%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN004-1 : 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 : n004.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 07:31:57 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 29 unt; 0 def)
% Number of atoms : 97 ( 16 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 92 ( 47 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 8 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal,axiom,
! [VAR_0,VAR_1] :
( quotient(VAR_0,VAR_1,zero)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal) ).
cnf(c_1,plain,
( quotient(A,B,zero)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal]) ).
fof(less_equal_quotient,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| ~ quotient(VAR_0,VAR_1,zero) ),
file('theBenchmark.p',less_equal_quotient) ).
cnf(c_2,plain,
( less_equal(A,B)
| ~ quotient(A,B,zero) ),
inference(clausify,[status(thm)],[less_equal_quotient]) ).
fof(divisor_existence,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_2,VAR_0)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',divisor_existence) ).
cnf(c_3,plain,
( less_equal(C,A)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[divisor_existence]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( less_equal(VAR_6,VAR_7)
| ~ quotient(VAR_2,VAR_3,VAR_7)
| ~ quotient(VAR_5,VAR_4,VAR_6)
| ~ quotient(VAR_0,VAR_3,VAR_5)
| ~ quotient(VAR_1,VAR_3,VAR_4)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
( less_equal(V6,V7)
| ~ quotient(C,D,V7)
| ~ quotient(F,E,V6)
| ~ quotient(A,D,F)
| ~ quotient(B,D,E)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : less_equal(zero,VAR_0),
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_5,plain,
less_equal(zero,A),
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(less_equal_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ less_equal(VAR_1,VAR_0)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',less_equal_and_equal) ).
cnf(c_6,plain,
( A = B
| ~ less_equal(B,A)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[less_equal_and_equal]) ).
fof(closure,axiom,
! [VAR_0,VAR_1] : quotient(VAR_0,VAR_1,divide(VAR_0,VAR_1)),
file('theBenchmark.p',closure) ).
cnf(c_8,plain,
quotient(A,B,divide(A,B)),
inference(clausify,[status(thm)],[closure]) ).
fof(prove_x_divde_zero_is_x,axiom,
~ quotient(x,zero,x),
file('theBenchmark.p',prove_x_divde_zero_is_x) ).
cnf(c_10,plain,
~ quotient(x,zero,x),
inference(clausify,[status(thm)],[prove_x_divde_zero_is_x]) ).
cnf(c_11,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_14,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_196,plain,
( less_equal(F,V6)
| ~ quotient(divide(D,A),B,V6)
| ~ quotient(E,C,F)
| ~ quotient(D,B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_197,plain,
( less_equal(D,E)
| ~ quotient(divide(A,zero),B,E)
| ~ quotient(C,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_196,c_11]) ).
cnf(c_198,plain,
( less_equal(C,D)
| ~ quotient(divide(A,zero),B,D)
| ~ quotient(divide(A,B),zero,C) ),
inference(resolve,[status(thm)],[c_197,c_8]) ).
cnf(c_199,plain,
( less_equal(divide(divide(A,B),zero),C)
| ~ quotient(divide(A,zero),B,C) ),
inference(resolve,[status(thm)],[c_198,c_8]) ).
cnf(c_16,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(resolve,[status(thm)],[c_199,c_8]) ).
cnf(c_20,plain,
quotient(divide(A,B),A,zero),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_200,plain,
( less_equal(F,V6)
| ~ quotient(divide(D,A),B,V6)
| ~ quotient(E,C,F)
| ~ quotient(D,B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_201,plain,
( less_equal(D,F)
| ~ quotient(divide(A,divide(B,E)),B,F)
| ~ quotient(C,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_200,c_20]) ).
cnf(c_202,plain,
( less_equal(C,E)
| ~ quotient(divide(A,divide(B,D)),B,E)
| ~ quotient(divide(A,B),zero,C) ),
inference(resolve,[status(thm)],[c_201,c_8]) ).
cnf(c_203,plain,
( less_equal(divide(divide(A,B),zero),D)
| ~ quotient(divide(A,divide(B,C)),B,D) ),
inference(resolve,[status(thm)],[c_202,c_8]) ).
cnf(c_22,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(resolve,[status(thm)],[c_203,c_20]) ).
cnf(c_204,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_205,plain,
zero = divide(divide(A,A),zero),
inference(resolve,[status(thm)],[c_204,c_22]) ).
cnf(c_27,plain,
divide(divide(A,A),zero) = zero,
inference(copy,[status(thm)],[c_205]) ).
cnf(c_40,plain,
quotient(divide(A,A),zero,zero),
inference(paramod,[status(thm)],[c_27,c_8]) ).
cnf(c_48,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_2,c_40]) ).
cnf(c_206,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_207,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_206,c_48]) ).
cnf(c_49,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_207]) ).
cnf(c_53,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramod,[status(thm)],[c_49,c_16]) ).
cnf(c_208,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_209,plain,
zero = divide(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_208,c_53]) ).
cnf(c_109,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(copy,[status(thm)],[c_209]) ).
cnf(c_111,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(paramod,[status(thm)],[c_109,c_8]) ).
cnf(c_121,plain,
less_equal(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_2,c_111]) ).
cnf(c_210,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_211,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_210,c_121]) ).
cnf(c_122,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_211]) ).
cnf(c_123,plain,
quotient(A,divide(A,zero),zero),
inference(paramod,[status(thm)],[c_122,c_8]) ).
cnf(c_156,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_123]) ).
cnf(c_212,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_14]) ).
cnf(c_158,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_212,c_156]) ).
cnf(c_194,plain,
quotient(A,zero,A),
inference(paramod,[status(thm)],[c_158,c_8]) ).
cnf(c_195,plain,
$false,
inference(resolve,[status(thm)],[c_194,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:55:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3592574 was started by sandbox on n004,
% 0.09/0.37 % Fri Sep 25 15:55:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.48
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.48
% 0.13/0.48 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.13/0.48 % Length of proof is 27.
% 0.13/0.48 % Level of proof is 17.
% 0.13/0.48 % Maximum clause weight is 39.000.
% 0.13/0.48 % Given clauses 52.
% 0.13/0.48
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------