%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP563-1 : 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 : n018.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 07:30:22 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.43s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,inverse(VAR_1)),VAR_2),divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,inverse(VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_174,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_175,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_174]) ).
cnf(c_176,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_2,c_175]) ).
cnf(c_177,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_2,c_176]) ).
cnf(c_4,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_5,plain,
divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(D)),divide(A,C)),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_178,plain,
divide(divide(A,divide(divide(divide(B,inverse(inverse(C))),D),divide(B,D))),A) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_16,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_1,c_178]) ).
cnf(c_19,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_28,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_179,plain,
divide(divide(divide(divide(A,A),inverse(B)),inverse(C)),C) = B,
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_30,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_28,c_179]) ).
cnf(c_180,plain,
divide(A,divide(A,divide(divide(B,B),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_28,c_180]) ).
cnf(c_181,plain,
divide(A,divide(A,inverse(inverse(B)))) = B,
inference(paramod,[status(thm)],[c_30,c_16]) ).
cnf(c_66,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_31,c_181]) ).
cnf(c_86,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_66,c_16]) ).
cnf(c_87,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_66,c_30]) ).
cnf(c_116,plain,
divide(A,divide(divide(B,inverse(A)),C)) = inverse(divide(B,C)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_182,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_31,c_86]) ).
cnf(c_125,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_182]) ).
cnf(c_126,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_86,c_30]) ).
cnf(c_138,plain,
divide(A,divide(divide(B,inverse(A)),C)) = divide(C,B),
inference(paramod,[status(thm)],[c_125,c_116]) ).
cnf(c_183,plain,
divide(a3,divide(inverse(c3),b3)) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_125,c_4]) ).
cnf(c_184,plain,
divide(a3,divide(inverse(b3),c3)) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_126,c_183]) ).
cnf(c_149,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3)),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_152,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_16,c_87]) ).
cnf(c_185,plain,
divide(divide(b3,inverse(a3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_152,c_149]) ).
cnf(c_186,plain,
divide(c3,inverse(divide(b3,inverse(a3)))) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_152,c_185]) ).
cnf(c_156,plain,
divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)),
inference(paramod,[status(thm)],[c_125,c_186]) ).
cnf(c_172,plain,
divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(divide(divide(A,b3),A),c3)),
inference(paramod,[status(thm)],[c_86,c_156]) ).
cnf(c_187,plain,
divide(C,B) = divide(A,divide(divide(B,inverse(A)),C)),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_173,plain,
$false,
inference(resolve,[status(thm)],[c_172,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP563-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 15:02:05 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 2249044 was started by sandbox2 on n018,
% 0.13/0.39 % Fri Sep 25 15:02:05 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 0.17/0.43
% 0.17/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.43
% 0.17/0.43 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.43 % Length of proof is 23.
% 0.17/0.43 % Level of proof is 12.
% 0.17/0.43 % Maximum clause weight is 17.000.
% 0.17/0.43 % Given clauses 20.
% 0.17/0.43
% 0.17/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------