%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN011-2 : 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 : n007.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 6.22s 1.24s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 33 unt; 0 def)
% Number of atoms : 131 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 73 ~; 67 |; 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 : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 96 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(one_inversion_equals_three,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ quotient(identity,VAR_2,VAR_3)
| ~ quotient(identity,VAR_1,VAR_2)
| ~ quotient(identity,VAR_0,VAR_1) ),
file('theBenchmark.p',one_inversion_equals_three) ).
cnf(c_18,plain,
( B = D
| ~ quotient(identity,C,D)
| ~ quotient(identity,B,C)
| ~ quotient(identity,A,B) ),
inference(clausify,[status(thm)],[one_inversion_equals_three]) ).
fof(identity_divide_a,axiom,
quotient(identity,a,idQa),
file('theBenchmark.p',identity_divide_a) ).
cnf(c_20,plain,
quotient(identity,a,idQa),
inference(clausify,[status(thm)],[identity_divide_a]) ).
fof(identity_divide_b,axiom,
quotient(identity,b,idQb),
file('theBenchmark.p',identity_divide_b) ).
cnf(c_21,plain,
quotient(identity,b,idQb),
inference(clausify,[status(thm)],[identity_divide_b]) ).
fof(identity_divide_idQb,axiom,
quotient(identity,idQb,idQ_idQb),
file('theBenchmark.p',identity_divide_idQb) ).
cnf(c_22,plain,
quotient(identity,idQb,idQ_idQb),
inference(clausify,[status(thm)],[identity_divide_idQb]) ).
fof(idQa_divide_idQ_idQb,axiom,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('theBenchmark.p',idQa_divide_idQ_idQb) ).
cnf(c_23,plain,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
inference(clausify,[status(thm)],[idQa_divide_idQ_idQb]) ).
fof(identity_divide_idQa,axiom,
quotient(identity,idQa,idQ_idQa),
file('theBenchmark.p',identity_divide_idQa) ).
cnf(c_24,plain,
quotient(identity,idQa,idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQa]) ).
fof(idQb_divide_idQ_idQa,axiom,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('theBenchmark.p',idQb_divide_idQ_idQa) ).
cnf(c_25,plain,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
inference(clausify,[status(thm)],[idQb_divide_idQ_idQa]) ).
fof(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa,axiom,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
cnf(c_26,plain,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
inference(clausify,[status(thm)],[prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa]) ).
cnf(c_27,plain,
idQb_Q__idQ_idQa != idQa_Q__idQ_idQb,
inference(copy,[status(thm)],[c_26]) ).
cnf(c_29,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_1104,plain,
( idQb = B
| ~ quotient(identity,A,B)
| ~ quotient(identity,idQb,A) ),
inference(resolve,[status(thm)],[c_18,c_21]) ).
cnf(c_1105,plain,
( idQb = A
| ~ quotient(identity,idQ_idQb,A) ),
inference(resolve,[status(thm)],[c_1104,c_22]) ).
cnf(c_1106,plain,
idQb = divide(identity,idQ_idQb),
inference(resolve,[status(thm)],[c_1105,c_8]) ).
cnf(c_69,plain,
divide(identity,idQ_idQb) = idQb,
inference(copy,[status(thm)],[c_1106]) ).
cnf(c_1107,plain,
( idQa = B
| ~ quotient(identity,A,B)
| ~ quotient(identity,idQa,A) ),
inference(resolve,[status(thm)],[c_18,c_20]) ).
cnf(c_1108,plain,
( idQa = A
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_1107,c_24]) ).
cnf(c_1109,plain,
idQa = divide(identity,idQ_idQa),
inference(resolve,[status(thm)],[c_1108,c_8]) ).
cnf(c_93,plain,
divide(identity,idQ_idQa) = idQa,
inference(copy,[status(thm)],[c_1109]) ).
cnf(c_1110,plain,
( less_equal(D,E)
| ~ quotient(idQ_idQa,A,E)
| ~ quotient(C,B,D)
| ~ quotient(identity,A,C)
| ~ quotient(idQa,A,B) ),
inference(resolve,[status(thm)],[c_4,c_24]) ).
cnf(c_1111,plain,
( less_equal(B,C)
| ~ quotient(idQ_idQa,idQ_idQb,C)
| ~ quotient(A,idQa_Q__idQ_idQb,B)
| ~ quotient(identity,idQ_idQb,A) ),
inference(resolve,[status(thm)],[c_1110,c_23]) ).
cnf(c_1112,plain,
( less_equal(A,B)
| ~ quotient(idQ_idQa,idQ_idQb,B)
| ~ quotient(divide(identity,idQ_idQb),idQa_Q__idQ_idQb,A) ),
inference(resolve,[status(thm)],[c_1111,c_8]) ).
cnf(c_1113,plain,
( less_equal(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),A)
| ~ quotient(idQ_idQa,idQ_idQb,A) ),
inference(resolve,[status(thm)],[c_1112,c_8]) ).
cnf(c_1114,plain,
less_equal(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(resolve,[status(thm)],[c_1113,c_8]) ).
cnf(c_102,plain,
less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(paramod,[status(thm)],[c_69,c_1114]) ).
cnf(c_1115,plain,
( less_equal(D,E)
| ~ quotient(idQ_idQb,A,E)
| ~ quotient(C,B,D)
| ~ quotient(identity,A,C)
| ~ quotient(idQb,A,B) ),
inference(resolve,[status(thm)],[c_4,c_22]) ).
cnf(c_1116,plain,
( less_equal(B,C)
| ~ quotient(idQ_idQb,idQ_idQa,C)
| ~ quotient(A,idQb_Q__idQ_idQa,B)
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_1115,c_25]) ).
cnf(c_1117,plain,
( less_equal(A,B)
| ~ quotient(idQ_idQb,idQ_idQa,B)
| ~ quotient(divide(identity,idQ_idQa),idQb_Q__idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_1116,c_8]) ).
cnf(c_1118,plain,
( less_equal(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),A)
| ~ quotient(idQ_idQb,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_1117,c_8]) ).
cnf(c_1119,plain,
less_equal(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(resolve,[status(thm)],[c_1118,c_8]) ).
cnf(c_115,plain,
less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(paramod,[status(thm)],[c_93,c_1119]) ).
cnf(c_1120,plain,
( less_equal(divide(idQb,idQa_Q__idQ_idQb),A)
| ~ less_equal(divide(idQ_idQa,idQ_idQb),A) ),
inference(resolve,[status(thm)],[c_14,c_102]) ).
cnf(c_704,plain,
less_equal(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),
inference(resolve,[status(thm)],[c_1120,c_29]) ).
cnf(c_1121,plain,
( less_equal(divide(idQa,idQb_Q__idQ_idQa),A)
| ~ less_equal(divide(idQ_idQb,idQ_idQa),A) ),
inference(resolve,[status(thm)],[c_14,c_115]) ).
cnf(c_826,plain,
less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
inference(resolve,[status(thm)],[c_1121,c_29]) ).
cnf(c_1122,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_1123,plain,
( less_equal(A,idQa_Q__idQ_idQb)
| ~ quotient(idQb,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_1122,c_704]) ).
cnf(c_1039,plain,
less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(resolve,[status(thm)],[c_1123,c_25]) ).
cnf(c_1124,plain,
( idQa_Q__idQ_idQb = idQb_Q__idQ_idQa
| ~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa) ),
inference(resolve,[status(thm)],[c_6,c_1039]) ).
cnf(c_1125,plain,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
inference(copy,[status(thm)],[c_27]) ).
cnf(c_1052,plain,
~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(resolve,[status(thm)],[c_1124,c_1125]) ).
cnf(c_1126,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_1127,plain,
( less_equal(idQa_Q__idQ_idQb,A)
| ~ less_equal(divide(idQa,A),idQ_idQb) ),
inference(resolve,[status(thm)],[c_1126,c_23]) ).
cnf(c_1102,plain,
~ less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
inference(resolve,[status(thm)],[c_1127,c_1052]) ).
cnf(c_1103,plain,
$false,
inference(resolve,[status(thm)],[c_1102,c_826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN011-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 15:56:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1414367 was started by sandbox2 on n007,
% 0.09/0.37 % Fri Sep 25 15:56:09 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 6.22/1.24
% 6.22/1.24 % SZS status Unsatisfiable for theBenchmark
% 6.22/1.24
% 6.22/1.24 % Proof 1 at 0.59 (+ 0.25) seconds.
% 6.22/1.24 % Length of proof is 26.
% 6.22/1.24 % Level of proof is 7.
% 6.22/1.24 % Maximum clause weight is 28.000.
% 6.22/1.24 % Given clauses 173.
% 6.22/1.24
% 6.22/1.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------