%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:23:42 AM UTC 2026
% Result : Unsatisfiable 81.27s 20.46s
% Output : CNFRefutation 81.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 39 ( 28 unt; 0 nHn; 13 RR)
% Number of literals : 50 ( 49 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutator,axiom,
multiply(X0,X1) = multiply(X1,multiply(X0,commutator(X0,X1))) ).
cnf(nilpotency,axiom,
multiply(commutator(X0,X1),X2) = multiply(X2,commutator(X0,X1)) ).
cnf(prove_commutator_is_associative,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(left_cancellation,axiom,
( X1 = X2
| multiply(X0,X1) != multiply(X0,X2) ) ).
cnf(c0,plain,
multiply(X0,multiply(X1,commutator(X1,X0))) = multiply(X1,X0),
inference(clausification,[status(esa)],[commutator]) ).
cnf(c1,plain,
multiply(X0,commutator(X1,X2)) = multiply(commutator(X1,X2),X0),
inference(clausification,[status(esa)],[nilpotency]) ).
cnf(c2,plain,
commutator(a,commutator(b,c)) != commutator(commutator(a,b),c),
inference(clausification,[status(esa)],[prove_commutator_is_associative]) ).
cnf(c3,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_multiply]) ).
cnf(c5,plain,
( X1 = X2
| multiply(X0,X1) != multiply(X0,X2) ),
inference(clausification,[status(esa)],[left_cancellation]) ).
cnf(d0,plain,
( multiply(X1,commutator(X1,X0)) = X2
| multiply(X1,X0) != multiply(X0,X2) ),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d1,plain,
multiply(X0,commutator(X0,X0)) = X0,
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( X1 = commutator(X0,X0)
| multiply(X0,X1) != X0 ),
inference(superposition,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( multiply(X0,commutator(X0,commutator(X1,X2))) = X3
| multiply(commutator(X1,X2),X0) != multiply(commutator(X1,X2),X3) ),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d4,plain,
multiply(X0,commutator(X0,commutator(X1,X2))) = X0,
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( commutator(X0,commutator(X1,X2)) = commutator(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
multiply(X0,multiply(commutator(X0,X0),X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d7,plain,
multiply(X0,commutator(commutator(X0,X0),X0)) = multiply(commutator(X0,X0),X0),
inference(superposition,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
multiply(X0,commutator(commutator(X0,X0),X0)) = multiply(X0,commutator(X0,X0)),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
multiply(X0,commutator(commutator(X0,X0),X0)) = X0,
inference(demodulation,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( commutator(commutator(X0,X0),X0) = commutator(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
commutator(commutator(X0,X0),X0) = commutator(X0,X0),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
multiply(X1,commutator(X1,commutator(X0,X0))) = X1,
inference(superposition,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
commutator(X0,commutator(X1,X2)) = commutator(X0,X0),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
commutator(a,a) != commutator(commutator(a,b),c),
inference(demodulation,[status(thm)],[c2,d14]) ).
cnf(d16,plain,
( multiply(commutator(X0,X0),X1) = X2
| multiply(X0,X1) != multiply(X0,X2) ),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d17,plain,
multiply(commutator(X0,X0),X1) = X1,
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
multiply(X1,commutator(X0,X0)) = X1,
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
commutator(X0,X0) = commutator(X1,X1),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
commutator(X0,commutator(X2,X3)) = commutator(X1,X1),
inference(superposition,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
( commutator(X0,commutator(X1,X2)) = X3
| X0 != multiply(X0,X3) ),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d22,plain,
( multiply(commutator(X0,X1),commutator(commutator(X0,X1),X2)) = X3
| multiply(X2,commutator(X0,X1)) != multiply(X2,X3) ),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d23,plain,
multiply(commutator(X0,X1),commutator(commutator(X0,X1),X2)) = commutator(X0,X1),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
( commutator(commutator(X0,X1),commutator(X3,X4)) = commutator(commutator(X0,X1),X2)
| commutator(X0,X1) != commutator(X0,X1) ),
inference(superposition,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
commutator(commutator(X0,X1),commutator(X2,X3)) = commutator(commutator(X0,X1),X4),
inference(resolution,[status(thm)],[d13,d24]) ).
cnf(d26,plain,
commutator(commutator(X0,X1),X4) = commutator(X5,X5),
inference(superposition,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
commutator(a,a) != commutator(X0,X0),
inference(superposition,[status(thm)],[d26,d15]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d19,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:52:15 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.27/20.46 % SZS status Unsatisfiable for theBenchmark.p
% 81.27/20.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------