%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN008-2 : 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 : n016.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 07:32:01 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.68s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 34 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 1 sgn 19 !; 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(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(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(zero_divide_anything_is_zero,axiom,
! [VAR_0] : quotient(zero,VAR_0,zero),
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(c_11,plain,
quotient(zero,A,zero),
inference(clausify,[status(thm)],[zero_divide_anything_is_zero]) ).
fof(x_divde_zero_is_x,axiom,
! [VAR_0] : quotient(VAR_0,zero,VAR_0),
file('theBenchmark.p',x_divde_zero_is_x) ).
cnf(c_13,plain,
quotient(A,zero,A),
inference(clausify,[status(thm)],[x_divde_zero_is_x]) ).
fof(xQyLEz_implies_xQzLEy,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( less_equal(VAR_4,VAR_1)
| ~ quotient(VAR_0,VAR_3,VAR_4)
| ~ less_equal(VAR_2,VAR_3)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(c_15,plain,
( less_equal(E,B)
| ~ quotient(A,D,E)
| ~ less_equal(C,D)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[xQyLEz_implies_xQzLEy]) ).
fof(aLEb,axiom,
less_equal(a,b),
file('theBenchmark.p',aLEb) ).
cnf(c_17,plain,
less_equal(a,b),
inference(clausify,[status(thm)],[aLEb]) ).
fof(aQc,axiom,
quotient(a,c,aQc),
file('theBenchmark.p',aQc) ).
cnf(c_18,plain,
quotient(a,c,aQc),
inference(clausify,[status(thm)],[aQc]) ).
fof(bQc,axiom,
quotient(b,c,bQc),
file('theBenchmark.p',bQc) ).
cnf(c_19,plain,
quotient(b,c,bQc),
inference(clausify,[status(thm)],[bQc]) ).
fof(prove_aQcLEbQc,axiom,
~ less_equal(aQc,bQc),
file('theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_20,plain,
~ less_equal(aQc,bQc),
inference(clausify,[status(thm)],[prove_aQcLEbQc]) ).
cnf(c_37,plain,
quotient(a,b,zero),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_235,plain,
( less_equal(D,B)
| ~ quotient(A,C,D)
| ~ less_equal(divide(A,B),C) ),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_236,plain,
( less_equal(A,B)
| ~ less_equal(divide(A,B),zero) ),
inference(resolve,[status(thm)],[c_235,c_13]) ).
cnf(c_64,plain,
~ less_equal(divide(aQc,bQc),zero),
inference(resolve,[status(thm)],[c_236,c_20]) ).
cnf(c_237,plain,
( less_equal(D,E)
| ~ quotient(zero,A,E)
| ~ quotient(C,B,D)
| ~ quotient(a,A,C)
| ~ quotient(b,A,B) ),
inference(resolve,[status(thm)],[c_4,c_37]) ).
cnf(c_238,plain,
( less_equal(B,C)
| ~ quotient(zero,c,C)
| ~ quotient(A,bQc,B)
| ~ quotient(a,c,A) ),
inference(resolve,[status(thm)],[c_237,c_19]) ).
cnf(c_239,plain,
( less_equal(A,B)
| ~ quotient(zero,c,B)
| ~ quotient(aQc,bQc,A) ),
inference(resolve,[status(thm)],[c_238,c_18]) ).
cnf(c_240,plain,
( less_equal(divide(aQc,bQc),A)
| ~ quotient(zero,c,A) ),
inference(resolve,[status(thm)],[c_239,c_8]) ).
cnf(c_233,plain,
less_equal(divide(aQc,bQc),zero),
inference(resolve,[status(thm)],[c_240,c_11]) ).
cnf(c_234,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n016.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Fri Sep 25 16:02:10 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.58 % Process 2808998 was started by sandbox on n016,
% 0.10/10.58 % Fri Sep 25 16:02:10 2026
% 0.10/10.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.59
% 0.10/10.59 % From the command line: assign(max_seconds, 300).
% 0.14/10.68
% 0.14/10.68 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.68
% 0.14/10.68 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.14/10.68 % Length of proof is 14.
% 0.14/10.68 % Level of proof is 3.
% 0.14/10.68 % Maximum clause weight is 25.000.
% 0.14/10.68 % Given clauses 38.
% 0.14/10.68
% 0.14/10.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------