%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP514-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:30:16 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.58s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_3,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_4,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_5,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(C,inverse(multiply(D,multiply(multiply(C,E),inverse(multiply(B,E)))))))))) = D,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_8,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_35,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_10,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_8,c_35]) ).
cnf(c_15,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_18,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_36,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),multiply(multiply(D,C),inverse(D))) = A,
inference(paramod,[status(thm)],[c_15,c_15]) ).
cnf(c_28,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A,
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_37,plain,
multiply(A,B) = multiply(B,multiply(C,inverse(multiply(C,inverse(A))))),
inference(paramod,[status(thm)],[c_28,c_10]) ).
cnf(c_30,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(C,A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_38,plain,
multiply(A,B) = multiply(A,multiply(C,inverse(multiply(C,inverse(B))))),
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_31,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(A,C),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_32,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_31,c_30]) ).
cnf(c_39,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_32,c_2]) ).
cnf(c_40,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(paramod,[status(thm)],[c_32,c_39]) ).
cnf(c_41,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_8,c_40]) ).
cnf(c_34,plain,
$false,
inference(copy,[status(thm)],[c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP514-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n004.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Fri Sep 25 14:58:06 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 3479044 was started by sandbox2 on n004,
% 0.09/0.57 % Fri Sep 25 14:58:06 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.57
% 0.12/0.57 % From the command line: assign(max_seconds, 300).
% 0.12/0.58
% 0.12/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.58
% 0.12/0.58 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.58 % Length of proof is 14.
% 0.12/0.58 % Level of proof is 8.
% 0.12/0.58 % Maximum clause weight is 97.000.
% 0.12/0.58 % Given clauses 11.
% 0.12/0.58
% 0.12/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------