%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN002-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of clauses : 31 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 57 ( 32 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(quotient_less_equal1,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(prove_zero_over_a_is_zero,negated_conjecture,
divide(zero,a) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_over_a_is_zero) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(i_0_8,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property,
[final] ).
cnf(i_0_9,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal,
[final] ).
cnf(i_0_10,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator,
[final] ).
cnf(i_0_11,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2,
[final] ).
cnf(i_0_12,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1,
[final] ).
cnf(i_0_13,negated_conjecture,
divide(zero,a) != zero,
prove_zero_over_a_is_zero,
[final] ).
cnf(i_0_14,axiom,
less_equal(zero,X1),
zero_is_smallest,
[final] ).
cnf(i_0_15,axiom,
less_equal(X1,identity),
identity_is_largest,
[final] ).
cnf(i_0_16,axiom,
X1 = X1 ).
cnf(i_0_17,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_19,axiom,
( X1 != X2
| divide(X1,X3) = divide(X2,X3) ) ).
cnf(i_0_20,axiom,
( X1 != X2
| divide(X3,X1) = divide(X3,X2) ) ).
cnf(i_0_21,axiom,
( X1 != X2
| ~ less_equal(X1,X3)
| less_equal(X2,X3) ) ).
cnf(i_0_22,axiom,
( X1 != X2
| ~ less_equal(X3,X1)
| less_equal(X3,X2) ) ).
cnf(i_0_16_001,axiom,
X1 = X1 ).
cnf(i_0_17_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_19_004,axiom,
( X1 != X2
| divide(X1,X3) = divide(X2,X3) ) ).
cnf(i_0_20_005,axiom,
( X1 != X2
| divide(X3,X1) = divide(X3,X2) ) ).
cnf(i_0_21_006,axiom,
( X1 != X2
| ~ less_equal(X1,X3)
| less_equal(X2,X3) ) ).
cnf(i_0_22_007,axiom,
( X1 != X2
| ~ less_equal(X3,X1)
| less_equal(X3,X2) ) ).
cnf(i_0_23,plain,
$false,
inference(scs_inference,[],[i_0_13,i_0_10,i_0_14,i_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN002-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:07:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.25/1.62 % Version : CSE_E---1.7
% 0.25/1.62 % Problem : theBenchmark.p
% 0.25/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.62 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------