%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP684-1 : 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 : 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 07:24:28 AM UTC 2026
% Result : Unsatisfiable 54.58s 8.42s
% Output : CNFRefutation 54.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 7 RR)
% Number of literals : 95 ( 94 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 200 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
ld(X0,mult(X0,X0)) = X0 ).
cnf(c02,axiom,
rd(mult(X0,X0),X0) = X0 ).
cnf(c03,axiom,
mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)) ).
cnf(c04,axiom,
mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1) ).
cnf(c05,axiom,
ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3) ).
cnf(c06,axiom,
rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)) ).
cnf(c07,axiom,
ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1) ).
cnf(goals,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c) ).
cnf(c_0,plain,
ld(X0,mult(X0,X0)) = X0,
inference(clausification,[status(esa)],[c01]) ).
cnf(c_1,plain,
rd(mult(X0,X0),X0) = X0,
inference(clausification,[status(esa)],[c02]) ).
cnf(c_2,plain,
mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(clausification,[status(esa)],[c03]) ).
cnf(c_3,plain,
mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(clausification,[status(esa)],[c04]) ).
cnf(c_4,plain,
ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(clausification,[status(esa)],[c05]) ).
cnf(c_5,plain,
rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(clausification,[status(esa)],[c06]) ).
cnf(c_6,plain,
ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(clausification,[status(esa)],[c07]) ).
cnf(c_7,plain,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[c_6,c_2]) ).
cnf(d1,plain,
mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[d0,c_3]) ).
cnf(d2,plain,
mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_1,c_3]) ).
cnf(d3,plain,
mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[d2,c_3]) ).
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)],[c_0,c_2]) ).
cnf(d6,plain,
mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[d5,c_2]) ).
cnf(d7,plain,
rd(X0,X0) = ld(X0,X0),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(demodulation,[status(thm)],[c_4,c_2]) ).
cnf(d9,plain,
mult(ld(X0,X2),ld(ld(X0,X2),mult(X1,X3))) = mult(mult(X0,ld(X0,X1)),X3),
inference(demodulation,[status(thm)],[d8,c_2]) ).
cnf(d10,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
mult(X0,ld(X0,rd(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d4,d7]) ).
cnf(d12,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(demodulation,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
mult(rd(X0,X0),ld(ld(X0,X0),X0)) = X0,
inference(superposition,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X0)) = X0,
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
mult(rd(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(superposition,[status(thm)],[d2,c_2]) ).
cnf(d17,plain,
X0 = ld(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
mult(X1,ld(X1,rd(X0,X0))) = mult(rd(rd(X1,X1),X0),X0),
inference(demodulation,[status(thm)],[d1,d7]) ).
cnf(d19,plain,
mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(demodulation,[status(thm)],[c_5,c_3]) ).
cnf(d20,plain,
mult(rd(mult(X2,X0),rd(X3,X1)),rd(X3,X1)) = mult(X2,mult(rd(X0,X1),X1)),
inference(demodulation,[status(thm)],[d19,c_3]) ).
cnf(d21,plain,
mult(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d5,d7]) ).
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)],[d21,d20]) ).
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,d18]) ).
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)],[d21,d9]) ).
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)],[d13,d25]) ).
cnf(d27,plain,
mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X0)) = X0,
inference(superposition,[status(thm)],[c_2,d13]) ).
cnf(d28,plain,
mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X0)) = X0,
inference(demodulation,[status(thm)],[d27,c_2]) ).
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)],[d13,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)],[c_2,d9]) ).
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(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(rd(X0,X0),X0),rd(X2,X2)),
inference(superposition,[status(thm)],[d17,d33]) ).
cnf(d35,plain,
mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,rd(X2,X2)),
inference(demodulation,[status(thm)],[d34,d17]) ).
cnf(d36,plain,
mult(X0,rd(X2,X2)) = mult(X0,mult(X0,ld(X0,rd(X2,X2)))),
inference(demodulation,[status(thm)],[d23,d35]) ).
cnf(d37,plain,
mult(rd(mult(X2,X3),mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)) = mult(X2,mult(rd(X3,X1),X1)),
inference(superposition,[status(thm)],[c_3,d20]) ).
cnf(d38,plain,
mult(rd(mult(X2,X3),mult(rd(X0,X1),X1)),mult(rd(X0,X1),X1)) = mult(X2,mult(rd(X3,X1),X1)),
inference(demodulation,[status(thm)],[d37,c_3]) ).
cnf(d39,plain,
X0 = mult(mult(X0,ld(X0,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d40,plain,
X0 = mult(rd(X0,X0),X0),
inference(demodulation,[status(thm)],[d39,d11]) ).
cnf(d41,plain,
mult(rd(mult(X1,X2),X0),mult(rd(X0,X0),X0)) = mult(X1,mult(rd(X2,X0),X0)),
inference(superposition,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
mult(rd(mult(X1,X2),X0),X0) = mult(X1,mult(rd(X2,X0),X0)),
inference(demodulation,[status(thm)],[d41,d2]) ).
cnf(d43,plain,
X0 = mult(mult(X0,ld(X0,X0)),rd(X0,X0)),
inference(superposition,[status(thm)],[d13,d24]) ).
cnf(d44,plain,
X0 = mult(mult(X0,rd(X0,X0)),rd(X0,X0)),
inference(demodulation,[status(thm)],[d43,d7]) ).
cnf(d45,plain,
X0 = mult(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[d44,d21]) ).
cnf(d46,plain,
mult(rd(X0,X1),X1) = mult(X0,mult(rd(rd(X0,X0),X1),X1)),
inference(superposition,[status(thm)],[d45,d42]) ).
cnf(d47,plain,
mult(rd(X0,X1),X1) = mult(X0,mult(X0,ld(X0,rd(X1,X1)))),
inference(demodulation,[status(thm)],[d46,d18]) ).
cnf(d48,plain,
mult(rd(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(demodulation,[status(thm)],[d47,d36]) ).
cnf(d49,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(demodulation,[status(thm)],[c_7,c_3]) ).
cnf(d50,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference(demodulation,[status(thm)],[d49,c_3]) ).
cnf(d51,plain,
mult(a,rd(mult(b,c),mult(b,c))) != mult(rd(a,c),c),
inference(demodulation,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
mult(a,rd(mult(b,c),mult(b,c))) != mult(a,rd(c,c)),
inference(demodulation,[status(thm)],[d51,d48]) ).
cnf(d53,plain,
mult(X0,rd(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c_3,d48]) ).
cnf(d54,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(d55,plain,
rd(X0,X1) = mult(rd(rd(X0,X1),rd(X2,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[d54,d40]) ).
cnf(d56,plain,
rd(X0,X1) = mult(rd(X0,X1),rd(X1,X1)),
inference(demodulation,[status(thm)],[d55,d35]) ).
cnf(d57,plain,
mult(rd(X0,X1),rd(X1,X1)) = rd(mult(X0,rd(X1,X1)),X1),
inference(superposition,[status(thm)],[d48,d53]) ).
cnf(d58,plain,
rd(X0,X1) = rd(mult(X0,rd(X1,X1)),X1),
inference(demodulation,[status(thm)],[d57,d56]) ).
cnf(d59,plain,
mult(X0,rd(rd(X1,X2),rd(X1,X2))) = mult(X0,rd(X2,X2)),
inference(demodulation,[status(thm)],[d35,d48]) ).
cnf(d60,plain,
rd(X0,rd(X1,X2)) = rd(mult(X0,rd(X2,X2)),rd(X1,X2)),
inference(superposition,[status(thm)],[d59,d58]) ).
cnf(d61,plain,
mult(X0,rd(X2,X2)) = mult(rd(X0,rd(X3,X2)),rd(X3,X2)),
inference(demodulation,[status(thm)],[d54,d35]) ).
cnf(d62,plain,
mult(X0,rd(X2,X2)) = mult(X0,rd(rd(X1,X2),rd(X1,X2))),
inference(demodulation,[status(thm)],[d61,d48]) ).
cnf(d63,plain,
mult(X2,rd(X1,X1)) = mult(X2,rd(mult(X0,rd(X1,X1)),rd(mult(X0,X1),X1))),
inference(superposition,[status(thm)],[d53,d62]) ).
cnf(d64,plain,
mult(X2,rd(X1,X1)) = mult(X2,rd(X0,rd(mult(X0,X1),X1))),
inference(demodulation,[status(thm)],[d63,d60]) ).
cnf(d65,plain,
mult(X2,rd(X1,X1)) = mult(X2,rd(X0,mult(X0,rd(X1,X1)))),
inference(demodulation,[status(thm)],[d64,d53]) ).
cnf(d66,plain,
mult(mult(rd(X0,X1),X1),X1) = mult(X0,mult(rd(X1,X1),X1)),
inference(superposition,[status(thm)],[c_3,d42]) ).
cnf(d67,plain,
mult(mult(rd(X1,X0),X0),X0) = mult(X1,X0),
inference(demodulation,[status(thm)],[d66,d2]) ).
cnf(d68,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(X0,rd(X0,X0)),
inference(superposition,[status(thm)],[d11,d23]) ).
cnf(d69,plain,
mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d68,d21]) ).
cnf(d70,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),rd(mult(X0,X1),X1)) = X1,
inference(superposition,[status(thm)],[c_3,d69]) ).
cnf(d71,plain,
mult(rd(X1,mult(rd(X0,X1),X1)),mult(rd(X0,X1),X1)) = X1,
inference(demodulation,[status(thm)],[d70,c_3]) ).
cnf(d72,plain,
mult(rd(X1,mult(mult(rd(X0,X1),X1),X1)),mult(rd(mult(X0,X1),X1),X1)) = X1,
inference(superposition,[status(thm)],[c_3,d71]) ).
cnf(d73,plain,
mult(rd(X1,mult(mult(rd(X0,X1),X1),X1)),mult(mult(rd(X0,X1),X1),X1)) = X1,
inference(demodulation,[status(thm)],[d72,c_3]) ).
cnf(d74,plain,
mult(rd(X1,mult(X0,X1)),mult(mult(rd(X0,X1),X1),X1)) = X1,
inference(demodulation,[status(thm)],[d73,d67]) ).
cnf(d75,plain,
mult(rd(X1,mult(X0,X1)),mult(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d74,d67]) ).
cnf(d76,plain,
mult(X0,rd(mult(X1,X0),mult(X1,X0))) = X0,
inference(demodulation,[status(thm)],[d75,d48]) ).
cnf(d77,plain,
mult(X2,rd(mult(X1,X0),mult(X1,X0))) = mult(X2,rd(X0,X0)),
inference(superposition,[status(thm)],[d76,d65]) ).
cnf(d78,plain,
$false,
inference(resolution,[status(thm)],[d77,d52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : 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 : n007.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 15:34:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.58/8.42 % SZS status Unsatisfiable for theBenchmark.p
% 54.58/8.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------