%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP688-1 : 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 : n001.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 : Unsatisfiable 187.76s 61.08s
% Output : CNFRefutation 187.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 12
% Syntax : Number of clauses : 197 ( 197 unt; 0 nHn; 53 RR)
% Number of literals : 197 ( 196 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(X0,ld(X0,X1)) = X1 ).
cnf(c02,axiom,
ld(X0,mult(X0,X1)) = X1 ).
cnf(c03,axiom,
mult(rd(X0,X1),X1) = X0 ).
cnf(c04,axiom,
rd(mult(X0,X1),X1) = X0 ).
cnf(c05,axiom,
mult(X0,unit) = X0 ).
cnf(c06,axiom,
mult(unit,X0) = X0 ).
cnf(c07,axiom,
mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(X1,X0)),X2) ).
cnf(c08,axiom,
mult(i(X0),mult(X0,X1)) = X1 ).
cnf(c09,axiom,
i(mult(X0,X1)) = mult(i(X0),i(X1)) ).
cnf(c10,axiom,
mult('op$uc',mult('op$uc',mult('op$uc','op$uc'))) = unit ).
cnf(c11,axiom,
mult('op$ud',mult('op$ud','op$ud')) = unit ).
cnf(goals,negated_conjecture,
mult('op$uc','op$ud') != mult('op$ud','op$uc') ).
cnf(c_0,plain,
mult(X0,ld(X0,X1)) = X1,
inference(clausification,[status(esa)],[c01]) ).
cnf(c_1,plain,
ld(X0,mult(X0,X1)) = X1,
inference(clausification,[status(esa)],[c02]) ).
cnf(c_2,plain,
mult(rd(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[c03]) ).
cnf(c_3,plain,
rd(mult(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[c04]) ).
cnf(c_4,plain,
mult(X0,unit) = X0,
inference(clausification,[status(esa)],[c05]) ).
cnf(c_5,plain,
mult(unit,X0) = X0,
inference(clausification,[status(esa)],[c06]) ).
cnf(c_6,plain,
mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(X1,X0)),X2),
inference(clausification,[status(esa)],[c07]) ).
cnf(c_7,plain,
mult(i(X0),mult(X0,X1)) = X1,
inference(clausification,[status(esa)],[c08]) ).
cnf(c_8,plain,
i(mult(X0,X1)) = mult(i(X0),i(X1)),
inference(clausification,[status(esa)],[c09]) ).
cnf(c_9,plain,
mult('op$uc',mult('op$uc',mult('op$uc','op$uc'))) = unit,
inference(clausification,[status(esa)],[c10]) ).
cnf(c_10,plain,
mult('op$ud',mult('op$ud','op$ud')) = unit,
inference(clausification,[status(esa)],[c11]) ).
cnf(c_11,plain,
mult('op$uc','op$ud') != mult('op$ud','op$uc'),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
mult(unit,mult(X0,mult(unit,X1))) = mult(mult(X0,unit),X1),
inference(superposition,[status(thm)],[c_5,c_6]) ).
cnf(d1,plain,
mult(X0,mult(unit,X1)) = mult(mult(X0,unit),X1),
inference(demodulation,[status(thm)],[d0,c_5]) ).
cnf(d2,plain,
mult(X1,X0) = mult(mult(X1,unit),X0),
inference(demodulation,[status(thm)],[d1,c_5]) ).
cnf(d3,plain,
mult(X0,X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[d2,c_4]) ).
cnf(d4,plain,
X1 = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_0,d3]) ).
cnf(d5,plain,
mult(i(X0),X1) = ld(X0,X1),
inference(superposition,[status(thm)],[c_0,c_7]) ).
cnf(d6,plain,
X0 = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_2,d3]) ).
cnf(d7,plain,
rd(X1,mult(X0,X1)) = i(X0),
inference(superposition,[status(thm)],[c_7,c_3]) ).
cnf(d8,plain,
mult(i(X0),X0) = unit,
inference(superposition,[status(thm)],[c_4,c_7]) ).
cnf(d9,plain,
ld(i(X0),unit) = X0,
inference(superposition,[status(thm)],[d8,c_1]) ).
cnf(d10,plain,
mult(i(i(X0)),unit) = X0,
inference(superposition,[status(thm)],[d8,c_7]) ).
cnf(d11,plain,
i(i(X0)) = X0,
inference(demodulation,[status(thm)],[d10,c_4]) ).
cnf(d12,plain,
ld(X0,unit) = i(X0),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
rd(X1,ld(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_0,c_3]) ).
cnf(d14,plain,
rd(unit,X0) = i(X0),
inference(superposition,[status(thm)],[d8,c_3]) ).
cnf(d15,plain,
i(ld(X0,unit)) = X0,
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
i(mult(ld(X0,unit),X1)) = mult(X0,i(X1)),
inference(superposition,[status(thm)],[d15,c_8]) ).
cnf(d17,plain,
i(mult(i(X0),X1)) = mult(X0,i(X1)),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
i(ld(X0,X1)) = mult(X0,i(X1)),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_2,c_1]) ).
cnf(d20,plain,
i(mult(X0,X1)) = ld(X0,i(X1)),
inference(demodulation,[status(thm)],[c_8,d5]) ).
cnf(d21,plain,
i(mult(rd(i(X0),X1),X0)) = X1,
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
i(X1) = mult(rd(i(X0),X1),X0),
inference(superposition,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
mult(X0,i(X0)) = unit,
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d24,plain,
mult(i(X0),unit) = i(X0),
inference(superposition,[status(thm)],[d23,c_7]) ).
cnf(d25,plain,
i(X0) = i(X0),
inference(demodulation,[status(thm)],[d24,c_4]) ).
cnf(d26,plain,
rd(X1,X0) = i(rd(X0,X1)),
inference(superposition,[status(thm)],[c_2,d7]) ).
cnf(d27,plain,
i(rd(X0,X1)) = rd(X1,X0),
inference(superposition,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
i(i(X1)) = rd(mult(X1,X0),X0),
inference(superposition,[status(thm)],[d7,d27]) ).
cnf(d29,plain,
X0 = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
ld(i(X0),X1) = mult(X0,X1),
inference(superposition,[status(thm)],[c_7,c_1]) ).
cnf(d31,plain,
mult(i(i(X0)),i(mult(X0,X1))) = i(X1),
inference(superposition,[status(thm)],[c_8,c_7]) ).
cnf(d32,plain,
ld(i(X0),i(mult(X0,X1))) = i(X1),
inference(demodulation,[status(thm)],[d31,d5]) ).
cnf(d33,plain,
mult(X0,i(mult(X0,X1))) = i(X1),
inference(demodulation,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
rd(i(X1),i(mult(X0,X1))) = X0,
inference(superposition,[status(thm)],[d33,c_3]) ).
cnf(d35,plain,
rd(i(X1),i(X0)) = rd(X0,X1),
inference(superposition,[status(thm)],[d6,d34]) ).
cnf(d36,plain,
i(mult(X1,ld(X0,unit))) = mult(i(X1),X0),
inference(superposition,[status(thm)],[d15,c_8]) ).
cnf(d37,plain,
i(mult(X1,i(X0))) = mult(i(X1),X0),
inference(demodulation,[status(thm)],[d36,d12]) ).
cnf(d38,plain,
i(mult(X0,i(X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[d37,d5]) ).
cnf(d39,plain,
rd(i(X2),ld(X0,X1)) = rd(mult(X0,i(X1)),X2),
inference(superposition,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
ld(X0,X1) = mult(i(X0),X1),
inference(superposition,[status(thm)],[d11,d30]) ).
cnf(d41,plain,
ld(rd(X0,X1),X2) = mult(rd(X1,X0),X2),
inference(superposition,[status(thm)],[d26,d40]) ).
cnf(d42,plain,
X2 = mult(rd(X0,X1),mult(rd(X1,X0),X2)),
inference(superposition,[status(thm)],[d41,d4]) ).
cnf(d43,plain,
rd(i(X1),X0) = rd(i(X0),X1),
inference(superposition,[status(thm)],[d11,d35]) ).
cnf(d44,plain,
ld(rd(i(X1),X0),X2) = mult(rd(X1,i(X0)),X2),
inference(superposition,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
mult(rd(X1,i(X0)),X2) = mult(rd(X0,i(X1)),X2),
inference(demodulation,[status(thm)],[d44,d41]) ).
cnf(d46,plain,
X1 = ld(X0,ld(i(X0),X1)),
inference(superposition,[status(thm)],[c_0,d5]) ).
cnf(d47,plain,
X1 = ld(X0,mult(X0,X1)),
inference(demodulation,[status(thm)],[d46,d30]) ).
cnf(d48,plain,
rd(mult(X0,mult(X1,mult(X0,X2))),X2) = mult(X0,mult(X1,X0)),
inference(superposition,[status(thm)],[c_6,c_3]) ).
cnf(d49,plain,
rd(mult(X1,X0),X2) = mult(X1,mult(rd(X0,mult(X1,X2)),X1)),
inference(superposition,[status(thm)],[c_2,d48]) ).
cnf(d50,plain,
rd(unit,mult('op$ud','op$ud')) = 'op$ud',
inference(superposition,[status(thm)],[c_10,c_3]) ).
cnf(d51,plain,
i(mult('op$ud','op$ud')) = 'op$ud',
inference(demodulation,[status(thm)],[d50,d14]) ).
cnf(d52,plain,
i('op$ud') = mult('op$ud','op$ud'),
inference(superposition,[status(thm)],[d51,d11]) ).
cnf(d53,plain,
rd(mult('op$ud',X0),'op$ud') = mult('op$ud',mult(rd(X0,i('op$ud')),'op$ud')),
inference(superposition,[status(thm)],[d52,d49]) ).
cnf(d54,plain,
mult(rd(X0,i('op$ud')),'op$ud') = ld('op$ud',rd(mult('op$ud',X0),'op$ud')),
inference(superposition,[status(thm)],[d53,d47]) ).
cnf(d55,plain,
mult(rd(ld('op$ud',X0),i('op$ud')),'op$ud') = ld('op$ud',rd(X0,'op$ud')),
inference(superposition,[status(thm)],[d4,d54]) ).
cnf(d56,plain,
mult(rd('op$ud',i(ld('op$ud',X0))),'op$ud') = ld('op$ud',rd(X0,'op$ud')),
inference(demodulation,[status(thm)],[d55,d45]) ).
cnf(d57,plain,
mult(rd('op$ud',mult('op$ud',i(X0))),'op$ud') = ld('op$ud',rd(X0,'op$ud')),
inference(demodulation,[status(thm)],[d56,d18]) ).
cnf(d58,plain,
'op$ud' = mult(rd(mult('op$ud',i(X0)),'op$ud'),ld('op$ud',rd(X0,'op$ud'))),
inference(superposition,[status(thm)],[d57,d42]) ).
cnf(d59,plain,
'op$ud' = mult(rd(i('op$ud'),ld('op$ud',X0)),ld('op$ud',rd(X0,'op$ud'))),
inference(demodulation,[status(thm)],[d58,d39]) ).
cnf(d60,plain,
ld(mult(X0,mult(X1,X0)),mult(X0,mult(X1,mult(X0,X2)))) = X2,
inference(superposition,[status(thm)],[c_6,c_1]) ).
cnf(d61,plain,
ld(mult(X0,mult(X2,X0)),mult(X0,mult(X2,X1))) = ld(X0,X1),
inference(superposition,[status(thm)],[c_0,d60]) ).
cnf(d62,plain,
ld(mult(X1,X0),mult(X1,mult(rd(X0,X1),X2))) = ld(X1,X2),
inference(superposition,[status(thm)],[d6,d61]) ).
cnf(d63,plain,
mult(rd(X0,X1),mult(rd(X1,X0),X2)) = X2,
inference(superposition,[status(thm)],[d41,c_0]) ).
cnf(d64,plain,
ld(mult(X1,X0),mult(X1,X2)) = ld(X1,mult(rd(X1,X0),X2)),
inference(superposition,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
rd(mult(X0,unit),X1) = mult(X0,mult(i(mult(X0,X1)),X0)),
inference(superposition,[status(thm)],[d8,d48]) ).
cnf(d66,plain,
rd(X0,X1) = mult(X0,mult(i(mult(X0,X1)),X0)),
inference(demodulation,[status(thm)],[d65,c_4]) ).
cnf(d67,plain,
rd(X0,X1) = mult(X0,ld(mult(X0,X1),X0)),
inference(demodulation,[status(thm)],[d66,d5]) ).
cnf(d68,plain,
rd(X0,ld(X0,X1)) = mult(X0,ld(X1,X0)),
inference(superposition,[status(thm)],[d4,d67]) ).
cnf(d69,plain,
X0 = i(ld(X0,unit)),
inference(superposition,[status(thm)],[d13,d14]) ).
cnf(d70,plain,
X0 = i(i(X0)),
inference(demodulation,[status(thm)],[d69,d12]) ).
cnf(d71,plain,
i(X1) = rd(ld(X1,X0),X0),
inference(superposition,[status(thm)],[d13,d27]) ).
cnf(d72,plain,
ld(mult(X0,X0),mult(X0,mult(unit,mult(X0,X1)))) = X1,
inference(superposition,[status(thm)],[c_5,d60]) ).
cnf(d73,plain,
ld(mult(X0,X0),mult(X0,mult(X0,X1))) = X1,
inference(demodulation,[status(thm)],[d72,c_5]) ).
cnf(d74,plain,
ld(mult(X0,X0),mult(X0,unit)) = i(X0),
inference(superposition,[status(thm)],[d23,d73]) ).
cnf(d75,plain,
ld(mult(X0,X0),X0) = i(X0),
inference(demodulation,[status(thm)],[d74,c_4]) ).
cnf(d76,plain,
i(mult(X0,X0)) = rd(i(X0),X0),
inference(superposition,[status(thm)],[d75,d71]) ).
cnf(d77,plain,
rd(mult(i(X0),mult(X1,unit)),X0) = mult(i(X0),mult(X1,i(X0))),
inference(superposition,[status(thm)],[d8,d48]) ).
cnf(d78,plain,
rd(ld(X0,mult(X1,unit)),X0) = mult(i(X0),mult(X1,i(X0))),
inference(demodulation,[status(thm)],[d77,d5]) ).
cnf(d79,plain,
rd(ld(X1,X0),X1) = mult(i(X1),mult(X0,i(X1))),
inference(demodulation,[status(thm)],[d78,c_4]) ).
cnf(d80,plain,
rd(ld(X0,X1),X0) = ld(X0,mult(X1,i(X0))),
inference(demodulation,[status(thm)],[d79,d5]) ).
cnf(d81,plain,
rd(mult(i(X0),mult(X2,X1)),mult(X0,X1)) = mult(i(X0),mult(X2,i(X0))),
inference(superposition,[status(thm)],[c_7,d48]) ).
cnf(d82,plain,
rd(ld(X0,mult(X1,X2)),mult(X0,X2)) = mult(i(X0),mult(X1,i(X0))),
inference(demodulation,[status(thm)],[d81,d5]) ).
cnf(d83,plain,
rd(ld(X0,mult(X1,X2)),mult(X0,X2)) = ld(X0,mult(X1,i(X0))),
inference(demodulation,[status(thm)],[d82,d5]) ).
cnf(d84,plain,
rd(ld(X0,mult(X1,X2)),mult(X0,X2)) = rd(ld(X0,X1),X0),
inference(demodulation,[status(thm)],[d83,d80]) ).
cnf(d85,plain,
rd(ld(X0,i('op$ud')),mult(X0,'op$ud')) = rd(ld(X0,'op$ud'),X0),
inference(superposition,[status(thm)],[d52,d84]) ).
cnf(d86,plain,
rd(i(mult(X0,'op$ud')),mult(X0,'op$ud')) = rd(ld(X0,'op$ud'),X0),
inference(demodulation,[status(thm)],[d85,d20]) ).
cnf(d87,plain,
i(mult(mult(X0,'op$ud'),mult(X0,'op$ud'))) = rd(ld(X0,'op$ud'),X0),
inference(demodulation,[status(thm)],[d86,d76]) ).
cnf(d88,plain,
mult(mult(X0,'op$ud'),mult(X0,'op$ud')) = i(rd(ld(X0,'op$ud'),X0)),
inference(superposition,[status(thm)],[d87,d70]) ).
cnf(d89,plain,
mult(mult(X0,'op$ud'),mult(X0,'op$ud')) = rd(X0,ld(X0,'op$ud')),
inference(demodulation,[status(thm)],[d88,d26]) ).
cnf(d90,plain,
mult(mult(X0,'op$ud'),mult(X0,'op$ud')) = mult(X0,ld('op$ud',X0)),
inference(demodulation,[status(thm)],[d89,d68]) ).
cnf(d91,plain,
mult(X0,'op$ud') = ld(mult(X0,'op$ud'),mult(X0,ld('op$ud',X0))),
inference(superposition,[status(thm)],[d90,d47]) ).
cnf(d92,plain,
mult(X0,'op$ud') = ld(X0,mult(rd(X0,'op$ud'),ld('op$ud',X0))),
inference(demodulation,[status(thm)],[d91,d64]) ).
cnf(d93,plain,
mult(rd(X0,'op$ud'),ld('op$ud',X0)) = mult(X0,mult(X0,'op$ud')),
inference(superposition,[status(thm)],[d92,d4]) ).
cnf(d94,plain,
rd(X0,'op$ud') = rd(mult(X0,mult(X0,'op$ud')),ld('op$ud',X0)),
inference(superposition,[status(thm)],[d93,d29]) ).
cnf(d95,plain,
X0 = rd(X1,ld(X0,X1)),
inference(superposition,[status(thm)],[d4,d29]) ).
cnf(d96,plain,
mult(X0,mult(X1,X0)) = rd(mult(X0,mult(X1,X2)),ld(X0,X2)),
inference(superposition,[status(thm)],[d61,d95]) ).
cnf(d97,plain,
mult('op$ud',mult('op$ud',mult('op$ud',X0))) = mult(unit,X0),
inference(superposition,[status(thm)],[c_10,c_6]) ).
cnf(d98,plain,
mult('op$ud',mult('op$ud',mult('op$ud',X0))) = X0,
inference(demodulation,[status(thm)],[d97,c_5]) ).
cnf(d99,plain,
ld('op$ud',X0) = mult('op$ud',mult('op$ud',X0)),
inference(superposition,[status(thm)],[d98,c_1]) ).
cnf(d100,plain,
mult('op$ud',X0) = ld('op$ud',ld('op$ud',X0)),
inference(superposition,[status(thm)],[d99,d47]) ).
cnf(d101,plain,
ld('op$uc',unit) = mult('op$uc',mult('op$uc','op$uc')),
inference(superposition,[status(thm)],[c_9,c_1]) ).
cnf(d102,plain,
i('op$uc') = mult('op$uc',mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d101,d12]) ).
cnf(d103,plain,
mult('op$uc','op$uc') = ld('op$uc',i('op$uc')),
inference(superposition,[status(thm)],[d102,d47]) ).
cnf(d104,plain,
mult('op$uc','op$uc') = i(mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d103,d20]) ).
cnf(d105,plain,
i(mult(X0,mult('op$uc','op$uc'))) = ld(X0,mult('op$uc','op$uc')),
inference(superposition,[status(thm)],[d104,d20]) ).
cnf(d106,plain,
ld(mult(mult('op$uc',mult('op$uc','op$uc')),unit),mult(mult('op$uc',mult('op$uc','op$uc')),mult('op$uc',mult(mult('op$uc',mult('op$uc','op$uc')),X0)))) = X0,
inference(superposition,[status(thm)],[c_9,d60]) ).
cnf(d107,plain,
ld(mult('op$uc',mult('op$uc',mult('op$uc',unit))),mult(mult('op$uc',mult('op$uc','op$uc')),mult('op$uc',mult(mult('op$uc',mult('op$uc','op$uc')),X0)))) = X0,
inference(demodulation,[status(thm)],[d106,c_6]) ).
cnf(d108,plain,
ld(mult('op$uc',mult('op$uc','op$uc')),mult(mult('op$uc',mult('op$uc','op$uc')),mult('op$uc',mult(mult('op$uc',mult('op$uc','op$uc')),X0)))) = X0,
inference(demodulation,[status(thm)],[d107,c_4]) ).
cnf(d109,plain,
mult('op$uc',mult(mult('op$uc',mult('op$uc','op$uc')),X0)) = X0,
inference(demodulation,[status(thm)],[d108,c_1]) ).
cnf(d110,plain,
mult('op$uc',mult('op$uc',mult('op$uc',mult('op$uc',X0)))) = X0,
inference(demodulation,[status(thm)],[d109,c_6]) ).
cnf(d111,plain,
mult('op$uc',mult('op$uc',mult('op$uc',X0))) = ld('op$uc',X0),
inference(superposition,[status(thm)],[d110,d47]) ).
cnf(d112,plain,
mult('op$uc',mult('op$uc',X0)) = ld('op$uc',ld('op$uc',X0)),
inference(superposition,[status(thm)],[d111,d47]) ).
cnf(d113,plain,
ld(mult(X0,X0),mult(X0,X1)) = ld(X0,X1),
inference(superposition,[status(thm)],[d4,d73]) ).
cnf(d114,plain,
ld(mult(X0,X0),X1) = ld(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[d4,d113]) ).
cnf(d115,plain,
rd(ld('op$ud',X0),mult('op$ud',X0)) = 'op$ud',
inference(superposition,[status(thm)],[d99,c_3]) ).
cnf(d116,plain,
ld(X0,i(X1)) = i(mult(X0,X1)),
inference(superposition,[status(thm)],[d33,c_1]) ).
cnf(d117,plain,
rd(i(mult('op$ud',X0)),mult('op$ud',i(X0))) = 'op$ud',
inference(superposition,[status(thm)],[d116,d115]) ).
cnf(d118,plain,
rd(i(mult('op$ud',mult('op$uc','op$uc'))),mult('op$ud',mult('op$uc','op$uc'))) = 'op$ud',
inference(superposition,[status(thm)],[d104,d117]) ).
cnf(d119,plain,
i(mult(mult('op$ud',mult('op$uc','op$uc')),mult('op$ud',mult('op$uc','op$uc')))) = 'op$ud',
inference(demodulation,[status(thm)],[d118,d76]) ).
cnf(d120,plain,
mult(mult('op$ud',mult('op$uc','op$uc')),'op$ud') = i(mult('op$ud',mult('op$uc','op$uc'))),
inference(superposition,[status(thm)],[d119,d33]) ).
cnf(d121,plain,
mult(mult('op$ud',mult('op$uc','op$uc')),'op$ud') = ld('op$ud',mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d120,d105]) ).
cnf(d122,plain,
rd('op$ud',ld('op$ud',mult('op$uc','op$uc'))) = i(mult('op$ud',mult('op$uc','op$uc'))),
inference(superposition,[status(thm)],[d121,d7]) ).
cnf(d123,plain,
mult('op$ud',ld(mult('op$uc','op$uc'),'op$ud')) = i(mult('op$ud',mult('op$uc','op$uc'))),
inference(demodulation,[status(thm)],[d122,d68]) ).
cnf(d124,plain,
mult('op$ud',ld('op$uc',ld('op$uc','op$ud'))) = i(mult('op$ud',mult('op$uc','op$uc'))),
inference(demodulation,[status(thm)],[d123,d114]) ).
cnf(d125,plain,
mult('op$ud',mult('op$uc',mult('op$uc','op$ud'))) = i(mult('op$ud',mult('op$uc','op$uc'))),
inference(demodulation,[status(thm)],[d124,d112]) ).
cnf(d126,plain,
mult('op$ud',mult('op$uc',mult('op$uc','op$ud'))) = ld('op$ud',mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d125,d105]) ).
cnf(d127,plain,
mult('op$uc',mult('op$uc','op$ud')) = ld('op$ud',ld('op$ud',mult('op$uc','op$uc'))),
inference(superposition,[status(thm)],[d126,d47]) ).
cnf(d128,plain,
mult('op$uc',mult('op$uc','op$ud')) = mult('op$ud',mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d127,d100]) ).
cnf(d129,plain,
mult('op$ud',mult('op$uc','op$ud')) = rd(mult('op$uc',mult('op$uc','op$ud')),ld('op$ud','op$uc')),
inference(superposition,[status(thm)],[d128,d96]) ).
cnf(d130,plain,
mult('op$ud',mult('op$uc','op$ud')) = rd('op$uc','op$ud'),
inference(demodulation,[status(thm)],[d129,d94]) ).
cnf(d131,plain,
ld('op$ud',rd('op$uc','op$ud')) = mult('op$uc','op$ud'),
inference(superposition,[status(thm)],[d130,c_1]) ).
cnf(d132,plain,
'op$ud' = mult(rd(i('op$ud'),ld('op$ud','op$uc')),mult('op$uc','op$ud')),
inference(superposition,[status(thm)],[d131,d59]) ).
cnf(d133,plain,
rd(i('op$ud'),ld('op$ud','op$uc')) = rd('op$ud',mult('op$uc','op$ud')),
inference(superposition,[status(thm)],[d132,d29]) ).
cnf(d134,plain,
rd(i('op$ud'),ld('op$ud','op$uc')) = i('op$uc'),
inference(demodulation,[status(thm)],[d133,d7]) ).
cnf(d135,plain,
i(ld('op$ud','op$uc')) = mult(i('op$uc'),'op$ud'),
inference(superposition,[status(thm)],[d134,d22]) ).
cnf(d136,plain,
mult('op$ud',i('op$uc')) = mult(i('op$uc'),'op$ud'),
inference(demodulation,[status(thm)],[d135,d18]) ).
cnf(d137,plain,
mult('op$ud',i('op$uc')) = ld('op$uc','op$ud'),
inference(demodulation,[status(thm)],[d136,d5]) ).
cnf(d138,plain,
rd(i('op$uc'),ld('op$uc','op$ud')) = i('op$ud'),
inference(superposition,[status(thm)],[d137,d7]) ).
cnf(d139,plain,
mult(X1,mult(rd(X0,X1),mult(X1,X2))) = mult(mult(X1,X0),X2),
inference(superposition,[status(thm)],[c_2,c_6]) ).
cnf(d140,plain,
mult(rd(X1,X0),mult(X0,X2)) = ld(X0,mult(mult(X0,X1),X2)),
inference(superposition,[status(thm)],[d139,d47]) ).
cnf(d141,plain,
mult('op$ud',mult('op$uc','op$uc')) = rd(ld('op$ud',mult('op$uc','op$uc')),'op$ud'),
inference(superposition,[status(thm)],[d121,d29]) ).
cnf(d142,plain,
mult('op$uc',mult('op$uc','op$ud')) = rd(ld('op$ud',mult('op$uc','op$uc')),'op$ud'),
inference(demodulation,[status(thm)],[d141,d128]) ).
cnf(d143,plain,
rd(mult('op$ud',mult(X0,i('op$ud'))),'op$ud') = mult('op$ud',mult(X0,'op$ud')),
inference(superposition,[status(thm)],[d52,d48]) ).
cnf(d144,plain,
mult(rd(X0,X1),i(X0)) = i(X1),
inference(superposition,[status(thm)],[d6,d33]) ).
cnf(d145,plain,
rd(mult('op$ud',i(X0)),'op$ud') = mult('op$ud',mult(rd('op$ud',X0),'op$ud')),
inference(superposition,[status(thm)],[d144,d143]) ).
cnf(d146,plain,
rd(i('op$ud'),ld('op$ud',X0)) = mult('op$ud',mult(rd('op$ud',X0),'op$ud')),
inference(demodulation,[status(thm)],[d145,d39]) ).
cnf(d147,plain,
mult(rd('op$ud',X0),'op$ud') = ld('op$ud',rd(i('op$ud'),ld('op$ud',X0))),
inference(superposition,[status(thm)],[d146,d47]) ).
cnf(d148,plain,
i(X0) = rd(X1,mult(X0,X1)),
inference(superposition,[status(thm)],[c_3,d27]) ).
cnf(d149,plain,
mult(X0,mult(unit,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(superposition,[status(thm)],[c_5,c_6]) ).
cnf(d150,plain,
mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(demodulation,[status(thm)],[d149,c_5]) ).
cnf(d151,plain,
i(mult(X0,X0)) = rd(X1,mult(X0,mult(X0,X1))),
inference(superposition,[status(thm)],[d150,d148]) ).
cnf(d152,plain,
ld(mult('op$uc','op$uc'),X0) = mult(mult('op$uc','op$uc'),X0),
inference(superposition,[status(thm)],[d104,d40]) ).
cnf(d153,plain,
ld(mult('op$uc','op$uc'),X0) = mult('op$uc',mult('op$uc',X0)),
inference(demodulation,[status(thm)],[d152,d150]) ).
cnf(d154,plain,
i(mult('op$uc',mult('op$uc',X0))) = mult(mult('op$uc','op$uc'),i(X0)),
inference(superposition,[status(thm)],[d153,d18]) ).
cnf(d155,plain,
i(mult('op$uc',mult('op$uc',X0))) = mult('op$uc',mult('op$uc',i(X0))),
inference(demodulation,[status(thm)],[d154,d150]) ).
cnf(d156,plain,
i(mult('op$uc',mult('op$uc','op$ud'))) = ld('op$ud',mult('op$uc','op$uc')),
inference(superposition,[status(thm)],[d128,d105]) ).
cnf(d157,plain,
mult('op$uc',mult('op$uc',i('op$ud'))) = ld('op$ud',mult('op$uc','op$uc')),
inference(demodulation,[status(thm)],[d156,d155]) ).
cnf(d158,plain,
i(mult('op$uc','op$uc')) = rd(i('op$ud'),ld('op$ud',mult('op$uc','op$uc'))),
inference(superposition,[status(thm)],[d157,d151]) ).
cnf(d159,plain,
mult('op$uc','op$uc') = rd(i('op$ud'),ld('op$ud',mult('op$uc','op$uc'))),
inference(demodulation,[status(thm)],[d158,d104]) ).
cnf(d160,plain,
mult(rd('op$ud',mult('op$uc','op$uc')),'op$ud') = ld('op$ud',mult('op$uc','op$uc')),
inference(superposition,[status(thm)],[d159,d147]) ).
cnf(d161,plain,
rd('op$ud',mult('op$uc','op$uc')) = rd(ld('op$ud',mult('op$uc','op$uc')),'op$ud'),
inference(superposition,[status(thm)],[d160,d29]) ).
cnf(d162,plain,
rd('op$ud',mult('op$uc','op$uc')) = mult('op$uc',mult('op$uc','op$ud')),
inference(demodulation,[status(thm)],[d161,d142]) ).
cnf(d163,plain,
'op$ud' = mult(mult('op$uc',mult('op$uc','op$ud')),mult('op$uc','op$uc')),
inference(superposition,[status(thm)],[d162,d6]) ).
cnf(d164,plain,
mult(rd(mult('op$uc','op$ud'),'op$uc'),mult('op$uc',mult('op$uc','op$uc'))) = ld('op$uc','op$ud'),
inference(superposition,[status(thm)],[d163,d140]) ).
cnf(d165,plain,
mult(rd(mult('op$uc','op$ud'),'op$uc'),i('op$uc')) = ld('op$uc','op$ud'),
inference(demodulation,[status(thm)],[d164,d102]) ).
cnf(d166,plain,
i('op$uc') = mult(rd('op$uc',mult('op$uc','op$ud')),ld('op$uc','op$ud')),
inference(superposition,[status(thm)],[d165,d42]) ).
cnf(d167,plain,
rd(i('op$uc'),ld('op$uc','op$ud')) = rd('op$uc',mult('op$uc','op$ud')),
inference(superposition,[status(thm)],[d166,c_3]) ).
cnf(d168,plain,
i('op$ud') = rd('op$uc',mult('op$uc','op$ud')),
inference(demodulation,[status(thm)],[d167,d138]) ).
cnf(d169,plain,
'op$uc' = mult(i('op$ud'),mult('op$uc','op$ud')),
inference(superposition,[status(thm)],[d168,d6]) ).
cnf(d170,plain,
'op$uc' = ld('op$ud',mult('op$uc','op$ud')),
inference(demodulation,[status(thm)],[d169,d5]) ).
cnf(d171,plain,
mult('op$uc','op$ud') = mult('op$ud','op$uc'),
inference(superposition,[status(thm)],[d170,d4]) ).
cnf(d172,plain,
$false,
inference(resolution,[status(thm)],[c_11,d171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP688-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:42:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.76/61.08 % SZS status Unsatisfiable for theBenchmark.p
% 187.76/61.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------