%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP518-1 : 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 : 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 07:30:16 AM UTC 2026
% Result : Unsatisfiable 0.02s 15.62s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 39 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(inverse(multiply(VAR_0,VAR_1)),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
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(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_60,plain,
multiply(A,multiply(B,C)) = multiply(multiply(inverse(multiply(inverse(multiply(A,C)),D)),B),D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_8,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_61,plain,
multiply(A,B) = multiply(multiply(inverse(multiply(inverse(B),C)),A),C),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_23,plain,
multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(multiply(inverse(D),A),multiply(C,D)),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_63,plain,
multiply(C,A) = multiply(multiply(inverse(D),A),multiply(C,D)),
inference(paramod,[status(thm)],[c_23,c_62]) ).
cnf(c_26,plain,
multiply(multiply(inverse(A),B),multiply(C,A)) = multiply(C,B),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_45,plain,
multiply(multiply(inverse(A),B),C) = multiply(multiply(inverse(A),C),B),
inference(paramod,[status(thm)],[c_8,c_26]) ).
cnf(c_64,plain,
multiply(multiply(inverse(b2),a2),b2) != a2,
inference(paramod,[status(thm)],[c_45,c_2]) ).
cnf(c_65,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_8,c_64]) ).
cnf(c_59,plain,
$false,
inference(copy,[status(thm)],[c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP518-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.60 % Computer : n016.cluster.edu
% 0.11/15.60 % Model : x86_64 x86_64
% 0.11/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.60 % Memory : 8046.5625MB
% 0.11/15.60 % OS : Linux 6.8.0-71-generic
% 0.02/15.60 % CPULimit : 300
% 0.02/15.60 % WCLimit : 300
% 0.02/15.60 % DateTime : Fri Sep 25 15:03:15 UTC 2026
% 0.02/15.60 % CPUTime :
% 0.02/15.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/15.60 % Process 2691586 was started by sandbox2 on n016,
% 0.02/15.60 % Fri Sep 25 15:03:15 2026
% 0.02/15.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/15.60
% 0.02/15.60 % From the command line: assign(max_seconds, 300).
% 0.02/15.62
% 0.02/15.62 % SZS status Unsatisfiable for theBenchmark
% 0.02/15.62
% 0.02/15.62 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.02/15.62 % Length of proof is 9.
% 0.02/15.62 % Level of proof is 6.
% 0.02/15.62 % Maximum clause weight is 72.000.
% 0.02/15.62 % Given clauses 9.
% 0.02/15.62
% 0.02/15.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------