%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP412-1 : 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 : n011.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 07:29:09 AM UTC 2026
% Result : Unsatisfiable 5.97s 1.32s
% Output : CNFRefutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 17 ( 3 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 : 146 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,inverse(multiply(multiply(multiply(inverse(VAR_1),VAR_1),inverse(multiply(inverse(multiply(VAR_0,inverse(VAR_1))),VAR_2))),VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C,
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,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),multiply(inverse(multiply(B,inverse(C))),D)))),A)) = D,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_6,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_1236,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(C,inverse(D))),B))),D)))),E)))),A)) = E,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)) = C,
inference(paramod,[status(thm)],[c_1,c_1236]) ).
cnf(c_1237,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(inverse(multiply(multiply(multiply(inverse(inverse(C)),inverse(C)),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(inverse(C)))),multiply(inverse(multiply(D,inverse(E))),B)))),inverse(C))),F)))),A)) = F,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_11,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C,
inference(paramod,[status(thm)],[c_9,c_1237]) ).
cnf(c_1238,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),C),B)))) = multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,C)))),D),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_19,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A) = multiply(inverse(multiply(D,inverse(E))),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),C),E)))),
inference(copy,[status(thm)],[c_1238]) ).
cnf(c_20,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_1239,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),multiply(F,B)))),E)))),multiply(D,C)),
inference(paramod,[status(thm)],[c_11,c_20]) ).
cnf(c_29,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_11,c_1239]) ).
cnf(c_1240,plain,
multiply(inverse(multiply(A,B)),C) = multiply(inverse(multiply(D,B)),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),C))),E)))),
inference(paramod,[status(thm)],[c_1,c_29]) ).
cnf(c_33,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,B)),E),
inference(copy,[status(thm)],[c_1240]) ).
cnf(c_41,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)),
inference(paramod,[status(thm)],[c_29,c_29]) ).
cnf(c_42,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))),
inference(paramod,[status(thm)],[c_29,c_29]) ).
cnf(c_1241,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A) = multiply(inverse(multiply(D,inverse(E))),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(F))),C))),F))),
inference(paramod,[status(thm)],[c_4,c_19]) ).
cnf(c_390,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A) = C,
inference(paramod,[status(thm)],[c_1,c_1241]) ).
cnf(c_476,plain,
multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),D)),E)),multiply(inverse(multiply(F,D)),multiply(F,A))) = multiply(inverse(multiply(V6,E)),multiply(V6,C)),
inference(paramod,[status(thm)],[c_390,c_42]) ).
cnf(c_1242,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C))))),multiply(inverse(multiply(F,B)),V6)) = multiply(inverse(multiply(inverse(multiply(D,V7)),E)),multiply(inverse(multiply(F,V7)),V6)),
inference(paramod,[status(thm)],[c_33,c_41]) ).
cnf(c_763,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(D,F)),E)),
inference(paramod,[status(thm)],[c_33,c_1242]) ).
cnf(c_1243,plain,
multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,D)),E)) = multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(F,inverse(D))),multiply(F,A)))),V6)),B)),multiply(inverse(multiply(C,V6)),E)),
inference(paramod,[status(thm)],[c_11,c_763]) ).
cnf(c_919,plain,
multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),D)),E)),multiply(inverse(multiply(F,D)),V6)) = multiply(inverse(multiply(C,E)),multiply(inverse(multiply(F,A)),V6)),
inference(copy,[status(thm)],[c_1243]) ).
cnf(c_1002,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,D)),multiply(C,D))) = multiply(inverse(multiply(E,B)),multiply(E,A)),
inference(paramod,[status(thm)],[c_919,c_476]) ).
cnf(c_1244,plain,
multiply(inverse(A),inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),B))) = multiply(inverse(multiply(D,E)),multiply(D,E)),
inference(paramod,[status(thm)],[c_1002,c_1]) ).
cnf(c_1245,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(D,E)),multiply(D,E)),
inference(paramod,[status(thm)],[c_11,c_1244]) ).
cnf(c_1007,plain,
multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(C),C),
inference(copy,[status(thm)],[c_1245]) ).
cnf(c_1246,plain,
multiply(inverse(A),multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),A))),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_1,c_1007]) ).
cnf(c_1234,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1,c_1246]) ).
cnf(c_1235,plain,
$false,
inference(resolve,[status(thm)],[c_1234,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:52:58 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2286580 was started by sandbox on n011,
% 0.17/0.44 % Fri Sep 25 14:52:58 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 5.97/1.32
% 5.97/1.32 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 5.97/1.32
% 5.97/1.32 % SZS status Unsatisfiable for theBenchmark
% 5.97/1.32
% 5.97/1.32 % Proof 1 at 0.65 (+ 0.18) seconds.
% 5.97/1.32 % Length of proof is 22.
% 5.97/1.32 % Level of proof is 13.
% 5.97/1.32 % Maximum clause weight is 100.000.
% 5.97/1.32 % Given clauses 37.
% 5.97/1.32
% 5.97/1.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------