%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN010-2 : 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 : n026.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 07:32:02 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.66s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 27 unt; 0 def)
% Number of atoms : 100 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 83 ( 3 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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_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(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_19,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_20,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_21,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_22,plain,
idQa != idQa_Q__idQ_idQa,
inference(clausify,[status(thm)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(c_23,plain,
idQa_Q__idQ_idQa != idQa,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_132,plain,
( idQa = B
| ~ quotient(identity,A,B)
| ~ quotient(identity,idQa,A) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_133,plain,
( idQa = A
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_132,c_20]) ).
cnf(c_134,plain,
idQa = divide(identity,idQ_idQa),
inference(resolve,[status(thm)],[c_133,c_8]) ).
cnf(c_49,plain,
divide(identity,idQ_idQa) = idQa,
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,plain,
( less_equal(C,D)
| ~ quotient(identity,B,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_136,plain,
( less_equal(idQa_Q__idQ_idQa,A)
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_135,c_21]) ).
cnf(c_137,plain,
less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),
inference(resolve,[status(thm)],[c_136,c_8]) ).
cnf(c_59,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(paramod,[status(thm)],[c_49,c_137]) ).
cnf(c_138,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_20]) ).
cnf(c_139,plain,
( less_equal(B,C)
| ~ quotient(idQ_idQa,idQ_idQa,C)
| ~ quotient(A,idQa_Q__idQ_idQa,B)
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_138,c_21]) ).
cnf(c_140,plain,
( less_equal(A,B)
| ~ quotient(idQ_idQa,idQ_idQa,B)
| ~ quotient(divide(identity,idQ_idQa),idQa_Q__idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_139,c_8]) ).
cnf(c_141,plain,
( less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),A)
| ~ quotient(idQ_idQa,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_140,c_8]) ).
cnf(c_142,plain,
less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(resolve,[status(thm)],[c_141,c_12]) ).
cnf(c_65,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(paramod,[status(thm)],[c_49,c_142]) ).
cnf(c_143,plain,
( idQa = idQa_Q__idQ_idQa
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolve,[status(thm)],[c_6,c_59]) ).
cnf(c_144,plain,
idQa != idQa_Q__idQ_idQa,
inference(copy,[status(thm)],[c_23]) ).
cnf(c_87,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(resolve,[status(thm)],[c_143,c_144]) ).
cnf(c_145,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_146,plain,
( less_equal(A,B)
| ~ less_equal(divide(A,B),zero) ),
inference(resolve,[status(thm)],[c_145,c_13]) ).
cnf(c_130,plain,
~ less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(resolve,[status(thm)],[c_146,c_87]) ).
cnf(c_131,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n026.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 16:00:24 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 2959969 was started by sandbox2 on n026,
% 0.18/0.46 % Fri Sep 25 16:00:24 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.25/0.66
% 0.25/0.66 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.66
% 0.25/0.66 % Proof 1 at 0.11 (+ 0.07) seconds.
% 0.25/0.66 % Length of proof is 20.
% 0.25/0.66 % Level of proof is 5.
% 0.25/0.66 % Maximum clause weight is 23.000.
% 0.25/0.66 % Given clauses 33.
% 0.25/0.66
% 0.25/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------