%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:45:36 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 44 ( 29 unt; 0 nHn; 25 RR)
% Number of literals : 63 ( 32 equ; 23 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 : 62 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(quotient_less_equal2,axiom,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(a_divide_b_LE_d,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
cnf(prove_a_divide_d_LE_b,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
cnf(c_0_10,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_11,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_12,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_13,axiom,
divide(zero,X1) = zero,
zero_divide_anything_is_zero ).
cnf(c_0_14,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_10 ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_11 ).
cnf(c_0_17,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_19,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_20,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_21,plain,
( ~ less_equal(X1,zero)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( ~ less_equal(X1,X2)
| divide(X2,X1) != zero
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_23,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_19 ).
cnf(c_0_25,plain,
( ~ less_equal(X1,divide(X1,X2))
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_26,plain,
( divide(X1,zero) != zero
| X1 = zero ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_27,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13])]) ).
cnf(c_0_28,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_29,hypothesis,
less_equal(divide(a,b),d),
a_divide_b_LE_d ).
cnf(c_0_30,plain,
( divide(X1,divide(X1,X2)) != zero
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_31,plain,
divide(X1,divide(X1,zero)) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
less_equal(divide(divide(divide(X1,X2),X3),divide(X1,X3)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_28]),c_0_13]) ).
cnf(c_0_33,hypothesis,
divide(divide(a,b),d) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
~ less_equal(divide(a,d),b),
inference(fof_simplification,[status(thm)],[prove_a_divide_d_LE_b]) ).
cnf(c_0_35,plain,
( divide(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) != zero
| divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_36,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_13])]) ).
cnf(c_0_38,hypothesis,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
~ less_equal(divide(a,d),b),
c_0_34 ).
cnf(c_0_40,plain,
divide(divide(X1,divide(X2,X3)),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_36]),c_0_36]),c_0_37])]) ).
cnf(c_0_41,hypothesis,
divide(divide(a,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_38]),c_0_13])]) ).
cnf(c_0_42,negated_conjecture,
divide(divide(a,d),b) != zero,
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_13]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:49:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % new_bool_3 with pid 3910365 completed with status 0
% 0.14/0.42 % Result found by new_bool_3
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % SubtermCWHack with pid 3910370 completed with status 0
% 0.14/0.42 % Result found by SubtermCWHack
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 12
% 0.14/0.42 % Removed by relevancy pruning/SinE : 2
% 0.14/0.42 % Initial clauses : 10
% 0.14/0.42 % Removed in clause preprocessing : 0
% 0.14/0.42 % Initial clauses in saturation : 10
% 0.14/0.42 % Processed clauses : 90
% 0.14/0.42 % ...of these trivial : 15
% 0.14/0.42 % ...subsumed : 13
% 0.14/0.42 % ...remaining for further processing : 62
% 0.14/0.42 % Other redundant clauses eliminated : 0
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 0
% 0.14/0.42 % Backward-rewritten : 18
% 0.14/0.42 % Generated clauses : 1165
% 0.14/0.42 % ...of the previous two non-redundant : 369
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 0
% 0.14/0.42 % Paramodulations : 1165
% 0.14/0.42 % Factorizations : 0
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 0
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 2029
% 0.14/0.42 % ...of those cached : 1684
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.42 % Propositional unsat core size : 0
% 0.14/0.42 % Propositional preprocessing time : 0.000
% 0.14/0.42 % Propositional encoding time : 0.000
% 0.14/0.42 % Propositional solver time : 0.000
% 0.14/0.42 % Success case prop preproc time : 0.000
% 0.14/0.42 % Success case prop encoding time : 0.000
% 0.14/0.42 % Success case prop solver time : 0.000
% 0.14/0.42 % Current number of processed clauses : 44
% 0.14/0.42 % Positive orientable unit clauses : 31
% 0.14/0.42 % Positive unorientable unit clauses: 0
% 0.14/0.42 % Negative unit clauses : 2
% 0.14/0.42 % Non-unit-clauses : 11
% 0.14/0.42 % Current number of unprocessed clauses: 222
% 0.14/0.42 % ...number of literals in the above : 271
% 0.14/0.42 % Current number of archived formulas : 0
% 0.14/0.42 % Current number of archived clauses : 18
% 0.14/0.42 % Clause-clause subsumption calls (NU) : 32
% 0.14/0.42 % Rec. Clause-clause subsumption calls : 32
% 0.14/0.42 % Non-unit clause-clause subsumptions : 13
% 0.14/0.42 % Unit Clause-clause subsumption calls : 3
% 0.14/0.42 % Rewrite failures with RHS unbound : 0
% 0.14/0.42 % BW rewrite match attempts : 67
% 0.14/0.42 % BW rewrite match successes : 16
% 0.14/0.42 % Condensation attempts : 0
% 0.14/0.42 % Condensation successes : 0
% 0.14/0.42 % Termbank termtop insertions : 13071
% 0.14/0.42 % Search garbage collected termcells : 15
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.007 s
% 0.14/0.42 % System time : 0.002 s
% 0.14/0.42 % Total time : 0.009 s
% 0.14/0.42 % Maximum resident set size: 3640 pages
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.009 s
% 0.14/0.42 % System time : 0.004 s
% 0.14/0.42 % Total time : 0.013 s
% 0.14/0.42 % Maximum resident set size: 4864 pages
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------