%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP419-1 : 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 : n026.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 30.36s 4.83s
% Output : CNFRefutation 30.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 18 ( 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 : 205 ( 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_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_12921,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_3,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_12921]) ).
cnf(c_5,plain,
inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_7,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_3,c_1]) ).
cnf(c_12922,plain,
multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(D,V6))),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_13,plain,
multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E)),
inference(paramod,[status(thm)],[c_1,c_12922]) ).
cnf(c_16,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_7,c_1]) ).
cnf(c_17,plain,
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) = inverse(multiply(inverse(multiply(E,inverse(multiply(D,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_25,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(multiply(E,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),inverse(multiply(B,inverse(multiply(multiply(D,F),inverse(multiply(inverse(multiply(D,F)),multiply(D,F))))))))),multiply(inverse(multiply(V6,inverse(multiply(E,inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),multiply(V6,V7)))),
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_12923,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_16,c_1]) ).
cnf(c_35,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_12923]) ).
cnf(c_12924,plain,
inverse(multiply(inverse(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)))))))),multiply(D,E)))) = B,
inference(paramod,[status(thm)],[c_35,c_1]) ).
cnf(c_57,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))) = B,
inference(paramod,[status(thm)],[c_7,c_12924]) ).
cnf(c_12925,plain,
multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(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)))))))),multiply(D,E))) = B,
inference(paramod,[status(thm)],[c_35,c_7]) ).
cnf(c_62,plain,
multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_7,c_12925]) ).
cnf(c_75,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),
inference(paramod,[status(thm)],[c_35,c_35]) ).
cnf(c_12926,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_75,c_1]) ).
cnf(c_76,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_12926]) ).
cnf(c_12927,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_76]) ).
cnf(c_131,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_12927]) ).
cnf(c_213,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_7,c_131]) ).
cnf(c_12928,plain,
multiply(inverse(A),multiply(inverse(multiply(B,inverse(multiply(inverse(inverse(A)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(B,C))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_7,c_213]) ).
cnf(c_293,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_7,c_12928]) ).
cnf(c_368,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_293,c_2]) ).
cnf(c_12929,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(C),C)))),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))),
inference(paramod,[status(thm)],[c_293,c_3]) ).
cnf(c_370,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)) = multiply(C,inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_1,c_12929]) ).
cnf(c_380,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(D),D)))))))),multiply(A,C)) = B,
inference(paramod,[status(thm)],[c_293,c_7]) ).
cnf(c_12930,plain,
inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(multiply(B,C)),multiply(B,C))),
inference(paramod,[status(thm)],[c_293,c_75]) ).
cnf(c_401,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,B))) = inverse(multiply(inverse(C),C)),
inference(copy,[status(thm)],[c_12930]) ).
cnf(c_406,plain,
inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(B,inverse(multiply(inverse(B),B)))))) = B,
inference(paramod,[status(thm)],[c_293,c_57]) ).
cnf(c_411,plain,
multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),inverse(multiply(inverse(inverse(B)),inverse(B)))))) = B,
inference(paramod,[status(thm)],[c_293,c_62]) ).
cnf(c_429,plain,
inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_293,c_401]) ).
cnf(c_550,plain,
inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(B,inverse(multiply(inverse(C),C)))))) = B,
inference(paramod,[status(thm)],[c_293,c_406]) ).
cnf(c_587,plain,
inverse(multiply(inverse(A),A)) = inverse(inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_293,c_550]) ).
cnf(c_633,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))) = inverse(multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_587,c_429]) ).
cnf(c_674,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,inverse(multiply(inverse(C),C)))))) = B,
inference(paramod,[status(thm)],[c_587,c_550]) ).
cnf(c_12931,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))),B) = inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(E),E)),inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(D,F))),
inference(paramod,[status(thm)],[c_550,c_17]) ).
cnf(c_12932,plain,
multiply(inverse(B),B) = inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(E),E)),inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(D,F))),
inference(paramod,[status(thm)],[c_380,c_12931]) ).
cnf(c_2390,plain,
multiply(inverse(A),A) = inverse(multiply(inverse(multiply(B,C)),multiply(B,C))),
inference(paramod,[status(thm)],[c_674,c_12932]) ).
cnf(c_2750,plain,
multiply(inverse(A),A) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_293,c_2390]) ).
cnf(c_2800,plain,
inverse(multiply(multiply(inverse(A),A),inverse(multiply(B,inverse(multiply(inverse(C),C)))))) = B,
inference(paramod,[status(thm)],[c_2390,c_674]) ).
cnf(c_2802,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_2390,c_674]) ).
cnf(c_2922,plain,
multiply(inverse(multiply(inverse(A),A)),a2) != a2,
inference(paramod,[status(thm)],[c_2750,c_368]) ).
cnf(c_3314,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),multiply(inverse(C),C))),a2) != a2,
inference(paramod,[status(thm)],[c_633,c_2922]) ).
cnf(c_4381,plain,
inverse(multiply(multiply(inverse(A),A),inverse(multiply(B,multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_2750,c_2800]) ).
cnf(c_4447,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(B,C)),multiply(B,D))))) = inverse(multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_75,c_2802]) ).
cnf(c_12933,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D))))),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))))),a2) != a2,
inference(paramod,[status(thm)],[c_25,c_3314]) ).
cnf(c_12934,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(multiply(inverse(D),D)),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))))),a2) != a2,
inference(paramod,[status(thm)],[c_4381,c_12933]) ).
cnf(c_12168,plain,
multiply(inverse(inverse(multiply(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(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))))),a2) != a2,
inference(paramod,[status(thm)],[c_674,c_12934]) ).
cnf(c_12935,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),C)))),multiply(B,D))))) = D,
inference(paramod,[status(thm)],[c_370,c_674]) ).
cnf(c_12479,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_4447,c_12935]) ).
cnf(c_12919,plain,
multiply(inverse(inverse(multiply(inverse(A),A))),B) = B,
inference(paramod,[status(thm)],[c_12479,c_411]) ).
cnf(c_12920,plain,
$false,
inference(resolve,[status(thm)],[c_12919,c_12168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:55:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2813220 was started by sandbox2 on n026,
% 0.10/0.38 % Fri Sep 25 14:55:56 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 30.36/4.83
% 30.36/4.83 % SZS status Unsatisfiable for theBenchmark
% 30.36/4.83
% 30.36/4.83 % Proof 1 at 3.68 (+ 0.58) seconds.
% 30.36/4.83 % Length of proof is 40.
% 30.36/4.83 % Level of proof is 19.
% 30.36/4.83 % Maximum clause weight is 98.000.
% 30.36/4.83 % Given clauses 124.
% 30.36/4.83
% 30.36/4.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------