%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP418-1 : 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 : 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 07:29:13 AM UTC 2026
% Result : Unsatisfiable 1.41s 0.60s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 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 : 14 ( 4 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 : 64 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(multiply(inverse(multiply(VAR_0,inverse(multiply(inverse(VAR_1),inverse(multiply(VAR_2,inverse(multiply(inverse(VAR_2),VAR_2)))))))),multiply(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),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_616,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))),
inference(copy,[status(thm)],[c_616]) ).
cnf(c_9,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_20,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),B)) = D,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_617,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(inverse(multiply(C,inverse(multiply(inverse(C),C)))))),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),inverse(multiply(inverse(B),inverse(multiply(multiply(D,E),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))))))),
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_41,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(inverse(multiply(E,D)),multiply(E,B))),
inference(copy,[status(thm)],[c_617]) ).
cnf(c_115,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),
inference(paramod,[status(thm)],[c_41,c_41]) ).
cnf(c_618,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(A,E))) = multiply(inverse(multiply(F,C)),multiply(F,D)),
inference(paramod,[status(thm)],[c_115,c_1]) ).
cnf(c_116,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_618]) ).
cnf(c_619,plain,
multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)) = multiply(inverse(multiply(E,multiply(B,C))),multiply(E,D)),
inference(paramod,[status(thm)],[c_1,c_116]) ).
cnf(c_163,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)),
inference(copy,[status(thm)],[c_619]) ).
cnf(c_514,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_9,c_163]) ).
cnf(c_620,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_514,c_3]) ).
cnf(c_615,plain,
$false,
inference(resolve,[status(thm)],[c_514,c_620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:55:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1654076 was started by sandbox on n015,
% 0.12/0.36 % Fri Sep 25 14:55:57 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 1.41/0.60
% 1.41/0.60 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.41/0.60
% 1.41/0.60 % SZS status Unsatisfiable for theBenchmark
% 1.41/0.60
% 1.41/0.60 % Proof 1 at 0.17 (+ 0.03) seconds.
% 1.41/0.60 % Length of proof is 12.
% 1.41/0.60 % Level of proof is 9.
% 1.41/0.60 % Maximum clause weight is 62.000.
% 1.41/0.60 % Given clauses 23.
% 1.41/0.60
% 1.41/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------