%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 23 unt; 0 def)
% Number of atoms : 67 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 17 !; 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(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(xLEy,axiom,
less_equal(x,y),
file('theBenchmark.p',xLEy) ).
cnf(c_10,plain,
less_equal(x,y),
inference(clausify,[status(thm)],[xLEy]) ).
fof(yLEz,axiom,
less_equal(y,z),
file('theBenchmark.p',yLEz) ).
cnf(c_11,plain,
less_equal(y,z),
inference(clausify,[status(thm)],[yLEz]) ).
fof(prove_transitivity_of_less_equal,axiom,
~ less_equal(x,z),
file('theBenchmark.p',prove_transitivity_of_less_equal) ).
cnf(c_12,plain,
~ less_equal(x,z),
inference(clausify,[status(thm)],[prove_transitivity_of_less_equal]) ).
cnf(c_13,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
quotient(x,y,zero),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_18,plain,
quotient(y,z,zero),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_20,plain,
~ quotient(x,z,zero),
inference(resolve,[status(thm)],[c_2,c_12]) ).
cnf(c_55,plain,
( less_equal(D,E)
| ~ quotient(zero,A,E)
| ~ quotient(C,B,D)
| ~ quotient(x,A,C)
| ~ quotient(y,A,B) ),
inference(resolve,[status(thm)],[c_4,c_17]) ).
cnf(c_56,plain,
( less_equal(B,C)
| ~ quotient(zero,z,C)
| ~ quotient(A,zero,B)
| ~ quotient(x,z,A) ),
inference(resolve,[status(thm)],[c_55,c_18]) ).
cnf(c_57,plain,
( less_equal(A,B)
| ~ quotient(zero,z,B)
| ~ quotient(divide(x,z),zero,A) ),
inference(resolve,[status(thm)],[c_56,c_8]) ).
cnf(c_58,plain,
( less_equal(divide(divide(x,z),zero),A)
| ~ quotient(zero,z,A) ),
inference(resolve,[status(thm)],[c_57,c_8]) ).
cnf(c_29,plain,
less_equal(divide(divide(x,z),zero),zero),
inference(resolve,[status(thm)],[c_58,c_13]) ).
cnf(c_59,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_60,plain,
zero = divide(divide(x,z),zero),
inference(resolve,[status(thm)],[c_59,c_29]) ).
cnf(c_43,plain,
divide(divide(x,z),zero) = zero,
inference(copy,[status(thm)],[c_60]) ).
cnf(c_46,plain,
quotient(divide(x,z),zero,zero),
inference(paramod,[status(thm)],[c_43,c_8]) ).
cnf(c_51,plain,
less_equal(divide(x,z),zero),
inference(resolve,[status(thm)],[c_2,c_46]) ).
cnf(c_61,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_62,plain,
zero = divide(x,z),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_52,plain,
divide(x,z) = zero,
inference(copy,[status(thm)],[c_62]) ).
cnf(c_53,plain,
quotient(x,z,zero),
inference(paramod,[status(thm)],[c_52,c_8]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 15:56:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2418189 was started by sandbox on n011,
% 0.11/0.38 % Fri Sep 25 15:56:13 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.42
% 0.11/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.42 % Length of proof is 20.
% 0.11/0.42 % Level of proof is 8.
% 0.11/0.42 % Maximum clause weight is 23.000.
% 0.11/0.42 % Given clauses 34.
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------