%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 07:28:47 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.68s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 25 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 17 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 72 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_multiply) ).
cnf(c_1,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity_of_multiply]) ).
fof(right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_2,VAR_1) ),
file('theBenchmark.p',right_cancellation) ).
cnf(c_2,plain,
( A = C
| multiply(A,B) != multiply(C,B) ),
inference(clausify,[status(thm)],[right_cancellation]) ).
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_0,VAR_2) ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_3,plain,
( B = C
| multiply(A,B) != multiply(A,C) ),
inference(clausify,[status(thm)],[left_cancellation]) ).
fof(commutator,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,multiply(VAR_0,commutator(VAR_0,VAR_1))),
file('theBenchmark.p',commutator) ).
cnf(c_4,plain,
multiply(A,B) = multiply(B,multiply(A,commutator(A,B))),
inference(clausify,[status(thm)],[commutator]) ).
cnf(c_5,plain,
multiply(A,multiply(B,commutator(B,A))) = multiply(B,A),
inference(copy,[status(thm)],[c_4]) ).
fof(nilpotency,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(commutator(VAR_0,VAR_1),VAR_2) = multiply(VAR_2,commutator(VAR_0,VAR_1)),
file('theBenchmark.p',nilpotency) ).
cnf(c_6,plain,
multiply(commutator(A,B),C) = multiply(C,commutator(A,B)),
inference(clausify,[status(thm)],[nilpotency]) ).
fof(prove_commutator_is_associative,axiom,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('theBenchmark.p',prove_commutator_is_associative) ).
cnf(c_7,plain,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
inference(clausify,[status(thm)],[prove_commutator_is_associative]) ).
cnf(c_8,plain,
( multiply(A,B) = D
| multiply(A,multiply(B,C)) != multiply(D,C) ),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
multiply(A,commutator(A,A)) = A,
inference(resolve,[status(thm)],[c_3,c_5]) ).
cnf(c_157,plain,
( multiply(A,commutator(A,B)) = C
| multiply(A,B) != multiply(B,C) ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_13,plain,
( multiply(C,commutator(C,A)) = B
| multiply(A,B) != multiply(C,A) ),
inference(copy,[status(thm)],[c_157]) ).
cnf(c_158,plain,
multiply(multiply(commutator(A,B),C),D) = multiply(multiply(C,D),commutator(A,B)),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_159,plain,
multiply(commutator(A,B),multiply(C,D)) = multiply(multiply(C,D),commutator(A,B)),
inference(paramod,[status(thm)],[c_1,c_158]) ).
cnf(c_16,plain,
multiply(commutator(A,B),multiply(C,D)) = multiply(C,multiply(D,commutator(A,B))),
inference(paramod,[status(thm)],[c_1,c_159]) ).
cnf(c_21,plain,
multiply(A,commutator(commutator(a,b),c)) != multiply(A,commutator(a,commutator(b,c))),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_160,plain,
( commutator(A,A) = B
| A != multiply(A,B) ),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_44,plain,
( commutator(A,A) = B
| multiply(A,B) != A ),
inference(copy,[status(thm)],[c_160]) ).
cnf(c_60,plain,
multiply(A,commutator(A,commutator(B,C))) = A,
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_161,plain,
commutator(A,A) = commutator(A,commutator(B,C)),
inference(resolve,[status(thm)],[c_44,c_60]) ).
cnf(c_95,plain,
commutator(A,commutator(B,C)) = commutator(A,A),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_112,plain,
multiply(A,commutator(commutator(a,b),c)) != multiply(A,commutator(a,a)),
inference(paramod,[status(thm)],[c_95,c_21]) ).
cnf(c_126,plain,
multiply(commutator(A,A),multiply(B,A)) = multiply(B,A),
inference(paramod,[status(thm)],[c_10,c_16]) ).
cnf(c_162,plain,
multiply(c,multiply(commutator(a,b),commutator(a,a))) != multiply(commutator(a,b),c),
inference(resolve,[status(thm)],[c_13,c_112]) ).
cnf(c_163,plain,
multiply(c,multiply(commutator(a,a),commutator(a,b))) != multiply(commutator(a,b),c),
inference(paramod,[status(thm)],[c_6,c_162]) ).
cnf(c_143,plain,
multiply(c,multiply(commutator(a,a),commutator(a,b))) != multiply(c,commutator(a,b)),
inference(paramod,[status(thm)],[c_6,c_163]) ).
cnf(c_145,plain,
multiply(commutator(A,A),B) = B,
inference(resolve,[status(thm)],[c_8,c_126]) ).
cnf(c_164,plain,
multiply(c,commutator(a,b)) != multiply(c,commutator(a,b)),
inference(paramod,[status(thm)],[c_145,c_143]) ).
cnf(c_156,plain,
$false,
inference(copy,[status(thm)],[c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.57 % Computer : n001.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Fri Sep 25 14:57:43 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.57 % Process 3601840 was started by sandbox on n001,
% 0.08/0.57 % Fri Sep 25 14:57:43 2026
% 0.08/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.58
% 0.08/0.58 % From the command line: assign(max_seconds, 300).
% 0.13/0.68
% 0.13/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.68
% 0.13/0.68 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.68 % Length of proof is 20.
% 0.13/0.68 % Level of proof is 7.
% 0.13/0.68 % Maximum clause weight is 27.000.
% 0.13/0.68 % Given clauses 38.
% 0.13/0.68
% 0.13/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------