%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP478-1 : 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 : n015.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 2.99s 0.84s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 237 ( 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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_1000,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1001,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_1000]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_1001]) ).
cnf(c_1002,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_1002]) ).
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_1003,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_1003]) ).
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_1004,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_1004]) ).
cnf(c_1005,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_1005]) ).
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_1006,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_1006]) ).
cnf(c_1007,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_1007]) ).
cnf(c_1008,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_1008]) ).
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_1009,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_517,plain,
divide(inverse(divide(A,divide(B,C))),inverse(divide(A,divide(divide(D,D),C)))) = B,
inference(paramod,[status(thm)],[c_42,c_1009]) ).
cnf(c_550,plain,
divide(inverse(divide(divide(A,B),divide(C,B))),inverse(divide(divide(A,D),divide(divide(E,E),D)))) = C,
inference(paramod,[status(thm)],[c_18,c_517]) ).
cnf(c_561,plain,
divide(inverse(divide(A,divide(divide(inverse(divide(B,C)),D),divide(E,D)))),inverse(divide(A,divide(divide(F,F),E)))) = divide(inverse(divide(V6,C)),inverse(divide(V6,B))),
inference(paramod,[status(thm)],[c_61,c_517]) ).
cnf(c_1010,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_517]) ).
cnf(c_617,plain,
divide(inverse(divide(A,B)),inverse(divide(A,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_24,c_1010]) ).
cnf(c_622,plain,
divide(A,divide(B,inverse(divide(divide(divide(C,C),B),divide(D,D))))) = A,
inference(paramod,[status(thm)],[c_617,c_1]) ).
cnf(c_1011,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_617,c_10]) ).
cnf(c_645,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_622,c_1011]) ).
cnf(c_1012,plain,
divide(A,B) = divide(divide(inverse(divide(divide(C,C),A)),D),divide(B,D)),
inference(paramod,[status(thm)],[c_617,c_61]) ).
cnf(c_1013,plain,
divide(A,B) = divide(inverse(divide(divide(C,C),A)),B),
inference(paramod,[status(thm)],[c_645,c_1012]) ).
cnf(c_664,plain,
divide(inverse(divide(divide(A,A),B)),C) = divide(B,C),
inference(copy,[status(thm)],[c_1013]) ).
cnf(c_744,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_617,c_78]) ).
cnf(c_1014,plain,
divide(inverse(divide(A,B)),inverse(divide(divide(inverse(divide(divide(divide(C,C),D),divide(A,D))),E),divide(F,F)))) = divide(B,E),
inference(paramod,[status(thm)],[c_24,c_617]) ).
cnf(c_1015,plain,
divide(inverse(divide(A,B)),inverse(divide(divide(inverse(divide(divide(C,C),A)),E),divide(F,F)))) = divide(B,E),
inference(paramod,[status(thm)],[c_645,c_1014]) ).
cnf(c_1016,plain,
divide(inverse(divide(A,B)),inverse(divide(divide(A,E),divide(F,F)))) = divide(B,E),
inference(paramod,[status(thm)],[c_664,c_1015]) ).
cnf(c_757,plain,
divide(inverse(divide(A,B)),inverse(divide(A,C))) = divide(B,C),
inference(paramod,[status(thm)],[c_744,c_1016]) ).
cnf(c_1017,plain,
divide(inverse(divide(A,divide(inverse(divide(B,C)),E))),inverse(divide(A,divide(divide(F,F),E)))) = divide(inverse(divide(V6,C)),inverse(divide(V6,B))),
inference(paramod,[status(thm)],[c_645,c_561]) ).
cnf(c_1018,plain,
divide(divide(inverse(divide(B,C)),E),divide(divide(F,F),E)) = divide(inverse(divide(V6,C)),inverse(divide(V6,B))),
inference(paramod,[status(thm)],[c_757,c_1017]) ).
cnf(c_1019,plain,
divide(inverse(divide(B,C)),divide(F,F)) = divide(inverse(divide(V6,C)),inverse(divide(V6,B))),
inference(paramod,[status(thm)],[c_645,c_1018]) ).
cnf(c_1020,plain,
inverse(divide(B,C)) = divide(inverse(divide(V6,C)),inverse(divide(V6,B))),
inference(paramod,[status(thm)],[c_744,c_1019]) ).
cnf(c_799,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_757,c_1020]) ).
cnf(c_1021,plain,
divide(inverse(divide(A,C)),inverse(divide(divide(A,D),divide(divide(E,E),D)))) = C,
inference(paramod,[status(thm)],[c_645,c_550]) ).
cnf(c_1022,plain,
divide(divide(C,A),inverse(divide(divide(A,D),divide(divide(E,E),D)))) = C,
inference(paramod,[status(thm)],[c_799,c_1021]) ).
cnf(c_1023,plain,
divide(divide(C,A),inverse(divide(A,divide(E,E)))) = C,
inference(paramod,[status(thm)],[c_645,c_1022]) ).
cnf(c_805,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_744,c_1023]) ).
cnf(c_996,plain,
inverse(A) = divide(divide(B,B),A),
inference(paramod,[status(thm)],[c_744,c_799]) ).
cnf(c_1024,plain,
divide(divide(divide(A,A),b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_996,c_4]) ).
cnf(c_1025,plain,
divide(A,A) != divide(inverse(a1),inverse(a1)),
inference(paramod,[status(thm)],[c_805,c_1024]) ).
cnf(c_1026,plain,
divide(inverse(a1),inverse(a1)) != divide(A,A),
inference(copy,[status(thm)],[c_1025]) ).
cnf(c_999,plain,
$false,
inference(copy,[status(thm)],[c_1026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP478-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:59:27 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1664394 was started by sandbox on n015,
% 0.16/0.43 % Fri Sep 25 14:59:27 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 2.99/0.84
% 2.99/0.84 % SZS status Unsatisfiable for theBenchmark
% 2.99/0.84
% 2.99/0.84 % Proof 1 at 0.30 (+ 0.09) seconds.
% 2.99/0.84 % Length of proof is 31.
% 2.99/0.84 % Level of proof is 16.
% 2.99/0.84 % Maximum clause weight is 99.000.
% 2.99/0.84 % Given clauses 47.
% 2.99/0.84
% 2.99/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------