%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-2 : 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 : n008.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 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 62 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 33 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(identity,idQ_idQa,idQ__idQ_idQa),
file('theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(c_20,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQ_idQa]) ).
fof(prove_one_inversion_equals_three,axiom,
idQa != idQ__idQ_idQa,
file('theBenchmark.p',prove_one_inversion_equals_three) ).
cnf(c_21,plain,
idQa != idQ__idQ_idQa,
inference(clausify,[status(thm)],[prove_one_inversion_equals_three]) ).
cnf(c_22,plain,
idQ__idQ_idQa != idQa,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_53,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_174,plain,
( less_equal(B,idQa)
| ~ quotient(identity,A,B)
| ~ less_equal(idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_175,plain,
( less_equal(A,idQa)
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_174,c_53]) ).
cnf(c_156,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(resolve,[status(thm)],[c_175,c_20]) ).
cnf(c_176,plain,
( less_equal(B,a)
| ~ quotient(identity,A,B)
| ~ less_equal(idQa,A) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_177,plain,
( less_equal(A,a)
| ~ quotient(identity,idQa,A) ),
inference(resolve,[status(thm)],[c_176,c_53]) ).
cnf(c_157,plain,
less_equal(idQ_idQa,a),
inference(resolve,[status(thm)],[c_177,c_19]) ).
cnf(c_178,plain,
( idQa = idQ__idQ_idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(resolve,[status(thm)],[c_156,c_6]) ).
cnf(c_179,plain,
( idQ__idQ_idQa = idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_161,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_22,c_179]) ).
cnf(c_180,plain,
( less_equal(B,C)
| ~ quotient(A,idQ_idQa,C)
| ~ quotient(A,a,B) ),
inference(resolve,[status(thm)],[c_16,c_157]) ).
cnf(c_181,plain,
( less_equal(idQa,A)
| ~ quotient(identity,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_180,c_18]) ).
cnf(c_182,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_181,c_20]) ).
cnf(c_173,plain,
$false,
inference(resolve,[status(thm)],[c_161,c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.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 15:58:24 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 1419147 was started by sandbox on n008,
% 0.09/0.35 % Fri Sep 25 15:58:24 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.43
% 0.13/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.43
% 0.13/0.43 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.13/0.43 % Length of proof is 15.
% 0.13/0.43 % Level of proof is 4.
% 0.13/0.43 % Maximum clause weight is 19.000.
% 0.13/0.43 % Given clauses 29.
% 0.13/0.43
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------