%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN011-4 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n002.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 04:28:36 PM UTC 2026
% Result : Unsatisfiable 2.03s 1.97s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 48 ( 30 unt; 0 nHn; 17 RR)
% Number of literals : 70 ( 21 equ; 24 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 : 102 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(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(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(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(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(property_of_divide2,axiom,
( less_equal(divide(X3,X2),divide(X3,X1))
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
cnf(prove_this,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_12,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_13,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_14,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,axiom,
( less_equal(divide(X1,X3),X2)
| ~ less_equal(divide(X1,X2),X3) ),
property_of_divide1 ).
cnf(c_0_17,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
divide(X1,divide(X1,zero)) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_22,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_23,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_24,plain,
divide(divide(X1,divide(X1,X2)),X2) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_25,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_26,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_22]),c_0_23])]) ).
cnf(c_0_27,axiom,
( less_equal(divide(X1,X3),divide(X2,X3))
| ~ less_equal(X1,X2) ),
property_of_divide3 ).
cnf(c_0_28,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_29,plain,
less_equal(divide(divide(X1,divide(X1,X2)),X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_15])]) ).
cnf(c_0_30,plain,
less_equal(divide(X1,X2),divide(divide(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_26]) ).
cnf(c_0_31,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_32,plain,
( less_equal(X1,X2)
| ~ less_equal(X1,divide(divide(X3,divide(X3,X2)),X4)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
less_equal(divide(divide(X1,divide(X1,X2)),X3),divide(X2,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
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_14,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
less_equal(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_36,plain,
( divide(divide(X1,X2),X3) = divide(X1,X3)
| ~ less_equal(divide(X1,X3),divide(divide(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_37,plain,
less_equal(divide(X1,divide(X1,X2)),divide(X2,divide(X1,X2))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,axiom,
( less_equal(divide(X3,X2),divide(X3,X1))
| ~ less_equal(X1,X2) ),
property_of_divide2 ).
cnf(c_0_39,plain,
less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_35]) ).
cnf(c_0_40,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_41,plain,
divide(divide(X1,X2),divide(X1,divide(X1,X2))) = divide(X1,divide(X1,divide(X1,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
less_equal(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_43,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_14,c_0_39]),c_0_39])]) ).
cnf(c_0_44,plain,
divide(X1,divide(X1,divide(X1,X2))) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
prove_this ).
cnf(c_0_46,plain,
divide(divide(X1,X2),divide(X1,divide(X1,X3))) = divide(divide(X1,X3),X2),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-4 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 19:09:31 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 2.03/1.97 % Version : CSE_E---1.7
% 2.03/1.97 % Problem : theBenchmark.p
% 2.03/1.97 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.97 % SZS output start CNFRefutation
% See solution above
% 2.03/1.97 % Total time : 1.373s
%------------------------------------------------------------------------------