%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP680-1 : 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 : n011.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 07:24:27 AM UTC 2026
% Result : Unsatisfiable 85.22s 24.01s
% Output : CNFRefutation 85.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 5 RR)
% Number of literals : 45 ( 44 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 66 ( 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,
mult('op$uc',X0) = mult(X0,'op$uc') ).
cnf(goals,negated_conjecture,
mult(i('op$uc'),a) != mult(a,i('op$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,
mult('op$uc',X0) = mult(X0,'op$uc'),
inference(clausification,[status(esa)],[c09]) ).
cnf(c_9,plain,
mult(i('op$uc'),a) != mult(a,i('op$uc')),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
mult(i(X0),X1) = ld(X0,X1),
inference(superposition,[status(thm)],[c_0,c_7]) ).
cnf(d1,plain,
ld('op$uc',a) != mult(a,i('op$uc')),
inference(demodulation,[status(thm)],[c_9,d0]) ).
cnf(d2,plain,
ld(i(X0),X1) = mult(X0,X1),
inference(superposition,[status(thm)],[c_7,c_1]) ).
cnf(d3,plain,
X1 = mult(X0,mult(i(X0),X1)),
inference(superposition,[status(thm)],[c_1,d2]) ).
cnf(d4,plain,
X1 = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_2,c_1]) ).
cnf(d6,plain,
X0 = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
mult(X0,mult(unit,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(superposition,[status(thm)],[c_5,c_6]) ).
cnf(d8,plain,
mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(demodulation,[status(thm)],[d7,c_5]) ).
cnf(d9,plain,
rd(mult(X0,mult(X1,mult(X0,X2))),X2) = mult(X0,mult(X1,X0)),
inference(superposition,[status(thm)],[c_6,c_3]) ).
cnf(d10,plain,
rd(mult(X0,mult(X0,X1)),X1) = mult(X0,mult(unit,X0)),
inference(superposition,[status(thm)],[c_5,d9]) ).
cnf(d11,plain,
rd(mult(X0,mult(X0,X1)),X1) = mult(X0,X0),
inference(demodulation,[status(thm)],[d10,c_5]) ).
cnf(d12,plain,
rd(mult('op$uc',mult(X0,'op$uc')),X0) = mult('op$uc','op$uc'),
inference(superposition,[status(thm)],[c_8,d11]) ).
cnf(d13,plain,
mult('op$uc',mult(X0,'op$uc')) = mult(mult('op$uc','op$uc'),X0),
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
mult('op$uc',mult(X0,'op$uc')) = mult('op$uc',mult('op$uc',X0)),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
mult(i(X0),X0) = unit,
inference(superposition,[status(thm)],[c_4,c_7]) ).
cnf(d16,plain,
mult('op$uc',i('op$uc')) = unit,
inference(superposition,[status(thm)],[d15,c_8]) ).
cnf(d17,plain,
rd(mult('op$uc',mult(X0,unit)),i('op$uc')) = mult('op$uc',mult(X0,'op$uc')),
inference(superposition,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
rd(mult('op$uc',X0),i('op$uc')) = mult('op$uc',mult(X0,'op$uc')),
inference(demodulation,[status(thm)],[d17,c_4]) ).
cnf(d19,plain,
rd(X0,i('op$uc')) = mult('op$uc',mult(ld('op$uc',X0),'op$uc')),
inference(superposition,[status(thm)],[d4,d18]) ).
cnf(d20,plain,
rd(X0,i('op$uc')) = mult('op$uc',mult('op$uc',ld('op$uc',X0))),
inference(demodulation,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
rd(X0,i('op$uc')) = mult('op$uc',X0),
inference(demodulation,[status(thm)],[d20,c_0]) ).
cnf(d22,plain,
X0 = mult(mult('op$uc',X0),i('op$uc')),
inference(superposition,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
ld('op$uc',X0) = mult(X0,i('op$uc')),
inference(superposition,[status(thm)],[d4,d22]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP680-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n011.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Fri Sep 25 15:36:13 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.22/24.01 % SZS status Unsatisfiable for theBenchmark.p
% 85.22/24.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------