%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:45:39 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 57 ( 43 unt; 0 nHn; 37 RR)
% Number of literals : 76 ( 43 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(id_divide_a_is_b,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
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(id_divide_c_is_d,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
cnf(prove_b_equals_d,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
cnf(c_0_11,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_12,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_13,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_14,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_11 ).
cnf(c_0_15,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_16,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_17,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_12 ).
cnf(c_0_18,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_13 ).
cnf(c_0_19,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_20,hypothesis,
divide(identity,a) = b,
id_divide_a_is_b ).
cnf(c_0_21,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_23,plain,
( ~ less_equal(X1,X2)
| divide(X2,X1) != zero
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,hypothesis,
less_equal(divide(divide(X1,a),b),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_25,hypothesis,
divide(divide(X1,a),b) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]) ).
cnf(c_0_26,hypothesis,
less_equal(divide(divide(X1,b),divide(a,b)),zero),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_27,hypothesis,
divide(identity,b) = c,
id_divide_b_is_c ).
cnf(c_0_28,hypothesis,
less_equal(divide(c,divide(a,b)),zero),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,hypothesis,
less_equal(divide(divide(X1,b),c),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_21]),c_0_22]) ).
cnf(c_0_30,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_31,plain,
( divide(X1,X2) != zero
| divide(X2,X1) != zero
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_32,hypothesis,
divide(c,divide(a,b)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_22])]) ).
cnf(c_0_33,hypothesis,
divide(divide(X1,b),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_22])]) ).
cnf(c_0_34,hypothesis,
divide(identity,c) = d,
id_divide_c_is_d ).
cnf(c_0_35,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_36,hypothesis,
divide(a,b) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,hypothesis,
less_equal(divide(divide(identity,X1),divide(c,X1)),divide(d,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_34]) ).
cnf(c_0_38,hypothesis,
divide(c,a) = zero,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,hypothesis,
less_equal(divide(b,zero),divide(d,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_20]) ).
cnf(c_0_40,hypothesis,
less_equal(divide(divide(X1,c),divide(b,c)),zero),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_41,plain,
( ~ less_equal(X1,divide(X1,X2))
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_42,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_23,c_0_19]) ).
cnf(c_0_43,hypothesis,
divide(divide(b,zero),divide(d,a)) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_39]) ).
cnf(c_0_44,hypothesis,
less_equal(divide(d,divide(b,c)),zero),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_45,hypothesis,
less_equal(divide(divide(X1,c),d),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_21]),c_0_22]) ).
cnf(c_0_46,plain,
( divide(X1,divide(X1,X2)) != zero
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_47,hypothesis,
divide(divide(b,divide(d,a)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_48,hypothesis,
divide(d,divide(b,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_22])]) ).
cnf(c_0_49,hypothesis,
divide(divide(X1,c),d) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_45]),c_0_22])]) ).
cnf(c_0_50,negated_conjecture,
b != d,
inference(fof_simplification,[status(thm)],[prove_b_equals_d]) ).
cnf(c_0_51,hypothesis,
divide(b,divide(d,a)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_47])]) ).
cnf(c_0_52,hypothesis,
divide(b,c) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_48]),c_0_49])]) ).
cnf(c_0_53,negated_conjecture,
b != d,
c_0_50 ).
cnf(c_0_54,hypothesis,
divide(d,a) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_25])]) ).
cnf(c_0_55,hypothesis,
~ less_equal(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_52]),c_0_53]) ).
cnf(c_0_56,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:48:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % sh5l with pid 166281 completed with status 0
% 0.10/0.44 % Result found by sh5l
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FHUSM-FFSS22-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 166288 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FHUSM-FFSS22-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 12
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 12
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 12
% 0.10/0.44 % Processed clauses : 160
% 0.10/0.44 % ...of these trivial : 23
% 0.10/0.44 % ...subsumed : 39
% 0.10/0.44 % ...remaining for further processing : 98
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 33
% 0.10/0.44 % Generated clauses : 1209
% 0.10/0.44 % ...of the previous two non-redundant : 636
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 1209
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 0
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 1768
% 0.10/0.44 % ...of those cached : 1412
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 65
% 0.10/0.44 % Positive orientable unit clauses : 42
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 3
% 0.10/0.44 % Non-unit-clauses : 20
% 0.10/0.44 % Current number of unprocessed clauses: 422
% 0.10/0.44 % ...number of literals in the above : 597
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 33
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 41
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 41
% 0.10/0.44 % Non-unit clause-clause subsumptions : 34
% 0.10/0.44 % Unit Clause-clause subsumption calls : 13
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 75
% 0.10/0.44 % BW rewrite match successes : 29
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 14542
% 0.10/0.44 % Search garbage collected termcells : 12
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.012 s
% 0.10/0.44 % System time : 0.005 s
% 0.10/0.44 % Total time : 0.017 s
% 0.10/0.44 % Maximum resident set size: 3640 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.014 s
% 0.10/0.44 % System time : 0.009 s
% 0.10/0.44 % Total time : 0.023 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------