%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HEN008-2 : 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 : n008.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 04:28:33 PM UTC 2026
% Result : Unsatisfiable 23.31s 14.16s
% Output : CNFRefutation 23.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 63 ( 26 unt; 0 nHn; 49 RR)
% Number of literals : 137 ( 10 equ; 76 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 : 140 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xQyLEz_implies_xQzLEy,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
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(aLEb,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
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(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(x_divide_x_is_zero,axiom,
quotient(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/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(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(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_0_17,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
xQyLEz_implies_xQzLEy ).
cnf(c_0_18,hypothesis,
quotient(a,c,aQc),
aQc ).
cnf(c_0_19,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_20,hypothesis,
less_equal(a,b),
aLEb ).
cnf(c_0_21,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_22,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_23,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_24,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
xLEy_implies_zQyLEzQx ).
cnf(c_0_25,hypothesis,
( less_equal(aQc,X1)
| ~ quotient(a,X1,X2)
| ~ less_equal(X2,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,hypothesis,
quotient(a,b,zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_28,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_30,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_31,plain,
( less_equal(X1,X2)
| ~ quotient(X1,X3,X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_32,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_33,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_34,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_35,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_21,c_0_23]) ).
cnf(c_0_36,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_37,hypothesis,
less_equal(aQc,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_38,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_39,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_40,plain,
( less_equal(divide(X1,X2),X3)
| ~ less_equal(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_41,plain,
( less_equal(X1,divide(X1,X2))
| ~ less_equal(X2,zero) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_42,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
( less_equal(divide(X1,X2),zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_44,plain,
( X1 = X2
| ~ quotient(X2,zero,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_45,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_35,c_0_36]) ).
cnf(c_0_46,hypothesis,
quotient(aQc,b,zero),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_47,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_48,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_49,plain,
( less_equal(divide(X1,divide(divide(X1,X2),X3)),X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36])]) ).
cnf(c_0_51,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_23]) ).
cnf(c_0_52,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(b,X3,X2)
| ~ quotient(aQc,X3,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,hypothesis,
quotient(b,c,bQc),
bQc ).
cnf(c_0_54,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_55,hypothesis,
( less_equal(aQc,divide(X1,c))
| ~ quotient(a,c,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_18]) ).
cnf(c_0_56,plain,
( less_equal(X1,X2)
| ~ less_equal(divide(X1,X2),X3)
| ~ less_equal(X3,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,hypothesis,
( less_equal(divide(X1,bQc),zero)
| ~ quotient(aQc,c,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,hypothesis,
divide(aQc,c) = aQc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_18])]) ).
cnf(c_0_59,negated_conjecture,
~ less_equal(aQc,bQc),
prove_aQcLEbQc ).
cnf(c_0_60,hypothesis,
( less_equal(X1,bQc)
| ~ quotient(aQc,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_27])]) ).
cnf(c_0_61,hypothesis,
quotient(aQc,c,aQc),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN008-2 : 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 : n008.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 19:08:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 23.31/14.16 % Version : CSE_E---1.7
% 23.31/14.16 % Problem : theBenchmark.p
% 23.31/14.16 % SZS status Unsatisfiable for theBenchmark.p
% 23.31/14.16 % SZS output start CNFRefutation
% See solution above
% 23.39/14.26 % Total time : 10.385s
%------------------------------------------------------------------------------