%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN006-1 : 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 : n015.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 3.81s 3.13s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of clauses : 64 ( 31 unt; 0 nHn; 45 RR)
% Number of literals : 128 ( 16 equ; 67 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(xQyLEz,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz) ).
cnf(xQz,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQz) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(xQy,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQy) ).
cnf(prove_xQzLEy,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xQzLEy) ).
cnf(c_0_12,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_13,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_14,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_15,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_16,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_21,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_22,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_23,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_25,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_27,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_28,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ quotient(X1,X2,zero) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_30,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_31,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_32,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_13,c_0_31]) ).
cnf(c_0_33,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_34,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_35,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_36,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_35,c_0_13]) ).
cnf(c_0_37,hypothesis,
less_equal(xQy,z),
xQyLEz ).
cnf(c_0_38,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_27])]) ).
cnf(c_0_39,hypothesis,
quotient(xQy,z,zero),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
cnf(c_0_40,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_13,c_0_38]) ).
cnf(c_0_41,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,z,X2)
| ~ quotient(X4,z,X1)
| ~ quotient(X4,X3,xQy) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_42,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_40]),c_0_27])]) ).
cnf(c_0_43,hypothesis,
( less_equal(divide(X1,divide(X2,z)),zero)
| ~ quotient(X3,z,X1)
| ~ quotient(X3,X2,xQy) ),
inference(spm,[status(thm)],[c_0_41,c_0_13]) ).
cnf(c_0_44,hypothesis,
quotient(x,z,xQz),
xQz ).
cnf(c_0_45,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_46,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_13,c_0_42]) ).
cnf(c_0_47,hypothesis,
( less_equal(divide(xQz,divide(X1,z)),zero)
| ~ quotient(x,X1,xQy) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_49,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_50,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_46]),c_0_18])]) ).
cnf(c_0_51,hypothesis,
( divide(xQz,divide(X1,z)) = zero
| ~ quotient(x,X1,xQy) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_47]),c_0_27])]) ).
cnf(c_0_52,plain,
( X1 = zero
| ~ quotient(zero,X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_27]) ).
cnf(c_0_53,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,hypothesis,
( quotient(xQz,divide(X1,z),zero)
| ~ quotient(x,X1,xQy) ),
inference(spm,[status(thm)],[c_0_13,c_0_51]) ).
cnf(c_0_55,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_52,c_0_13]) ).
cnf(c_0_56,hypothesis,
( less_equal(X1,zero)
| ~ quotient(x,X2,xQy)
| ~ quotient(xQz,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_57,hypothesis,
quotient(x,y,xQy),
xQy ).
cnf(c_0_58,hypothesis,
( less_equal(X1,zero)
| ~ quotient(xQz,y,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_59,hypothesis,
( X1 = zero
| ~ quotient(xQz,y,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_58]),c_0_27])]) ).
cnf(c_0_60,negated_conjecture,
~ less_equal(xQz,y),
prove_xQzLEy ).
cnf(c_0_61,hypothesis,
divide(xQz,y) = zero,
inference(spm,[status(thm)],[c_0_59,c_0_13]) ).
cnf(c_0_62,negated_conjecture,
~ quotient(xQz,y,zero),
inference(spm,[status(thm)],[c_0_60,c_0_22]) ).
cnf(c_0_63,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN006-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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 : n015.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 19:09:17 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 3.81/3.13 % Version : CSE_E---1.7
% 3.81/3.13 % Problem : theBenchmark.p
% 3.81/3.13 % SZS status Unsatisfiable for theBenchmark.p
% 3.81/3.13 % SZS output start CNFRefutation
% See solution above
% 3.81/3.15 % Total time : 2.374s
%------------------------------------------------------------------------------