%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP480-1 : 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 : n010.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 07:29:51 AM UTC 2026
% Result : Unsatisfiable 3.82s 1.03s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 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 : 187 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(inverse(divide(divide(divide(VAR_0,VAR_0),VAR_1),divide(VAR_2,divide(VAR_1,VAR_3)))),VAR_3) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(B,D)))),D) = C,
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_763,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_764,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_763]) ).
cnf(c_765,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_2,c_764]) ).
cnf(c_766,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_2,c_765]) ).
cnf(c_4,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3)),
inference(copy,[status(thm)],[c_766]) ).
cnf(c_767,plain,
divide(inverse(divide(divide(divide(A,A),B),C)),D) = inverse(divide(divide(divide(E,E),F),divide(C,divide(F,divide(B,D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(divide(divide(divide(A,A),B),divide(C,divide(B,divide(D,E))))) = divide(inverse(divide(divide(divide(F,F),D),C)),E),
inference(copy,[status(thm)],[c_767]) ).
cnf(c_6,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),divide(B,D)) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
inverse(divide(divide(divide(A,A),B),divide(divide(C,divide(D,E)),divide(B,divide(D,E))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_768,plain,
inverse(divide(divide(divide(A,A),B),C)) = divide(inverse(divide(divide(divide(D,D),E),divide(inverse(divide(divide(divide(F,F),B),C)),divide(E,V6)))),V6),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_9,plain,
inverse(divide(divide(divide(A,A),B),C)) = inverse(divide(divide(divide(D,D),B),C)),
inference(paramod,[status(thm)],[c_1,c_768]) ).
cnf(c_10,plain,
divide(divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),E),divide(F,E)) = divide(C,divide(F,divide(B,D))),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_11,plain,
divide(divide(inverse(divide(A,B)),C),divide(divide(D,inverse(divide(divide(divide(E,E),D),A))),C)) = B,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_769,plain,
inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(B,divide(inverse(divide(divide(divide(E,E),F),divide(D,divide(F,V6)))),V6))))) = C,
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_12,plain,
inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(B,D)))) = C,
inference(paramod,[status(thm)],[c_1,c_769]) ).
cnf(c_770,plain,
inverse(divide(A,B)) = inverse(divide(divide(divide(C,C),divide(D,inverse(divide(divide(divide(E,E),D),A)))),B)),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_15,plain,
inverse(divide(divide(divide(A,A),divide(B,inverse(divide(divide(divide(C,C),B),D)))),E)) = inverse(divide(D,E)),
inference(copy,[status(thm)],[c_770]) ).
cnf(c_18,plain,
divide(divide(A,B),divide(C,B)) = divide(divide(A,D),divide(C,D)),
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_24,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),D),divide(E,D)) = divide(C,E),
inference(paramod,[status(thm)],[c_18,c_6]) ).
cnf(c_771,plain,
inverse(divide(divide(divide(A,A),divide(inverse(divide(B,C)),D)),divide(E,C))) = divide(inverse(divide(divide(divide(F,F),divide(V6,inverse(divide(divide(divide(V7,V7),V6),B)))),E)),D),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_42,plain,
inverse(divide(divide(divide(A,A),divide(inverse(divide(B,C)),D)),divide(E,C))) = divide(inverse(divide(B,E)),D),
inference(paramod,[status(thm)],[c_15,c_771]) ).
cnf(c_772,plain,
divide(divide(divide(inverse(divide(divide(divide(A,A),divide(B,inverse(divide(divide(divide(C,C),B),D)))),E)),F),V6),divide(divide(inverse(divide(D,V7)),F),V6)) = divide(E,V7),
inference(paramod,[status(thm)],[c_11,c_10]) ).
cnf(c_46,plain,
divide(divide(divide(inverse(divide(A,B)),C),D),divide(divide(inverse(divide(A,E)),C),D)) = divide(B,E),
inference(paramod,[status(thm)],[c_15,c_772]) ).
cnf(c_773,plain,
divide(divide(inverse(divide(A,B)),C),divide(D,C)) = divide(divide(inverse(divide(E,B)),inverse(divide(E,A))),D),
inference(paramod,[status(thm)],[c_46,c_6]) ).
cnf(c_61,plain,
divide(divide(inverse(divide(A,B)),inverse(divide(A,C))),D) = divide(divide(inverse(divide(C,B)),E),divide(D,E)),
inference(copy,[status(thm)],[c_773]) ).
cnf(c_78,plain,
divide(divide(inverse(divide(A,B)),inverse(divide(A,divide(divide(C,C),D)))),D) = B,
inference(paramod,[status(thm)],[c_61,c_6]) ).
cnf(c_774,plain,
inverse(divide(divide(divide(A,A),divide(inverse(divide(B,C)),inverse(divide(B,divide(divide(D,D),E))))),divide(divide(F,E),C))) = F,
inference(paramod,[status(thm)],[c_78,c_12]) ).
cnf(c_518,plain,
divide(inverse(divide(A,divide(B,C))),inverse(divide(A,divide(divide(D,D),C)))) = B,
inference(paramod,[status(thm)],[c_42,c_774]) ).
cnf(c_775,plain,
divide(inverse(divide(A,B)),inverse(divide(divide(inverse(divide(divide(divide(C,C),D),divide(A,D))),E),divide(divide(F,F),E)))) = B,
inference(paramod,[status(thm)],[c_24,c_518]) ).
cnf(c_619,plain,
divide(inverse(divide(A,B)),inverse(divide(A,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_24,c_775]) ).
cnf(c_625,plain,
divide(A,divide(B,inverse(divide(divide(divide(C,C),B),divide(D,D))))) = A,
inference(paramod,[status(thm)],[c_619,c_1]) ).
cnf(c_776,plain,
divide(divide(A,B),divide(C,B)) = divide(A,divide(C,divide(D,inverse(divide(divide(divide(E,E),D),divide(F,F)))))),
inference(paramod,[status(thm)],[c_619,c_10]) ).
cnf(c_648,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_625,c_776]) ).
cnf(c_777,plain,
divide(A,B) = divide(divide(inverse(divide(divide(C,C),A)),D),divide(B,D)),
inference(paramod,[status(thm)],[c_619,c_61]) ).
cnf(c_778,plain,
divide(A,B) = divide(inverse(divide(divide(C,C),A)),B),
inference(paramod,[status(thm)],[c_648,c_777]) ).
cnf(c_667,plain,
divide(inverse(divide(divide(A,A),B)),C) = divide(B,C),
inference(copy,[status(thm)],[c_778]) ).
cnf(c_749,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_619,c_78]) ).
cnf(c_779,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),inverse(divide(D,divide(E,E)))),F) = divide(C,inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_619,c_24]) ).
cnf(c_780,plain,
divide(divide(inverse(divide(divide(A,A),C)),inverse(divide(D,divide(E,E)))),F) = divide(C,inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_648,c_779]) ).
cnf(c_781,plain,
divide(divide(inverse(divide(divide(A,A),C)),inverse(D)),F) = divide(C,inverse(divide(D,F))),
inference(paramod,[status(thm)],[c_749,c_780]) ).
cnf(c_761,plain,
divide(divide(A,inverse(B)),C) = divide(A,inverse(divide(B,C))),
inference(paramod,[status(thm)],[c_667,c_781]) ).
cnf(c_782,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_762,plain,
$false,
inference(resolve,[status(thm)],[c_761,c_782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP480-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:56:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1033718 was started by sandbox2 on n010,
% 0.10/0.37 % Fri Sep 25 14:56:30 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 3.82/1.03
% 3.82/1.03 % SZS status Unsatisfiable for theBenchmark
% 3.82/1.03
% 3.82/1.03 % Proof 1 at 0.48 (+ 0.17) seconds.
% 3.82/1.03 % Length of proof is 26.
% 3.82/1.03 % Level of proof is 14.
% 3.82/1.03 % Maximum clause weight is 99.000.
% 3.82/1.03 % Given clauses 46.
% 3.82/1.03
% 3.82/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------