%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:27:17 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 25 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 101 ( 59 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(VAR_1,VAR_2),inverse(multiply(VAR_0,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_2,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_185,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_3,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_4,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(A,multiply(multiply(B,multiply(multiply(C,D),inverse(multiply(A,D)))),inverse(C))) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_186,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_12,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_9,c_186]) ).
cnf(c_17,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_24,plain,
multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(C,B),
inference(paramod,[status(thm)],[c_17,c_4]) ).
cnf(c_39,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(A,a2),multiply(multiply(inverse(b2),b2),inverse(A))) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_73,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(paramod,[status(thm)],[c_12,c_5]) ).
cnf(c_110,plain,
multiply(multiply(A,B),C) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_73,c_24]) ).
cnf(c_114,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),a2),b2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_73,c_39]) ).
cnf(c_130,plain,
multiply(A,multiply(multiply(B,inverse(A)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_110,c_12]) ).
cnf(c_140,plain,
multiply(A,inverse(multiply(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_130,c_9]) ).
cnf(c_187,plain,
multiply(A,B) = multiply(B,multiply(C,inverse(multiply(C,inverse(A))))),
inference(paramod,[status(thm)],[c_17,c_130]) ).
cnf(c_145,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_140,c_187]) ).
cnf(c_152,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_130,c_73]) ).
cnf(c_188,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),a2),b2) != a2
| multiply(b1,inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_145,c_114]) ).
cnf(c_189,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),a2),b2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_145,c_188]) ).
cnf(c_190,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a2,inverse(b2)),b2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_145,c_189]) ).
cnf(c_191,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b2,multiply(a2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_145,c_190]) ).
cnf(c_192,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_12,c_191]) ).
cnf(c_193,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_145,c_192]) ).
cnf(c_194,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_145,c_193]) ).
cnf(c_195,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_168,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[status(thm)],[c_152,c_196]) ).
cnf(c_197,plain,
multiply(A,multiply(B,C)) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_145,c_110]) ).
cnf(c_182,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_198,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_145,c_110]) ).
cnf(c_199,plain,
multiply(B,multiply(A,C)) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_182,c_198]) ).
cnf(c_200,plain,
multiply(B,multiply(A,C)) = multiply(A,multiply(C,B)),
inference(paramod,[status(thm)],[c_182,c_199]) ).
cnf(c_183,plain,
multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,plain,
multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3)),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_184,plain,
$false,
inference(resolve,[status(thm)],[c_183,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 14:24:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1563360 was started by sandbox on n015,
% 0.09/0.36 % Fri Sep 25 14:24:57 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.39 % Length of proof is 21.
% 0.09/0.39 % Level of proof is 12.
% 0.09/0.39 % Maximum clause weight is 40.000.
% 0.09/0.39 % Given clauses 16.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------