%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP754-1 : 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 : n026.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 07:24:36 AM UTC 2026
% Result : Unsatisfiable 173.22s 62.44s
% Output : CNFRefutation 173.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 3 RR)
% Number of literals : 59 ( 58 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(X0,ld(X0,X1)) = X1 ).
cnf(f02,axiom,
ld(X0,mult(X0,X1)) = X1 ).
cnf(f03,axiom,
mult(rd(X0,X1),X1) = X0 ).
cnf(f04,axiom,
rd(mult(X0,X1),X1) = X0 ).
cnf(f05,axiom,
mult(X0,mult(X1,X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)) ).
cnf(f06,axiom,
mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,ld(X2,X2))) ).
cnf(goals,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)) ).
cnf(c0,plain,
mult(X0,ld(X0,X1)) = X1,
inference(clausification,[status(esa)],[f01]) ).
cnf(c1,plain,
ld(X0,mult(X0,X1)) = X1,
inference(clausification,[status(esa)],[f02]) ).
cnf(c2,plain,
mult(rd(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[f03]) ).
cnf(c3,plain,
rd(mult(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[f04]) ).
cnf(c4,plain,
mult(X0,mult(X1,X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)),
inference(clausification,[status(esa)],[f05]) ).
cnf(c5,plain,
mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,ld(X2,X2))),
inference(clausification,[status(esa)],[f06]) ).
cnf(c6,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
ld(mult(rd(X0,X0),X1),mult(X0,mult(X1,X2))) = mult(X0,X2),
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
ld(X0,mult(X0,mult(X0,X1))) = mult(X0,X1),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
mult(X0,X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
X1 = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
rd(X1,ld(X0,X1)) = X0,
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d5,plain,
ld(mult(X0,X1),mult(mult(X0,X2),X1)) = mult(X2,ld(X1,X1)),
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d6,plain,
ld(mult(X0,X2),mult(X1,X2)) = mult(ld(X0,X1),ld(X2,X2)),
inference(superposition,[status(thm)],[d3,d5]) ).
cnf(d7,plain,
X0 = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d8,plain,
ld(X0,mult(X2,X1)) = mult(ld(rd(X0,X1),X2),ld(X1,X1)),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
rd(ld(X0,mult(X2,X1)),ld(X1,X1)) = ld(rd(X0,X1),X2),
inference(superposition,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
rd(X1,ld(X1,X1)) = ld(rd(X0,X1),X0),
inference(superposition,[status(thm)],[c1,d9]) ).
cnf(d11,plain,
X0 = ld(rd(X1,X0),X1),
inference(demodulation,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d13,plain,
rd(mult(X0,mult(X1,X2)),mult(X0,X2)) = mult(rd(X0,X0),X1),
inference(superposition,[status(thm)],[c4,c3]) ).
cnf(d14,plain,
rd(mult(X2,X0),mult(X2,X1)) = mult(rd(X2,X2),rd(X0,X1)),
inference(superposition,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
rd(mult(X0,X2),X1) = mult(rd(X0,X0),rd(X2,ld(X0,X1))),
inference(superposition,[status(thm)],[d3,d14]) ).
cnf(d16,plain,
ld(rd(X0,X0),rd(mult(X0,X1),X2)) = rd(X1,ld(X0,X2)),
inference(superposition,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
ld(rd(X0,X0),X0) = rd(X1,ld(X0,X1)),
inference(superposition,[status(thm)],[c3,d16]) ).
cnf(d18,plain,
X0 = rd(X1,ld(X0,X1)),
inference(demodulation,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
X0 = rd(mult(X0,X1),X1),
inference(superposition,[status(thm)],[c1,d18]) ).
cnf(d20,plain,
X1 = ld(X0,mult(X0,X1)),
inference(superposition,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
ld(mult(rd(X2,X2),X0),mult(X2,X1)) = mult(X2,ld(X0,X1)),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d22,plain,
ld(mult(rd(X0,X0),X2),X1) = mult(X0,ld(X2,ld(X0,X1))),
inference(superposition,[status(thm)],[d3,d21]) ).
cnf(d23,plain,
mult(X0,mult(X2,ld(X0,X1))) = mult(mult(rd(X0,X0),X2),X1),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d24,plain,
ld(mult(rd(X0,X0),X2),mult(X0,mult(X1,ld(X0,X2)))) = mult(X1,ld(X2,X2)),
inference(superposition,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
mult(X0,ld(X1,ld(X0,mult(X0,mult(X2,ld(X0,X1)))))) = mult(X2,ld(X1,X1)),
inference(demodulation,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
mult(X0,ld(X2,mult(X1,ld(X0,X2)))) = mult(X1,ld(X2,X2)),
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
ld(X1,mult(X2,ld(X0,X1))) = ld(X0,mult(X2,ld(X1,X1))),
inference(superposition,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
mult(X1,ld(X2,X0)) = mult(X0,ld(X2,mult(X1,ld(X0,X0)))),
inference(superposition,[status(thm)],[d27,d3]) ).
cnf(d29,plain,
mult(ld(rd(X0,X1),X2),ld(X3,X1)) = mult(X1,ld(X3,ld(X0,mult(X2,X1)))),
inference(superposition,[status(thm)],[d8,d28]) ).
cnf(d30,plain,
mult(X0,ld(mult(X0,X1),mult(X2,X1))) = mult(X2,ld(mult(X0,X1),mult(X0,X1))),
inference(superposition,[status(thm)],[c1,d26]) ).
cnf(d31,plain,
mult(X0,mult(ld(X0,X2),ld(X1,X1))) = mult(X2,ld(mult(X0,X1),mult(X0,X1))),
inference(demodulation,[status(thm)],[d30,d6]) ).
cnf(d32,plain,
mult(X0,mult(ld(X0,X2),ld(X1,X1))) = mult(X2,mult(ld(X0,X0),ld(X1,X1))),
inference(demodulation,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
mult(mult(rd(X0,X1),X2),X1) = mult(X0,mult(X2,ld(X1,X1))),
inference(superposition,[status(thm)],[c2,c5]) ).
cnf(d34,plain,
mult(X2,X1) = mult(X0,mult(ld(rd(X0,X1),X2),ld(X1,X1))),
inference(superposition,[status(thm)],[d3,d33]) ).
cnf(d35,plain,
mult(X3,mult(X0,X2)) = mult(mult(X0,X1),mult(ld(mult(rd(X0,X0),rd(X1,X2)),X3),ld(mult(X0,X2),mult(X0,X2)))),
inference(superposition,[status(thm)],[d14,d34]) ).
cnf(d36,plain,
mult(X3,mult(X0,X2)) = mult(mult(X0,X1),mult(mult(X0,ld(rd(X1,X2),ld(X0,X3))),ld(mult(X0,X2),mult(X0,X2)))),
inference(demodulation,[status(thm)],[d35,d22]) ).
cnf(d37,plain,
mult(X2,mult(X0,X1)) = mult(mult(X0,X3),mult(mult(X0,ld(rd(X3,X1),ld(X0,X2))),mult(ld(X0,X0),ld(X1,X1)))),
inference(demodulation,[status(thm)],[d36,d6]) ).
cnf(d38,plain,
mult(X3,mult(X0,X2)) = mult(mult(X0,X1),mult(X0,mult(ld(X0,mult(X0,ld(rd(X1,X2),ld(X0,X3)))),ld(X2,X2)))),
inference(demodulation,[status(thm)],[d37,d32]) ).
cnf(d39,plain,
mult(X3,mult(X0,X2)) = mult(mult(X0,X1),mult(X0,mult(ld(rd(X1,X2),ld(X0,X3)),ld(X2,X2)))),
inference(demodulation,[status(thm)],[d38,c1]) ).
cnf(d40,plain,
mult(X3,mult(X2,X1)) = mult(mult(X2,X0),mult(X2,mult(X1,ld(X1,ld(X0,mult(ld(X2,X3),X1)))))),
inference(demodulation,[status(thm)],[d39,d29]) ).
cnf(d41,plain,
mult(X3,mult(X2,X0)) = mult(mult(X2,X1),mult(X2,ld(X1,mult(ld(X2,X3),X0)))),
inference(demodulation,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
mult(mult(X0,X0),mult(ld(X0,X1),X2)) = mult(X1,mult(X0,X2)),
inference(superposition,[status(thm)],[d41,c5]) ).
cnf(d43,plain,
mult(mult(X0,X0),mult(X1,X2)) = mult(mult(X0,X1),mult(X0,X2)),
inference(superposition,[status(thm)],[c1,d42]) ).
cnf(d44,plain,
$false,
inference(resolution,[status(thm)],[d43,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n026.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 15:46:39 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 173.22/62.44 % SZS status Unsatisfiable for theBenchmark.p
% 173.22/62.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------