%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP513-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:30:15 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 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 : 57 ( 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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_3,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(copy,[status(thm)],[c_2]) ).
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_6,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_4,c_1]) ).
cnf(c_9,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_68,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_9,c_68]) ).
cnf(c_16,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(paramod,[status(thm)],[c_11,c_4]) ).
cnf(c_19,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_69,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),multiply(multiply(D,C),inverse(D))) = A,
inference(paramod,[status(thm)],[c_16,c_16]) ).
cnf(c_29,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A,
inference(paramod,[status(thm)],[c_19,c_69]) ).
cnf(c_70,plain,
multiply(A,B) = multiply(B,multiply(C,inverse(multiply(C,inverse(A))))),
inference(paramod,[status(thm)],[c_29,c_11]) ).
cnf(c_31,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(C,A),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
multiply(A,B) = multiply(A,multiply(C,inverse(multiply(C,inverse(B))))),
inference(paramod,[status(thm)],[c_29,c_19]) ).
cnf(c_32,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(A,C),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_33,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_32,c_31]) ).
cnf(c_72,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_35,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(paramod,[status(thm)],[c_33,c_72]) ).
cnf(c_48,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(paramod,[status(thm)],[c_33,c_9]) ).
cnf(c_66,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_48,c_9]) ).
cnf(c_67,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP513-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n016.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 15:02:30 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.18/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.41 % Process 2689880 was started by sandbox on n016,
% 0.18/0.41 % Fri Sep 25 15:02:30 2026
% 0.18/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 0.18/0.44
% 0.18/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.44
% 0.18/0.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.44 % Length of proof is 18.
% 0.18/0.44 % Level of proof is 10.
% 0.18/0.44 % Maximum clause weight is 97.000.
% 0.18/0.44 % Given clauses 17.
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------