%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP474-1 : 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 : n019.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 07:29:50 AM UTC 2026
% Result : Unsatisfiable 2.66s 0.85s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 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 : 193 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(divide(inverse(divide(VAR_0,VAR_1)),divide(divide(VAR_2,VAR_3),VAR_0)),divide(VAR_3,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,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_1546,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1547,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_1546]) ).
cnf(c_1548,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_2,c_1547]) ).
cnf(c_1549,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_2,c_1548]) ).
cnf(c_4,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(copy,[status(thm)],[c_1549]) ).
cnf(c_5,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(F,E),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
divide(divide(inverse(divide(divide(A,B),C)),D),divide(divide(divide(B,A),E),inverse(divide(E,D)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(E),divide(divide(F,V6),divide(inverse(divide(V7,E)),divide(divide(B,A),V7)))))),divide(D,C)) = divide(V6,F),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_1550,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(divide(V6,V7),divide(inverse(V8),divide(divide(V7,V6),divide(inverse(divide(V9,V8)),divide(divide(F,E),V9))))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_1551,plain,
divide(F,E) = divide(divide(V6,V7),divide(inverse(V8),divide(divide(V7,V6),divide(inverse(divide(V9,V8)),divide(divide(F,E),V9))))),
inference(paramod,[status(thm)],[c_5,c_1550]) ).
cnf(c_20,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(divide(E,F),D))))) = divide(E,F),
inference(copy,[status(thm)],[c_1551]) ).
cnf(c_1552,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = divide(divide(inverse(divide(F,E)),divide(divide(V6,V7),F)),divide(V7,V6)),
inference(paramod,[status(thm)],[c_1,c_20]) ).
cnf(c_107,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = E,
inference(paramod,[status(thm)],[c_1,c_1552]) ).
cnf(c_232,plain,
divide(divide(inverse(divide(A,B)),divide(B,A)),divide(C,D)) = divide(D,C),
inference(paramod,[status(thm)],[c_107,c_9]) ).
cnf(c_241,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(divide(E,F)),divide(F,E)))),divide(D,C)) = divide(B,A),
inference(paramod,[status(thm)],[c_232,c_1]) ).
cnf(c_254,plain,
divide(a3,inverse(divide(divide(inverse(divide(A,B)),divide(B,A)),divide(inverse(c3),b3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_232,c_4]) ).
cnf(c_1553,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(divide(F,E),divide(inverse(divide(V6,V7)),divide(V7,V6))),
inference(paramod,[status(thm)],[c_232,c_5]) ).
cnf(c_1554,plain,
divide(F,E) = divide(divide(F,E),divide(inverse(divide(V6,V7)),divide(V7,V6))),
inference(paramod,[status(thm)],[c_5,c_1553]) ).
cnf(c_260,plain,
divide(divide(A,B),divide(inverse(divide(C,D)),divide(D,C))) = divide(A,B),
inference(copy,[status(thm)],[c_1554]) ).
cnf(c_357,plain,
divide(divide(inverse(divide(A,B)),divide(C,D)),divide(D,C)) = divide(B,A),
inference(paramod,[status(thm)],[c_260,c_241]) ).
cnf(c_1555,plain,
divide(divide(inverse(divide(divide(inverse(divide(A,B)),divide(B,A)),C)),divide(D,E)),divide(E,D)) = C,
inference(paramod,[status(thm)],[c_260,c_1]) ).
cnf(c_359,plain,
divide(A,divide(inverse(divide(B,C)),divide(C,B))) = A,
inference(paramod,[status(thm)],[c_357,c_1555]) ).
cnf(c_387,plain,
divide(divide(A,B),divide(inverse(C),divide(B,A))) = C,
inference(paramod,[status(thm)],[c_260,c_107]) ).
cnf(c_1556,plain,
divide(inverse(divide(divide(A,B),C)),divide(divide(divide(B,A),D),inverse(divide(D,divide(inverse(divide(E,F)),divide(F,E)))))) = C,
inference(paramod,[status(thm)],[c_359,c_7]) ).
cnf(c_403,plain,
divide(inverse(divide(divide(A,B),C)),divide(divide(divide(B,A),D),inverse(D))) = C,
inference(paramod,[status(thm)],[c_359,c_1556]) ).
cnf(c_621,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(D,E))),divide(C,B)) = divide(inverse(A),divide(E,D)),
inference(paramod,[status(thm)],[c_387,c_1]) ).
cnf(c_622,plain,
divide(divide(inverse(divide(A,B)),divide(C,A)),divide(divide(inverse(C),divide(D,E)),divide(E,D))) = B,
inference(paramod,[status(thm)],[c_387,c_1]) ).
cnf(c_634,plain,
divide(divide(inverse(divide(A,B)),C),divide(divide(divide(divide(inverse(A),divide(D,E)),divide(E,D)),F),inverse(divide(F,C)))) = B,
inference(paramod,[status(thm)],[c_387,c_7]) ).
cnf(c_635,plain,
divide(divide(inverse(A),B),divide(divide(divide(C,D),E),inverse(divide(E,B)))) = divide(inverse(A),divide(C,D)),
inference(paramod,[status(thm)],[c_387,c_7]) ).
cnf(c_1557,plain,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(E),divide(F,E)))),divide(D,C)) = divide(divide(B,A),F),
inference(paramod,[status(thm)],[c_387,c_9]) ).
cnf(c_662,plain,
divide(inverse(divide(A,B)),divide(divide(C,D),inverse(D))) = divide(divide(B,A),C),
inference(paramod,[status(thm)],[c_621,c_1557]) ).
cnf(c_681,plain,
divide(A,divide(inverse(B),divide(divide(inverse(B),divide(C,D)),divide(D,C)))) = A,
inference(paramod,[status(thm)],[c_387,c_359]) ).
cnf(c_695,plain,
divide(a3,inverse(divide(divide(inverse(A),divide(divide(inverse(A),divide(B,C)),divide(C,B))),divide(inverse(c3),b3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_387,c_254]) ).
cnf(c_809,plain,
divide(inverse(divide(A,B)),divide(divide(inverse(A),divide(C,D)),divide(D,C))) = B,
inference(paramod,[status(thm)],[c_635,c_634]) ).
cnf(c_820,plain,
divide(divide(A,divide(B,C)),divide(C,B)) = A,
inference(paramod,[status(thm)],[c_662,c_403]) ).
cnf(c_831,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(paramod,[status(thm)],[c_820,c_809]) ).
cnf(c_841,plain,
divide(a3,inverse(divide(divide(inverse(A),inverse(A)),divide(inverse(c3),b3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_820,c_695]) ).
cnf(c_846,plain,
divide(A,divide(inverse(B),inverse(B))) = A,
inference(paramod,[status(thm)],[c_820,c_681]) ).
cnf(c_867,plain,
divide(divide(inverse(divide(A,B)),divide(C,A)),inverse(C)) = B,
inference(paramod,[status(thm)],[c_820,c_622]) ).
cnf(c_868,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_820,c_357]) ).
cnf(c_876,plain,
divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A,
inference(paramod,[status(thm)],[c_868,c_867]) ).
cnf(c_1558,plain,
divide(a3,divide(divide(inverse(c3),b3),divide(inverse(A),inverse(A)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_868,c_841]) ).
cnf(c_898,plain,
divide(a3,divide(inverse(c3),b3)) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(paramod,[status(thm)],[c_846,c_1558]) ).
cnf(c_905,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_868,c_831]) ).
cnf(c_1559,plain,
inverse(divide(divide(inverse(A),divide(B,C)),divide(C,B))) = A,
inference(paramod,[status(thm)],[c_387,c_868]) ).
cnf(c_1330,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_820,c_1559]) ).
cnf(c_1354,plain,
inverse(A) = divide(inverse(B),divide(A,B)),
inference(paramod,[status(thm)],[c_905,c_868]) ).
cnf(c_1560,plain,
divide(a3,divide(inverse(c3),b3)) != divide(divide(a3,divide(inverse(A),divide(b3,A))),inverse(c3)),
inference(paramod,[status(thm)],[c_1354,c_898]) ).
cnf(c_1395,plain,
divide(divide(a3,divide(inverse(A),divide(b3,A))),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(copy,[status(thm)],[c_1560]) ).
cnf(c_1433,plain,
divide(divide(a3,divide(A,divide(b3,inverse(A)))),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_1330,c_1395]) ).
cnf(c_1544,plain,
divide(divide(A,divide(B,divide(C,D))),inverse(B)) = divide(A,divide(D,C)),
inference(paramod,[status(thm)],[c_820,c_876]) ).
cnf(c_1545,plain,
$false,
inference(resolve,[status(thm)],[c_1544,c_1433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP474-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 % Computer : n019.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Fri Sep 25 14:56:04 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.46 % Process 3036618 was started by sandbox on n019,
% 0.21/0.46 % Fri Sep 25 14:56:04 2026
% 0.21/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/0.47
% 0.21/0.47 % From the command line: assign(max_seconds, 300).
% 2.66/0.85
% 2.66/0.85 % SZS status Unsatisfiable for theBenchmark
% 2.66/0.85
% 2.66/0.85 % Proof 1 at 0.33 (+ 0.04) seconds.
% 2.66/0.85 % Length of proof is 40.
% 2.66/0.85 % Level of proof is 15.
% 2.66/0.85 % Maximum clause weight is 34.000.
% 2.66/0.85 % Given clauses 50.
% 2.66/0.85
% 2.66/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------