%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN005-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:31:58 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.54s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 30 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 26 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 7 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1)),divide(divide(VAR_0,VAR_2),VAR_1)) = zero,
file('theBenchmark.p',quotient_property) ).
cnf(c_2,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : divide(zero,VAR_0) = zero,
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_3,plain,
divide(zero,A) = zero,
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(divide_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| divide(VAR_1,VAR_0) != zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',divide_and_equal) ).
cnf(c_4,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[divide_and_equal]) ).
fof(a_divide_b_is_zero,axiom,
divide(a,b) = zero,
file('theBenchmark.p',a_divide_b_is_zero) ).
cnf(c_6,plain,
divide(a,b) = zero,
inference(clausify,[status(thm)],[a_divide_b_is_zero]) ).
cnf(c_7,plain,
zero = divide(a,b),
inference(copy,[status(thm)],[c_6]) ).
fof(b_divide_c_is_zero,axiom,
divide(b,c) = zero,
file('theBenchmark.p',b_divide_c_is_zero) ).
cnf(c_8,plain,
divide(b,c) = zero,
inference(clausify,[status(thm)],[b_divide_c_is_zero]) ).
cnf(c_43,plain,
divide(b,c) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_9,plain,
divide(a,b) = divide(b,c),
inference(copy,[status(thm)],[c_43]) ).
fof(prove_transitivity_of_divide_to_zero,axiom,
divide(a,c) != zero,
file('theBenchmark.p',prove_transitivity_of_divide_to_zero) ).
cnf(c_10,plain,
divide(a,c) != zero,
inference(clausify,[status(thm)],[prove_transitivity_of_divide_to_zero]) ).
cnf(c_44,plain,
divide(a,c) != divide(a,b),
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_11,plain,
divide(a,c) != divide(b,c),
inference(paramod,[status(thm)],[c_9,c_44]) ).
cnf(c_45,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_46,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != divide(b,c) ),
inference(paramod,[status(thm)],[c_9,c_45]) ).
cnf(c_47,plain,
( A = B
| divide(B,A) != divide(a,b)
| divide(A,B) != divide(b,c) ),
inference(paramod,[status(thm)],[c_7,c_46]) ).
cnf(c_48,plain,
( A = B
| divide(B,A) != divide(b,c)
| divide(A,B) != divide(b,c) ),
inference(paramod,[status(thm)],[c_9,c_47]) ).
cnf(c_49,plain,
( A = B
| divide(B,A) != divide(b,c)
| divide(b,c) != divide(A,B) ),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_13,plain,
( A = B
| divide(b,c) != divide(B,A)
| divide(b,c) != divide(A,B) ),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_50,plain,
divide(divide(a,b),A) = zero,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_51,plain,
divide(divide(b,c),A) = zero,
inference(paramod,[status(thm)],[c_9,c_50]) ).
cnf(c_52,plain,
divide(divide(b,c),A) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_51]) ).
cnf(c_14,plain,
divide(divide(b,c),A) = divide(b,c),
inference(paramod,[status(thm)],[c_9,c_52]) ).
cnf(c_53,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_15,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(b,c),
inference(paramod,[status(thm)],[c_9,c_53]) ).
cnf(c_54,plain,
divide(b,c) = divide(divide(b,c),A),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_55,plain,
( A = divide(b,c)
| divide(b,c) != divide(A,divide(b,c)) ),
inference(resolve,[status(thm)],[c_13,c_54]) ).
cnf(c_56,plain,
divide(b,c) != divide(divide(a,c),divide(b,c)),
inference(resolve,[status(thm)],[c_55,c_11]) ).
cnf(c_25,plain,
divide(divide(a,c),divide(b,c)) != divide(b,c),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
divide(divide(divide(a,A),divide(b,A)),divide(divide(b,c),A)) = divide(b,c),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_29,plain,
divide(divide(divide(a,A),divide(b,A)),divide(b,c)) = divide(b,c),
inference(paramod,[status(thm)],[c_14,c_57]) ).
cnf(c_58,plain,
divide(b,c) = divide(divide(b,c),A),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_59,plain,
( A = divide(b,c)
| divide(b,c) != divide(A,divide(b,c)) ),
inference(resolve,[status(thm)],[c_13,c_58]) ).
cnf(c_60,plain,
divide(b,c) != divide(divide(divide(a,c),divide(b,c)),divide(b,c)),
inference(resolve,[status(thm)],[c_59,c_25]) ).
cnf(c_61,plain,
divide(b,c) != divide(b,c),
inference(paramod,[status(thm)],[c_29,c_60]) ).
cnf(c_42,plain,
$false,
inference(copy,[status(thm)],[c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n026.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Fri Sep 25 15:59:10 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.52 % Process 2957367 was started by sandbox on n026,
% 0.10/0.52 % Fri Sep 25 15:59:10 2026
% 0.10/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.52
% 0.10/0.52 % From the command line: assign(max_seconds, 300).
% 0.10/0.54
% 0.10/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.54
% 0.10/0.54 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.54 % Length of proof is 15.
% 0.10/0.54 % Level of proof is 5.
% 0.10/0.54 % Maximum clause weight is 17.000.
% 0.10/0.54 % Given clauses 10.
% 0.10/0.54
% 0.10/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------