67,plain,
mult(rd(X0,X0),ld(rd(X0,X0),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(demodulation,[status(thm)],[d66,d7]) ).
cnf(d68,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X0)) = mult(mult(X1,ld(X1,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d2,d67]) ).
cnf(d69,plain,
X0 = mult(mult(X0,ld(X0,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d70,plain,
X0 = mult(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d69,d12]) ).
cnf(d71,plain,
rd(X0,X0) = mult(X0,ld(X0,rd(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[status(thm)],[d19,d70]) ).
cnf(d72,plain,
mult(rd(X0,X0),ld(rd(X0,X0),rd(X0,X0))) = mult(rd(X0,X0),rd(X0,X0)),
inference(superposition,[status(thm)],[d71,d68]) ).
cnf(d73,plain,
mult(rd(X0,X0),rd(rd(X0,X0),rd(X0,X0))) = mult(rd(X0,X0),rd(X0,X0)),
inference(demodulation,[status(thm)],[d72,d7]) ).
cnf(d74,plain,
rd(X0,X0) = mult(rd(X0,X0),rd(X0,X0)),
inference(demodulation,[status(thm)],[d73,d8]) ).
cnf(d75,plain,
mult(X0,ld(X0,ld(rd(X0,X0),rd(X0,X0)))) = rd(X0,X0),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d76,plain,
mult(X0,ld(X0,rd(rd(X0,X0),rd(X0,X0)))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d75,d7]) ).
cnf(d77,plain,
mult(ld(X0,X1),ld(ld(X0,X1),rd(X0,X0))) = mult(rd(X0,X0),rd(X0,X0)),
inference(superposition,[status(thm)],[d76,d11]) ).
cnf(d78,plain,
mult(ld(X0,X1),ld(ld(X0,X1),rd(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d77,d74]) ).
cnf(d79,plain,
rd(rd(ld(X0,X1),ld(X0,X1)),X0) = rd(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d78,d55]) ).
cnf(d80,plain,
rd(rd(rd(X0,X0),ld(X0,X0)),X0) = rd(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d7,d79]) ).
cnf(d81,plain,
rd(rd(rd(X0,X0),rd(X0,X0)),X0) = rd(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d80,d7]) ).
cnf(d82,plain,
mult(rd(rd(X0,X0),X0),X0) = rd(rd(X0,X0),rd(X0,X0)),
inference(superposition,[status(thm)],[d81,d65]) ).
cnf(d83,plain,
mult(X0,ld(X0,rd(X0,X0))) = rd(rd(X0,X0),rd(X0,X0)),
inference(demodulation,[status(thm)],[d82,d19]) ).
cnf(d84,plain,
rd(X0,X0) = rd(rd(X0,X0),rd(X0,X0)),
inference(demodulation,[status(thm)],[d83,d12]) ).
cnf(d85,plain,
rd(rd(X1,X1),rd(X0,X0)) = rd(mult(X1,ld(X1,rd(X0,X0))),rd(X0,X0)),
inference(superposition,[status(thm)],[d84,d55]) ).
cnf(d86,plain,
mult(rd(X0,X0),rd(X1,X1)) = rd(mult(X0,ld(X0,rd(X1,X1))),rd(X1,X1)),
inference(demodulation,[status(thm)],[d85,d51]) ).
cnf(d87,plain,
mult(rd(X0,X0),rd(X1,X1)) = mult(mult(X0,ld(X0,rd(X1,X1))),rd(X1,X1)),
inference(demodulation,[status(thm)],[d86,d51]) ).
cnf(d88,plain,
mult(rd(X0,X0),rd(X1,X1)) = mult(X0,mult(rd(ld(X0,rd(X1,X1)),X1),X1)),
inference(demodulation,[status(thm)],[d87,d52]) ).
cnf(d89,plain,
mult(rd(mult(X0,ld(X0,rd(X1,X1))),rd(X2,X3)),rd(X2,X3)) = mult(rd(rd(X0,X0),X1),mult(rd(X1,X3),X3)),
inference(superposition,[status(thm)],[d19,d21]) ).
cnf(d90,plain,
mult(X0,mult(rd(ld(X0,rd(X1,X1)),X3),X3)) = mult(rd(rd(X0,X0),X1),mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[d89,d21]) ).
cnf(d91,plain,
mult(X1,mult(rd(ld(X1,rd(X0,X0)),X0),X0)) = mult(rd(rd(X1,X1),X0),X0),
inference(superposition,[status(thm)],[d70,d90]) ).
cnf(d92,plain,
mult(rd(X0,X0),rd(X1,X1)) = mult(rd(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[d91,d88]) ).
cnf(d93,plain,
mult(rd(X0,X0),rd(X1,X1)) = mult(X0,ld(X0,rd(X1,X1))),
inference(demodulation,[status(thm)],[d92,d19]) ).
cnf(d94,plain,
mult(X1,rd(rd(X0,X0),rd(X0,X0))) = mult(rd(X1,X0),rd(X0,rd(X0,X0))),
inference(superposition,[status(thm)],[d62,d49]) ).
cnf(d95,plain,
mult(X1,mult(rd(X0,X0),rd(X0,X0))) = mult(rd(X1,X0),rd(X0,rd(X0,X0))),
inference(demodulation,[status(thm)],[d94,d51]) ).
cnf(d96,plain,
mult(X1,mult(X0,ld(X0,rd(X0,X0)))) = mult(rd(X1,X0),rd(X0,rd(X0,X0))),
inference(demodulation,[status(thm)],[d95,d93]) ).
cnf(d97,plain,
mult(X1,rd(X0,X0)) = mult(rd(X1,X0),rd(X0,rd(X0,X0))),
inference(demodulation,[status(thm)],[d96,d12]) ).
cnf(d98,plain,
mult(X1,rd(X0,X0)) = mult(rd(X1,X0),mult(X0,rd(X0,X0))),
inference(demodulation,[status(thm)],[d97,d51]) ).
cnf(d99,plain,
mult(X1,rd(X0,X0)) = mult(rd(X1,X0),X0),
inference(demodulation,[status(thm)],[d98,d8]) ).
cnf(d100,plain,
mult(X0,rd(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c3,d99]) ).
cnf(d101,plain,
mult(rd(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)),rd(X2,X3)) = rd(mult(X0,mult(rd(X1,X3),X3)),rd(X2,X3)),
inference(superposition,[status(thm)],[d21,c3]) ).
cnf(d102,plain,
rd(mult(X0,X1),rd(X2,X3)) = rd(mult(X0,mult(rd(X1,X3),X3)),rd(X2,X3)),
inference(demodulation,[status(thm)],[d101,d47]) ).
cnf(d103,plain,
rd(mult(rd(X0,X0),X0),rd(X2,X1)) = rd(mult(X0,rd(X1,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[d37,d102]) ).
cnf(d104,plain,
rd(X0,rd(X1,X2)) = rd(mult(X0,rd(X2,X2)),rd(X1,X2)),
inference(demodulation,[status(thm)],[d103,d2]) ).
cnf(d105,plain,
rd(X2,rd(mult(X0,X1),X1)) = rd(mult(X2,rd(X1,X1)),mult(rd(X0,X1),X1)),
inference(superposition,[status(thm)],[c3,d104]) ).
cnf(d106,plain,
rd(X2,mult(X0,rd(X1,X1))) = rd(mult(X2,rd(X1,X1)),mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d105,d100]) ).
cnf(d107,plain,
rd(X2,mult(X0,rd(X1,X1))) = rd(mult(X2,rd(X1,X1)),mult(X0,rd(X1,X1))),
inference(demodulation,[status(thm)],[d106,d99]) ).
cnf(d108,plain,
mult(rd(X2,mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)) = mult(X2,rd(X1,X1)),
inference(superposition,[status(thm)],[c3,d39]) ).
cnf(d109,plain,
mult(rd(X2,mult(X0,rd(X1,X1))),rd(mult(X0,X1),X1)) = mult(X2,rd(X1,X1)),
inference(demodulation,[status(thm)],[d108,d99]) ).
cnf(d110,plain,
mult(rd(X2,mult(X0,rd(X1,X1))),mult(X0,rd(X1,X1))) = mult(X2,rd(X1,X1)),
inference(demodulation,[status(thm)],[d109,d100]) ).
cnf(d111,plain,
mult(X0,rd(mult(X1,rd(X2,X2)),mult(X1,rd(X2,X2)))) = mult(X0,rd(X2,X2)),
inference(demodulation,[status(thm)],[d110,d99]) ).
cnf(d112,plain,
mult(X2,rd(X0,mult(X0,rd(X1,X1)))) = mult(X2,rd(X1,X1)),
inference(demodulation,[status(thm)],[d111,d107]) ).
cnf(d113,plain,
mult(rd(X0,rd(X2,rd(X1,X0))),rd(X2,rd(X1,X0))) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d42,d38]) ).
cnf(d114,plain,
mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = X0,
inference(demodulation,[status(thm)],[d113,d2]) ).
cnf(d115,plain,
mult(X0,rd(rd(X2,X0),rd(X2,X0))) = X0,
inference(demodulation,[status(thm)],[d114,d49]) ).
cnf(d116,plain,
mult(X1,rd(mult(X0,rd(X1,X1)),rd(mult(X0,X1),X1))) = X1,
inference(superposition,[status(thm)],[d100,d115]) ).
cnf(d117,plain,
mult(X1,rd(X0,rd(mult(X0,X1),X1))) = X1,
inference(demodulation,[status(thm)],[d116,d104]) ).
cnf(d118,plain,
mult(X1,rd(X0,mult(X0,rd(X1,X1)))) = X1,
inference(demodulation,[status(thm)],[d117,d100]) ).
cnf(d119,plain,
mult(mult(X2,X0),rd(X1,X1)) = mult(X2,mult(X0,rd(X1,X1))),
inference(demodulation,[status(thm)],[d52,d99]) ).
cnf(d120,plain,
mult(X2,rd(mult(X0,X1),mult(X0,mult(X1,rd(X2,X2))))) = X2,
inference(superposition,[status(thm)],[d119,d118]) ).
cnf(d121,plain,
mult(X0,rd(mult(X1,X0),mult(X1,X0))) = X0,
inference(superposition,[status(thm)],[d8,d120]) ).
cnf(d122,plain,
mult(X2,rd(X0,X0)) = mult(X2,rd(mult(X1,X0),mult(X1,X0))),
inference(superposition,[status(thm)],[d121,d112]) ).
cnf(d123,plain,
mult(X0,mult(rd(X1,X3),X3)) = mult(rd(mult(X0,X1),rd(X4,X3)),rd(X4,X3)),
inference(superposition,[status(thm)],[d21,d40]) ).
cnf(d124,plain,
mult(X0,mult(rd(X1,X3),X3)) = mult(mult(X0,X1),rd(X3,X3)),
inference(demodulation,[status(thm)],[d123,d49]) ).
cnf(d125,plain,
mult(X2,mult(X0,rd(X1,X1))) = mult(mult(X2,X0),rd(X1,X1)),
inference(demodulation,[status(thm)],[d124,d99]) ).
cnf(d126,plain,
mult(mult(X0,X1),rd(X1,X1)) = mult(mult(X0,rd(X1,X1)),X1),
inference(superposition,[status(thm)],[d100,d99]) ).
cnf(d127,plain,
mult(X0,mult(X1,rd(X1,X1))) = mult(mult(X0,rd(X1,X1)),X1),
inference(demodulation,[status(thm)],[d126,d125]) ).
cnf(d128,plain,
mult(X1,X0) = mult(mult(X1,rd(X0,X0)),X0),
inference(demodulation,[status(thm)],[d127,d8]) ).
cnf(d129,plain,
mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,rd(X2,X2))),X2),
inference(superposition,[status(thm)],[d119,d128]) ).
cnf(d130,plain,
mult(rd(X0,X0),X1) = mult(mult(X0,ld(X0,rd(X1,X1))),X1),
inference(superposition,[status(thm)],[d93,d128]) ).
cnf(d131,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X0)) = mult(mult(X1,ld(X1,X0)),rd(X0,X0)),
inference(superposition,[status(thm)],[d8,d67]) ).
cnf(d132,plain,
mult(ld(X0,X2),ld(ld(X0,X2),X1)) = mult(rd(X0,X0),ld(rd(X0,X0),X1)),
inference(superposition,[status(thm)],[d131,d24]) ).
cnf(d133,plain,
mult(mult(X0,ld(X0,rd(X2,X2))),X2) = mult(rd(X0,X0),ld(rd(X0,X0),X2)),
inference(superposition,[status(thm)],[d11,d132]) ).
cnf(d134,plain,
mult(rd(X0,X0),X1) = mult(rd(X0,X0),ld(rd(X0,X0),X1)),
inference(demodulation,[status(thm)],[d133,d130]) ).
cnf(d135,plain,
mult(mult(X0,ld(X0,rd(X2,X2))),X2) = mult(ld(X0,X3),ld(ld(X0,X3),X2)),
inference(superposition,[status(thm)],[d11,d25]) ).
cnf(d136,plain,
mult(rd(X0,X0),X1) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(demodulation,[status(thm)],[d135,d130]) ).
cnf(d137,plain,
mult(ld(X0,X2),ld(ld(X0,X2),ld(rd(X0,X0),X1))) = ld(rd(X0,X0),X1),
inference(superposition,[status(thm)],[d132,d30]) ).
cnf(d138,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X2)) = ld(rd(X0,X0),X2),
inference(demodulation,[status(thm)],[d137,d136]) ).
cnf(d139,plain,
mult(rd(X0,X0),X1) = ld(rd(X0,X0),X1),
inference(demodulation,[status(thm)],[d138,d134]) ).
cnf(d140,plain,
mult(ld(rd(X0,X0),X0),ld(X0,X1)) = mult(mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))),X1),
inference(superposition,[status(thm)],[d18,d11]) ).
cnf(d141,plain,
mult(mult(rd(X0,X0),X0),ld(X0,X1)) = mult(mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))),X1),
inference(demodulation,[status(thm)],[d140,d139]) ).
cnf(d142,plain,
mult(mult(X0,rd(X0,X0)),ld(X0,X1)) = mult(mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))),X1),
inference(demodulation,[status(thm)],[d141,d99]) ).
cnf(d143,plain,
mult(X0,ld(X0,X1)) = mult(mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))),X1),
inference(demodulation,[status(thm)],[d142,d8]) ).
cnf(d144,plain,
mult(X0,ld(X0,X1)) = mult(mult(rd(X0,X0),mult(rd(X0,X0),rd(X1,X1))),X1),
inference(demodulation,[status(thm)],[d143,d139]) ).
cnf(d145,plain,
mult(X0,ld(X0,X1)) = mult(mult(rd(X0,X0),rd(X0,X0)),X1),
inference(demodulation,[status(thm)],[d144,d129]) ).
cnf(d146,plain,
mult(X0,ld(X0,X1)) = mult(mult(X0,ld(X0,rd(X0,X0))),X1),
inference(demodulation,[status(thm)],[d145,d93]) ).
cnf(d147,plain,
mult(X0,ld(X0,X1)) = mult(rd(X0,X0),X1),
inference(demodulation,[status(thm)],[d146,d12]) ).
cnf(d148,plain,
mult(X1,rd(mult(rd(X0,X0),X1),mult(X0,ld(X0,X1)))) = X1,
inference(superposition,[status(thm)],[d147,d121]) ).
cnf(d149,plain,
mult(X1,rd(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))) = X1,
inference(demodulation,[status(thm)],[d148,d147]) ).
cnf(d150,plain,
mult(X0,rd(ld(X1,X0),ld(X1,X0))) = X0,
inference(demodulation,[status(thm)],[d149,d122]) ).
cnf(d151,plain,
mult(X2,rd(X0,X0)) = mult(X2,rd(ld(X1,X0),ld(X1,X0))),
inference(superposition,[status(thm)],[d150,d112]) ).
cnf(d152,plain,
mult(rd(rd(X0,rd(X0,X0)),rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,rd(X0,X0)),mult(rd(rd(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[d59,d21]) ).
cnf(d153,plain,
mult(rd(X0,rd(X0,X0)),rd(X2,X2)) = mult(rd(X0,rd(X0,X0)),mult(rd(rd(X0,X0),X2),X2)),
inference(demodulation,[status(thm)],[d152,d49]) ).
cnf(d154,plain,
mult(X0,rd(X1,X1)) = mult(rd(X0,rd(X0,X0)),mult(rd(rd(X0,X0),X1),X1)),
inference(demodulation,[status(thm)],[d153,d62]) ).
cnf(d155,plain,
mult(X0,rd(X1,X1)) = mult(X0,mult(rd(rd(X0,X0),X1),X1)),
inference(demodulation,[status(thm)],[d154,d62]) ).
cnf(d156,plain,
mult(X0,rd(X1,X1)) = mult(X0,mult(X0,ld(X0,rd(X1,X1)))),
inference(demodulation,[status(thm)],[d155,d19]) ).
cnf(d157,plain,
( rd(mult(sK16,rd(sK17,sK18)),rd(sK17,sK18)) != rd(mult(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != rd(mult(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[c7,c3]) ).
cnf(d158,plain,
( rd(mult(sK16,rd(sK17,sK18)),rd(sK17,sK18)) != rd(mult(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[d157,c3]) ).
cnf(d159,plain,
( mult(rd(sK16,rd(sK17,sK18)),rd(sK17,sK18)) != rd(mult(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[d158,c3]) ).
cnf(d160,plain,
( mult(rd(sK16,rd(sK17,sK18)),rd(sK17,sK18)) != mult(rd(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[d159,c3]) ).
cnf(d161,plain,
( mult(sK16,mult(sK16,ld(sK16,rd(sK18,sK18)))) != mult(rd(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[d160,d23]) ).
cnf(d162,plain,
( mult(sK16,rd(sK18,sK18)) != mult(rd(sK16,sK18),sK18)
| mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18) ),
inference(demodulation,[status(thm)],[d161,d156]) ).
cnf(d163,plain,
mult(rd(sK16,ld(sK17,sK18)),ld(sK17,sK18)) != mult(rd(sK16,sK18),sK18),
inference(resolution,[status(thm)],[d99,d162]) ).
cnf(d164,plain,
mult(sK16,rd(ld(sK17,sK18),ld(sK17,sK18))) != mult(rd(sK16,sK18),sK18),
inference(demodulation,[status(thm)],[d163,d99]) ).
cnf(d165,plain,
mult(sK16,rd(ld(sK17,sK18),ld(sK17,sK18))) != mult(sK16,rd(sK18,sK18)),
inference(demodulation,[status(thm)],[d164,d99]) ).
cnf(d166,plain,
mult(sK16,rd(sK18,sK18)) != mult(sK16,rd(sK18,sK18)),
inference(demodulation,[status(thm)],[d165,d151]) ).
cnf(d167,plain,
mult(X0,ld(X0,ld(X0,ld(X0,X0)))) = ld(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[d6,c2]) ).
cnf(d168,plain,
mult(X0,ld(X0,ld(X0,rd(X0,X0)))) = ld(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[d167,d7]) ).
cnf(d169,plain,
mult(X0,ld(X0,ld(X0,rd(X0,X0)))) = ld(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d168,d7]) ).
cnf(d170,plain,
mult(ld(X0,rd(X0,X0)),ld(mult(X0,ld(X0,ld(X0,rd(X0,X0)))),X0)) = X0,
inference(superposition,[status(thm)],[d169,d28]) ).
cnf(d171,plain,
mult(ld(X0,rd(X0,X0)),ld(ld(X0,rd(X0,X0)),X0)) = X0,
inference(demodulation,[status(thm)],[d170,d169]) ).
cnf(d172,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d171,d26]) ).
cnf(d173,plain,
$false,
inference(resolution,[status(thm)],[d172,d166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685+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 : n020.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 15:38:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.67/9.01 % SZS status Theorem for theBenchmark.p
% 58.67/9.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------