%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN002-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:28:28 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of clauses : 39 ( 13 unt; 0 nHn; 29 RR)
% Number of literals : 89 ( 26 equ; 52 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(prove_zero_divide_anything_is_zero,negated_conjecture,
~ quotient(zero,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_divide_anything_is_zero) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(everything_divide_identity_is_zero,axiom,
quotient(X1,identity,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(i_0_11,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property,
[final] ).
cnf(i_0_12,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined,
[final] ).
cnf(i_0_13,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence,
[final] ).
cnf(i_0_14,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient,
[final] ).
cnf(i_0_15,axiom,
quotient(X1,X2,divide(X1,X2)),
closure,
[final] ).
cnf(i_0_16,negated_conjecture,
~ quotient(zero,x,zero),
prove_zero_divide_anything_is_zero,
[final] ).
cnf(i_0_17,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal,
[final] ).
cnf(i_0_18,axiom,
quotient(X1,identity,zero),
everything_divide_identity_is_zero,
[final] ).
cnf(i_0_19,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal,
[final] ).
cnf(i_0_20,axiom,
less_equal(zero,X1),
zero_is_smallest,
[final] ).
cnf(i_0_21,axiom,
less_equal(X1,identity),
identity_is_largest,
[final] ).
cnf(i_0_22,axiom,
X1 = X1 ).
cnf(i_0_23,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_24,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_25,axiom,
( X1 != X2
| ~ less_equal(X1,X3)
| less_equal(X2,X3) ) ).
cnf(i_0_26,axiom,
( X1 != X2
| ~ less_equal(X3,X1)
| less_equal(X3,X2) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| ~ quotient(X1,X3,X4)
| quotient(X2,X3,X4) ) ).
cnf(i_0_28,axiom,
( X1 != X2
| ~ quotient(X3,X1,X4)
| quotient(X3,X2,X4) ) ).
cnf(i_0_29,axiom,
( X1 != X2
| ~ quotient(X3,X4,X1)
| quotient(X3,X4,X2) ) ).
cnf(i_0_22_001,axiom,
X1 = X1 ).
cnf(i_0_23_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_24_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_25_004,axiom,
( X1 != X2
| ~ less_equal(X1,X3)
| less_equal(X2,X3) ) ).
cnf(i_0_26_005,axiom,
( X1 != X2
| ~ less_equal(X3,X1)
| less_equal(X3,X2) ) ).
cnf(i_0_27_006,axiom,
( X1 != X2
| ~ quotient(X1,X3,X4)
| quotient(X2,X3,X4) ) ).
cnf(i_0_28_007,axiom,
( X1 != X2
| ~ quotient(X3,X1,X4)
| quotient(X3,X2,X4) ) ).
cnf(i_0_29_008,axiom,
( X1 != X2
| ~ quotient(X3,X4,X1)
| quotient(X3,X4,X2) ) ).
cnf(i_0_30,plain,
$false,
inference(scs_inference,[],[i_0_16,i_0_20,i_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN002-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:07:59 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.62 % Total time : 1.271s
%------------------------------------------------------------------------------