%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN006-3 : 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 04:28:31 PM UTC 2026
% Result : Unsatisfiable 1.11s 1.86s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of clauses : 37 ( 31 unt; 0 nHn; 16 RR)
% Number of literals : 45 ( 17 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(a_divide_b_LE_d,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
cnf(prove_a_divide_d_LE_b,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
cnf(c_0_8,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_9,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_10,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_11,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_13,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_15,plain,
divide(divide(X1,X1),divide(X2,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_16,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_17,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_18,plain,
divide(divide(X1,X1),zero) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_21,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_19]),c_0_14])]) ).
cnf(c_0_22,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_22]),c_0_14])]) ).
cnf(c_0_24,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_25,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_14])]) ).
cnf(c_0_26,hypothesis,
less_equal(divide(a,b),d),
a_divide_b_LE_d ).
cnf(c_0_27,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_28,hypothesis,
divide(divide(a,b),d) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_26]) ).
cnf(c_0_29,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_27]),c_0_9])]) ).
cnf(c_0_30,hypothesis,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_31,plain,
less_equal(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_29]) ).
cnf(c_0_32,hypothesis,
divide(divide(a,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_14])]) ).
cnf(c_0_33,hypothesis,
less_equal(divide(divide(a,d),b),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_16]) ).
cnf(c_0_34,hypothesis,
divide(divide(a,d),b) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_33]),c_0_29]) ).
cnf(c_0_35,negated_conjecture,
~ less_equal(divide(a,d),b),
prove_a_divide_d_LE_b ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.18 % Problem : HEN006-3 : TPTP v9.2.1. Released v1.0.0.
% 0.07/0.18 % 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
% 0.12/0.41 % Computer : n019.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8042.1875MB
% 0.12/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon May 4 19:09:14 EDT 2026
% 0.12/0.43 % CPUTime :
% 0.14/0.45 % start to proof: theBenchmark
% 1.11/1.86 % Version : CSE_E---1.7
% 1.11/1.86 % Problem : theBenchmark.p
% 1.11/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.86 % SZS output start CNFRefutation
% See solution above
% 1.11/1.86 % Total time : 1.382s
%------------------------------------------------------------------------------