%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN009-6 : 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 : n029.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 04:28:34 PM UTC 2026
% Result : Unsatisfiable 1.32s 1.78s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 24 unt; 0 nHn; 29 RR)
% Number of literals : 59 ( 20 equ; 22 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_divide3,axiom,
( less_equal(divide(X1,X3),divide(X2,X3))
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(property_of_divide1,axiom,
( less_equal(divide(X1,X3),X2)
| ~ less_equal(divide(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
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_less_equal1,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(id_divide_c_is_d,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(prove_b_equals_d,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
cnf(c_0_11,axiom,
( less_equal(divide(X1,X3),divide(X2,X3))
| ~ less_equal(X1,X2) ),
property_of_divide3 ).
cnf(c_0_12,hypothesis,
divide(identity,a) = b,
id_divide_a_is_b ).
cnf(c_0_13,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_14,axiom,
( less_equal(divide(X1,X3),X2)
| ~ less_equal(divide(X1,X2),X3) ),
property_of_divide1 ).
cnf(c_0_15,hypothesis,
less_equal(divide(X1,a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,hypothesis,
( less_equal(divide(identity,X1),a)
| ~ less_equal(b,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_17,hypothesis,
divide(identity,b) = c,
id_divide_b_is_c ).
cnf(c_0_18,hypothesis,
less_equal(b,b),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_19,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_20,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_21,hypothesis,
less_equal(c,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_22,hypothesis,
divide(identity,c) = d,
id_divide_c_is_d ).
cnf(c_0_23,hypothesis,
less_equal(divide(X1,b),c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_17]),c_0_13])]) ).
cnf(c_0_24,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_25,plain,
( divide(X1,X2) = divide(X3,X2)
| ~ less_equal(divide(X1,X2),divide(X3,X2))
| ~ less_equal(X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_26,hypothesis,
divide(c,a) = zero,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_28,hypothesis,
less_equal(divide(X1,c),d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_13])]) ).
cnf(c_0_29,hypothesis,
( less_equal(divide(identity,X1),b)
| ~ less_equal(c,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_30,hypothesis,
less_equal(c,c),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_31,plain,
( less_equal(divide(X1,X2),X3)
| divide(divide(X1,X3),X2) != zero ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_32,hypothesis,
( divide(X1,a) = zero
| ~ less_equal(X1,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_33,hypothesis,
less_equal(divide(X1,d),c),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_34,hypothesis,
less_equal(d,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
b != d,
prove_b_equals_d ).
cnf(c_0_36,hypothesis,
( less_equal(b,X1)
| divide(divide(identity,X1),a) != zero ),
inference(spm,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_37,hypothesis,
divide(divide(X1,d),a) = zero,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
~ less_equal(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_35]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-6 : 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
% 0.12/0.31 % Computer : n029.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 4 19:09:59 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 1.32/1.78 % Version : CSE_E---1.7
% 1.32/1.78 % Problem : theBenchmark.p
% 1.32/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.32/1.78 % SZS output start CNFRefutation
% See solution above
% 1.32/1.78 % Total time : 1.373s
%------------------------------------------------------------------------------