%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN010-3 : 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 : n001.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 1.54s 1.82s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of clauses : 50 ( 42 unt; 0 nHn; 11 RR)
% Number of literals : 60 ( 29 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 106 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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(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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_inversion) ).
cnf(c_0_7,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_8,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_9,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_10,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_11,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_7,c_0_8]) ).
cnf(c_0_12,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_14,plain,
divide(divide(X1,X1),divide(X2,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_15,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_16,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_17,plain,
divide(divide(X1,X1),zero) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_20,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_13])]) ).
cnf(c_0_21,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_21]),c_0_13])]) ).
cnf(c_0_23,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_24,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_13])]) ).
cnf(c_0_25,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_26,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_25]),c_0_10])]) ).
cnf(c_0_27,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_15]),c_0_15]),c_0_13])]) ).
cnf(c_0_28,plain,
less_equal(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_12]),c_0_26]) ).
cnf(c_0_29,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_30,plain,
divide(divide(X1,divide(X2,X3)),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_28]),c_0_29])]) ).
cnf(c_0_31,plain,
less_equal(divide(X1,X2),divide(divide(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_20]),c_0_26]) ).
cnf(c_0_32,plain,
less_equal(divide(divide(divide(X1,X2),X3),X1),zero),
inference(spm,[status(thm)],[c_0_29,c_0_12]) ).
cnf(c_0_33,plain,
less_equal(divide(X1,X2),divide(X1,divide(X2,X3))),
inference(spm,[status(thm)],[c_0_10,c_0_30]) ).
cnf(c_0_34,plain,
divide(divide(X1,X2),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_31]),c_0_29])]) ).
cnf(c_0_35,plain,
divide(divide(divide(X1,X2),X3),X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_32]),c_0_13])]) ).
cnf(c_0_36,plain,
less_equal(divide(X1,X2),divide(divide(X1,X2),divide(X2,X3))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
less_equal(divide(divide(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_16,c_0_35]) ).
cnf(c_0_38,plain,
divide(divide(X1,X2),divide(X2,X3)) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_36]),c_0_10])]) ).
cnf(c_0_39,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,divide(X2,X4))),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_40,plain,
divide(divide(divide(X1,X2),X3),divide(X2,X4)) = divide(divide(X1,X2),divide(X3,divide(X2,X4))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_38]),c_0_39])]) ).
cnf(c_0_41,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_42,plain,
divide(divide(divide(X1,X2),X3),X2) = divide(divide(X1,X2),divide(X3,X2)),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_43,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).
cnf(c_0_44,plain,
less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),
inference(rw,[status(thm)],[c_0_8,c_0_43]) ).
cnf(c_0_45,plain,
divide(divide(X1,X2),X3) = divide(divide(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_44]),c_0_44])]) ).
cnf(c_0_46,plain,
divide(divide(X1,X2),divide(divide(X3,X2),X4)) = divide(divide(X1,X2),divide(X3,X4)),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
prove_property_of_inversion ).
cnf(c_0_48,plain,
divide(divide(X1,X2),divide(X3,divide(X3,X2))) = divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_20]),c_0_26]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN010-3 : 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
% 0.15/0.33 % Computer : n001.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 19:10:18 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.54/1.82 % Version : CSE_E---1.7
% 1.54/1.82 % Problem : theBenchmark.p
% 1.54/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.54/1.82 % SZS output start CNFRefutation
% See solution above
% 1.54/1.82 % Total time : 1.371s
%------------------------------------------------------------------------------