%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN009-3 : 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 : n017.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 52 ( 41 unt; 0 nHn; 33 RR)
% Number of literals : 67 ( 42 equ; 18 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_a_is_b) ).
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(id_divide_b_is_c,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_b_is_c) ).
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(id_divide_c_is_d,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_c_is_d) ).
cnf(prove_b_equals_d,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_d) ).
cnf(c_0_11,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_12,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_13,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_14,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,plain,
( divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2)
| ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
divide(identity,a) = b,
id_divide_a_is_b ).
cnf(c_0_18,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_20,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_21,hypothesis,
divide(divide(X1,a),b) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_18]),c_0_19]),c_0_15])]) ).
cnf(c_0_22,plain,
( X1 = X2
| divide(X2,X1) != zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_23,hypothesis,
divide(divide(X1,b),divide(a,b)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_15])]) ).
cnf(c_0_24,hypothesis,
divide(identity,b) = c,
id_divide_b_is_c ).
cnf(c_0_25,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_26,plain,
( X1 = X2
| divide(X2,X1) != zero
| divide(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,hypothesis,
divide(c,divide(a,b)) = zero,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
divide(divide(X1,b),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_18]),c_0_19]),c_0_18]),c_0_19]),c_0_15])]) ).
cnf(c_0_29,hypothesis,
divide(identity,c) = d,
id_divide_c_is_d ).
cnf(c_0_30,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_31,hypothesis,
divide(a,b) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,hypothesis,
less_equal(divide(divide(identity,X1),divide(c,X1)),divide(d,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_29]) ).
cnf(c_0_33,hypothesis,
divide(c,a) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,hypothesis,
less_equal(divide(b,zero),divide(d,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17]) ).
cnf(c_0_35,hypothesis,
less_equal(divide(divide(identity,X1),divide(b,X1)),divide(c,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_36,hypothesis,
divide(c,c) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_37,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_38,hypothesis,
divide(divide(b,zero),divide(d,a)) = zero,
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_39,hypothesis,
less_equal(divide(d,divide(b,c)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29]) ).
cnf(c_0_40,plain,
( divide(X1,X2) = X1
| divide(X1,divide(X1,X2)) != zero ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_41,hypothesis,
divide(divide(divide(X1,c),d),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_18]),c_0_19]) ).
cnf(c_0_42,hypothesis,
divide(divide(b,divide(d,a)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_19]),c_0_19]),c_0_15])]) ).
cnf(c_0_43,hypothesis,
divide(d,divide(b,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_19])]) ).
cnf(c_0_44,hypothesis,
divide(divide(X1,c),d) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_45,hypothesis,
divide(b,divide(d,a)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_42])]) ).
cnf(c_0_46,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_47,hypothesis,
divide(b,c) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_43]),c_0_44])]) ).
cnf(c_0_48,negated_conjecture,
b != d,
prove_b_equals_d ).
cnf(c_0_49,hypothesis,
divide(d,a) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_21])]) ).
cnf(c_0_50,hypothesis,
~ less_equal(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-3 : 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
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:08:27 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------