%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP439-1 : 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 : n001.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 07:29:33 AM UTC 2026
% Result : Unsatisfiable 7.93s 1.45s
% Output : CNFRefutation 7.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 18 ( 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 : 136 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : inverse(multiply(VAR_0,multiply(VAR_1,multiply(multiply(inverse(VAR_1),VAR_2),inverse(multiply(VAR_3,multiply(VAR_0,VAR_2))))))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D,
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,
inverse(multiply(A,multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(B,D)))))),multiply(multiply(E,F),inverse(multiply(V6,multiply(A,F))))))) = V6,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),C),inverse(multiply(D,multiply(E,C))))),D)))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_13,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(F,D))))),E)),F)))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_5979,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(C,D),inverse(multiply(E,multiply(F,D))))),E)),F)))) = multiply(V6,multiply(V7,multiply(multiply(inverse(V7),V8),inverse(multiply(C,multiply(V6,V8)))))),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_19,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),multiply(multiply(D,V6),inverse(multiply(V7,multiply(V8,V6))))),V7)),V8)))),
inference(copy,[status(thm)],[c_5979]) ).
cnf(c_536,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(inverse(D),multiply(A,C)))))) = D,
inference(paramod,[status(thm)],[c_19,c_13]) ).
cnf(c_672,plain,
inverse(multiply(A,multiply(B,multiply(C,inverse(multiply(D,multiply(A,multiply(E,multiply(multiply(inverse(E),F),inverse(multiply(inverse(C),multiply(inverse(B),F)))))))))))) = D,
inference(paramod,[status(thm)],[c_536,c_1]) ).
cnf(c_5980,plain,
inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,inverse(multiply(D,multiply(E,multiply(multiply(inverse(E),multiply(multiply(inverse(D),multiply(multiply(inverse(B),F),inverse(multiply(V6,multiply(V7,F))))),V6)),V7)))))))))) = C,
inference(paramod,[status(thm)],[c_19,c_672]) ).
cnf(c_1418,plain,
inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,B)))))) = C,
inference(paramod,[status(thm)],[c_13,c_5980]) ).
cnf(c_5981,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),multiply(multiply(inverse(A),V6),inverse(multiply(V7,multiply(V8,V6))))),V7)),V8)))),
inference(paramod,[status(thm)],[c_1418,c_19]) ).
cnf(c_1544,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))) = A,
inference(paramod,[status(thm)],[c_13,c_5981]) ).
cnf(c_5982,plain,
inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,multiply(multiply(inverse(D),multiply(E,inverse(multiply(F,E)))),F))))))))) = C,
inference(paramod,[status(thm)],[c_1418,c_672]) ).
cnf(c_1578,plain,
inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))) = C,
inference(paramod,[status(thm)],[c_1544,c_5982]) ).
cnf(c_1710,plain,
inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),multiply(D,multiply(inverse(D),B)))) = C,
inference(paramod,[status(thm)],[c_1578,c_1578]) ).
cnf(c_5983,plain,
multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),multiply(A,multiply(D,multiply(multiply(inverse(D),multiply(E,inverse(multiply(F,E)))),F)))))))) = C,
inference(paramod,[status(thm)],[c_1544,c_536]) ).
cnf(c_1781,plain,
multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),A))))) = C,
inference(paramod,[status(thm)],[c_1544,c_5983]) ).
cnf(c_1814,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(multiply(D,E)))),D)),E))) = A,
inference(paramod,[status(thm)],[c_1578,c_1544]) ).
cnf(c_1939,plain,
multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),multiply(D,multiply(inverse(D),C))) = A,
inference(paramod,[status(thm)],[c_1418,c_1781]) ).
cnf(c_5984,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)),multiply(E,multiply(multiply(inverse(E),multiply(F,inverse(multiply(V6,F)))),V6))))) = A,
inference(paramod,[status(thm)],[c_1544,c_1814]) ).
cnf(c_4545,plain,
multiply(A,multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))) = A,
inference(paramod,[status(thm)],[c_1544,c_5984]) ).
cnf(c_4757,plain,
multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B)))) = A,
inference(paramod,[status(thm)],[c_4545,c_1939]) ).
cnf(c_5985,plain,
inverse(multiply(inverse(A),A)) = multiply(multiply(B,multiply(inverse(B),inverse(C))),C),
inference(paramod,[status(thm)],[c_4757,c_1]) ).
cnf(c_5359,plain,
multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(multiply(inverse(C),C)),
inference(copy,[status(thm)],[c_5985]) ).
cnf(c_5986,plain,
inverse(inverse(multiply(inverse(A),A))) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_5359,c_1710]) ).
cnf(c_5905,plain,
multiply(inverse(A),A) = inverse(inverse(multiply(inverse(B),B))),
inference(copy,[status(thm)],[c_5986]) ).
cnf(c_5987,plain,
inverse(inverse(multiply(inverse(A),A))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_5905,c_3]) ).
cnf(c_5988,plain,
multiply(inverse(a1),a1) != inverse(inverse(multiply(inverse(A),A))),
inference(copy,[status(thm)],[c_5987]) ).
cnf(c_5978,plain,
$false,
inference(resolve,[status(thm)],[c_5905,c_5988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:59:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3605134 was started by sandbox on n001,
% 0.09/0.35 % Fri Sep 25 14:59:55 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 7.93/1.45
% 7.93/1.45 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 7.93/1.45
% 7.93/1.45 % SZS status Unsatisfiable for theBenchmark
% 7.93/1.45
% 7.93/1.45 % Proof 1 at 0.91 (+ 0.11) seconds.
% 7.93/1.45 % Length of proof is 21.
% 7.93/1.45 % Level of proof is 13.
% 7.93/1.45 % Maximum clause weight is 41.000.
% 7.93/1.45 % Given clauses 47.
% 7.93/1.45
% 7.93/1.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------