%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN007-1 : 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 04:28:32 PM UTC 2026
% Result : Unsatisfiable 8.94s 5.72s
% Output : CNFRefutation 8.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of clauses : 79 ( 39 unt; 0 nHn; 60 RR)
% Number of literals : 154 ( 18 equ; 78 neg)
% Maximal clause size : 6 ( 1 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 : 149 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(xLEy,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQy) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQx) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
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,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_38,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_39,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_27])]) ).
cnf(c_0_40,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_41,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
cnf(c_0_42,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_43,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_18])]) ).
cnf(c_0_44,hypothesis,
less_equal(x,y),
xLEy ).
cnf(c_0_45,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X3,X2) ),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,hypothesis,
quotient(z,y,zQy),
zQy ).
cnf(c_0_47,hypothesis,
quotient(x,y,zero),
inference(spm,[status(thm)],[c_0_15,c_0_44]) ).
cnf(c_0_48,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_49,hypothesis,
( less_equal(zQy,divide(X1,y))
| ~ quotient(z,y,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,hypothesis,
( less_equal(divide(X1,zero),divide(X2,y))
| ~ quotient(X3,y,X1)
| ~ quotient(X3,x,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_51,hypothesis,
divide(zQy,y) = zQy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46])]) ).
cnf(c_0_52,hypothesis,
( less_equal(X1,divide(X2,y))
| ~ quotient(X3,y,X1)
| ~ quotient(X3,x,X2) ),
inference(rw,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_53,hypothesis,
quotient(zQy,y,zQy),
inference(spm,[status(thm)],[c_0_13,c_0_51]) ).
cnf(c_0_54,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_55,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_40,c_0_18]) ).
cnf(c_0_56,hypothesis,
( less_equal(zQy,divide(X1,y))
| ~ quotient(zQy,x,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( X1 = zero
| ~ quotient(zero,X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_58,hypothesis,
less_equal(zQy,z),
inference(spm,[status(thm)],[c_0_12,c_0_46]) ).
cnf(c_0_59,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(rw,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_60,hypothesis,
( quotient(zQy,divide(X1,y),zero)
| ~ quotient(zQy,x,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_56]) ).
cnf(c_0_61,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_57,c_0_13]) ).
cnf(c_0_62,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_63,hypothesis,
quotient(zQy,z,zero),
inference(spm,[status(thm)],[c_0_15,c_0_58]) ).
cnf(c_0_64,hypothesis,
( less_equal(X1,zero)
| ~ quotient(zQy,x,X2)
| ~ quotient(zQy,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_65,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(z,X3,X2)
| ~ quotient(zQy,X3,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,hypothesis,
quotient(z,x,zQx),
zQx ).
cnf(c_0_67,hypothesis,
( less_equal(X1,zero)
| ~ quotient(zQy,divide(zQy,x),X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_13]) ).
cnf(c_0_68,hypothesis,
( less_equal(divide(X1,zQx),zero)
| ~ quotient(zQy,x,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,hypothesis,
less_equal(divide(zQy,divide(zQy,x)),zero),
inference(spm,[status(thm)],[c_0_67,c_0_13]) ).
cnf(c_0_70,hypothesis,
( divide(X1,zQx) = zero
| ~ quotient(zQy,x,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_68]),c_0_27])]) ).
cnf(c_0_71,hypothesis,
divide(zQy,divide(zQy,x)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_69]),c_0_27])]) ).
cnf(c_0_72,hypothesis,
( quotient(X1,zQx,zero)
| ~ quotient(zQy,x,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_70]) ).
cnf(c_0_73,hypothesis,
quotient(zQy,divide(zQy,x),zero),
inference(spm,[status(thm)],[c_0_13,c_0_71]) ).
cnf(c_0_74,negated_conjecture,
~ less_equal(zQy,zQx),
prove_zQyLEzQx ).
cnf(c_0_75,hypothesis,
quotient(divide(zQy,x),zQx,zero),
inference(spm,[status(thm)],[c_0_72,c_0_13]) ).
cnf(c_0_76,hypothesis,
divide(zQy,x) = zQy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_73]),c_0_18])]) ).
cnf(c_0_77,negated_conjecture,
~ quotient(zQy,zQx,zero),
inference(spm,[status(thm)],[c_0_74,c_0_22]) ).
cnf(c_0_78,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN007-1 : 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
% 0.14/0.33 % Computer : n017.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:07:42 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 8.94/5.72 % Version : CSE_E---1.7
% 8.94/5.72 % Problem : theBenchmark.p
% 8.94/5.72 % SZS status Unsatisfiable for theBenchmark.p
% 8.94/5.72 % SZS output start CNFRefutation
% See solution above
% 8.94/5.75 % Total time : 4.372s
%------------------------------------------------------------------------------