%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN010-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:32:03 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.49s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 68 ( 33 unt; 0 def)
% Number of atoms : 142 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 80 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 128 ( 10 sgn 41 !; 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(identity_is_largest,axiom,
! [VAR_0] : less_equal(VAR_0,identity),
file('theBenchmark.p',identity_is_largest) ).
cnf(c_7,plain,
less_equal(A,identity),
inference(clausify,[status(thm)],[identity_is_largest]) ).
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(x_divide_x_is_zero,axiom,
! [VAR_0] : quotient(VAR_0,VAR_0,zero),
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(c_12,plain,
quotient(A,A,zero),
inference(clausify,[status(thm)],[x_divide_x_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(transitivity_of_less_equal,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_0,VAR_2)
| ~ less_equal(VAR_1,VAR_2)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less_equal) ).
cnf(c_14,plain,
( less_equal(A,C)
| ~ less_equal(B,C)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_equal]) ).
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(xLEy_implies_zQyLEzQx,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( less_equal(VAR_3,VAR_4)
| ~ quotient(VAR_2,VAR_0,VAR_4)
| ~ quotient(VAR_2,VAR_1,VAR_3)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(c_16,plain,
( less_equal(D,E)
| ~ quotient(C,A,E)
| ~ quotient(C,B,D)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[xLEy_implies_zQyLEzQx]) ).
fof(xLEy_implies_xQzLEyQz,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( less_equal(VAR_3,VAR_4)
| ~ quotient(VAR_1,VAR_2,VAR_4)
| ~ quotient(VAR_0,VAR_2,VAR_3)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',xLEy_implies_xQzLEyQz) ).
cnf(c_17,plain,
( less_equal(D,E)
| ~ quotient(B,C,E)
| ~ quotient(A,C,D)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[xLEy_implies_xQzLEyQz]) ).
fof(identity_divide_a,axiom,
quotient(identity,a,idQa),
file('theBenchmark.p',identity_divide_a) ).
cnf(c_18,plain,
quotient(identity,a,idQa),
inference(clausify,[status(thm)],[identity_divide_a]) ).
fof(identity_divide_idQa,axiom,
quotient(identity,idQa,idQ_idQa),
file('theBenchmark.p',identity_divide_idQa) ).
cnf(c_19,plain,
quotient(identity,idQa,idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQa]) ).
fof(identity_divide_idQ_idQa,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(c_20,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQ_idQa]) ).
fof(prove_idQa_equals_idQa_Q__idQ_idQa,axiom,
idQa != idQa_Q__idQ_idQa,
file('theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(c_21,plain,
idQa != idQa_Q__idQ_idQa,
inference(clausify,[status(thm)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(c_22,plain,
idQa_Q__idQ_idQa != idQa,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_24,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_34,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_2,c_12]) ).
cnf(c_348,plain,
( less_equal(C,D)
| ~ quotient(identity,B,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_349,plain,
( less_equal(divide(C,A),B)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_348,c_8]) ).
cnf(c_38,plain,
less_equal(divide(A,a),idQa),
inference(resolve,[status(thm)],[c_349,c_18]) ).
cnf(c_350,plain,
( less_equal(D,E)
| ~ quotient(idQa,A,E)
| ~ quotient(C,B,D)
| ~ quotient(identity,A,C)
| ~ quotient(a,A,B) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_351,plain,
( less_equal(B,C)
| ~ quotient(idQa,a,C)
| ~ quotient(A,zero,B)
| ~ quotient(identity,a,A) ),
inference(resolve,[status(thm)],[c_350,c_12]) ).
cnf(c_352,plain,
( less_equal(A,B)
| ~ quotient(idQa,a,B)
| ~ quotient(idQa,zero,A) ),
inference(resolve,[status(thm)],[c_351,c_18]) ).
cnf(c_353,plain,
( less_equal(idQa,A)
| ~ quotient(idQa,a,A) ),
inference(resolve,[status(thm)],[c_352,c_13]) ).
cnf(c_41,plain,
less_equal(idQa,divide(idQa,a)),
inference(resolve,[status(thm)],[c_353,c_8]) ).
cnf(c_354,plain,
( less_equal(C,D)
| ~ quotient(A,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_355,plain,
( less_equal(idQa_Q__idQ_idQa,A)
| ~ quotient(idQa,zero,A) ),
inference(resolve,[status(thm)],[c_354,c_20]) ).
cnf(c_57,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolve,[status(thm)],[c_355,c_13]) ).
cnf(c_356,plain,
( less_equal(B,a)
| ~ quotient(identity,A,B)
| ~ less_equal(idQa,A) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_357,plain,
( less_equal(A,a)
| ~ quotient(identity,idQa,A) ),
inference(resolve,[status(thm)],[c_356,c_34]) ).
cnf(c_90,plain,
less_equal(idQ_idQa,a),
inference(resolve,[status(thm)],[c_357,c_19]) ).
cnf(c_358,plain,
( idQa = idQa_Q__idQ_idQa
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolve,[status(thm)],[c_6,c_57]) ).
cnf(c_359,plain,
idQa != idQa_Q__idQ_idQa,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_98,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(resolve,[status(thm)],[c_358,c_359]) ).
cnf(c_105,plain,
quotient(idQ_idQa,a,zero),
inference(resolve,[status(thm)],[c_1,c_90]) ).
cnf(c_360,plain,
( less_equal(A,B)
| ~ less_equal(A,divide(B,C)) ),
inference(resolve,[status(thm)],[c_14,c_24]) ).
cnf(c_136,plain,
~ less_equal(idQa,divide(idQa_Q__idQ_idQa,A)),
inference(resolve,[status(thm)],[c_360,c_98]) ).
cnf(c_361,plain,
( less_equal(D,E)
| ~ quotient(idQa_Q__idQ_idQa,A,E)
| ~ quotient(C,B,D)
| ~ quotient(idQa,A,C)
| ~ quotient(idQ_idQa,A,B) ),
inference(resolve,[status(thm)],[c_4,c_20]) ).
cnf(c_362,plain,
( less_equal(B,C)
| ~ quotient(idQa_Q__idQ_idQa,a,C)
| ~ quotient(A,zero,B)
| ~ quotient(idQa,a,A) ),
inference(resolve,[status(thm)],[c_361,c_105]) ).
cnf(c_363,plain,
( less_equal(A,B)
| ~ quotient(idQa_Q__idQ_idQa,a,B)
| ~ quotient(divide(idQa,a),zero,A) ),
inference(resolve,[status(thm)],[c_362,c_8]) ).
cnf(c_364,plain,
( less_equal(divide(idQa,a),A)
| ~ quotient(idQa_Q__idQ_idQa,a,A) ),
inference(resolve,[status(thm)],[c_363,c_13]) ).
cnf(c_247,plain,
less_equal(divide(idQa,a),divide(idQa_Q__idQ_idQa,a)),
inference(resolve,[status(thm)],[c_364,c_8]) ).
cnf(c_365,plain,
( divide(A,a) = idQa
| ~ less_equal(idQa,divide(A,a)) ),
inference(resolve,[status(thm)],[c_6,c_38]) ).
cnf(c_345,plain,
divide(idQa,a) = idQa,
inference(resolve,[status(thm)],[c_365,c_41]) ).
cnf(c_346,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference(paramod,[status(thm)],[c_345,c_247]) ).
cnf(c_347,plain,
$false,
inference(resolve,[status(thm)],[c_346,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:58:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3305858 was started by sandbox2 on n020,
% 0.09/0.35 % Fri Sep 25 15:58:48 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.83/0.49
% 0.83/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.49
% 0.83/0.49 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.83/0.49 % Length of proof is 32.
% 0.83/0.49 % Level of proof is 6.
% 0.83/0.49 % Maximum clause weight is 28.000.
% 0.83/0.49 % Given clauses 55.
% 0.83/0.49
% 0.83/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------