%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN010-3 : 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 : n008.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 0.48s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 60 ( 44 unt; 0 nHn; 21 RR)
% Number of literals : 81 ( 49 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 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(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(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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_inversion) ).
cnf(c_0_8,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_9,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_8 ).
cnf(c_0_10,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_11,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_12,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_13,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_14,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_11 ).
cnf(c_0_17,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_12 ).
cnf(c_0_18,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_20,plain,
( ~ less_equal(X1,divide(X1,X2))
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_21,plain,
( ~ less_equal(X1,X2)
| divide(X2,X1) != zero
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( divide(X1,divide(X1,X2)) != zero
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_24,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19])]) ).
cnf(c_0_25,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_26,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_27,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).
cnf(c_0_28,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_29,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_30,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
divide(divide(divide(X1,X2),divide(identity,X2)),zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19]) ).
cnf(c_0_32,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_19])]) ).
cnf(c_0_33,plain,
( divide(X1,X2) != zero
| divide(X2,X1) != zero
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_34,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_31]),c_0_31])]) ).
cnf(c_0_35,plain,
( ~ less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),divide(X2,X3)))
| divide(divide(X1,X2),X3) = divide(divide(X1,X3),divide(X2,X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_36,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_32]),c_0_32])]) ).
cnf(c_0_37,plain,
( divide(divide(identity,X1),divide(X2,X1)) != zero
| divide(identity,X1) = divide(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
divide(divide(X1,divide(identity,X2)),divide(X2,divide(identity,X2))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_15])]) ).
cnf(c_0_39,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_40,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_36]),c_0_14])]) ).
cnf(c_0_41,plain,
divide(identity,divide(identity,X1)) = divide(X1,divide(identity,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
less_equal(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
divide(divide(X1,divide(X1,X2)),divide(X2,divide(X1,X2))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_27]),c_0_15])]) ).
cnf(c_0_44,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
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_14]),c_0_19]),c_0_19]),c_0_15])]) ).
cnf(c_0_45,plain,
divide(divide(identity,divide(identity,X1)),X1) = zero,
inference(spm,[status(thm)],[c_0_14,c_0_41]) ).
cnf(c_0_46,plain,
less_equal(divide(divide(X1,divide(X1,X2)),X2),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_19]) ).
cnf(c_0_47,plain,
divide(divide(divide(identity,divide(identity,X1)),X2),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40]) ).
cnf(c_0_48,plain,
divide(divide(X1,divide(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_46]),c_0_40]) ).
cnf(c_0_49,plain,
divide(divide(identity,divide(identity,divide(identity,divide(identity,X1)))),X1) = zero,
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_50,plain,
( divide(X2,divide(X1,divide(X1,X2))) != zero
| divide(X1,divide(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_51,plain,
divide(divide(identity,X1),divide(divide(identity,divide(identity,divide(identity,X1))),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_49]),c_0_40]) ).
cnf(c_0_52,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(fof_simplification,[status(thm)],[prove_property_of_inversion]) ).
cnf(c_0_53,plain,
divide(divide(identity,divide(identity,divide(identity,X1))),X1) = divide(identity,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40]),c_0_40]),c_0_34])]) ).
cnf(c_0_54,plain,
less_equal(divide(identity,divide(identity,X1)),X1),
inference(spm,[status(thm)],[c_0_10,c_0_41]) ).
cnf(c_0_55,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
c_0_52 ).
cnf(c_0_56,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_53]),c_0_54])]) ).
cnf(c_0_57,negated_conjecture,
divide(identity,divide(a,divide(identity,a))) != divide(identity,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_41]),c_0_41]) ).
cnf(c_0_58,plain,
divide(identity,divide(X1,divide(identity,X1))) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-3 : 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 : n008.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 20:47:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.47 % Version: 3.5.1
% 0.10/0.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.47 % Starting sh5l with 300s (1) cores
% 0.10/0.47 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3580174 completed with status 0
% 0.10/0.47 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.10/0.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.47 % No SInE strategy applied
% 0.10/0.47 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.10/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.10/0.47 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.10/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.48 % U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3580179 completed with status 0
% 0.10/0.48 % Result found by U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.48 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.48 % No SInE strategy applied
% 0.10/0.48 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.10/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.48 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.10/0.48 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.48 % Preprocessing time : 0.001 s
% 0.10/0.48 % Presaturation interreduction done
% 0.10/0.48
% 0.10/0.48 % Proof found!
% 0.10/0.48 % SZS status Unsatisfiable
% 0.10/0.48 % SZS output start CNFRefutation
% See solution above
% 0.10/0.48 % Parsed axioms : 8
% 0.10/0.48 % Removed by relevancy pruning/SinE : 0
% 0.10/0.48 % Initial clauses : 8
% 0.10/0.48 % Removed in clause preprocessing : 0
% 0.10/0.48 % Initial clauses in saturation : 8
% 0.10/0.48 % Processed clauses : 275
% 0.10/0.48 % ...of these trivial : 33
% 0.10/0.48 % ...subsumed : 135
% 0.10/0.48 % ...remaining for further processing : 107
% 0.10/0.48 % Other redundant clauses eliminated : 0
% 0.10/0.48 % Clauses deleted for lack of memory : 0
% 0.10/0.48 % Backward-subsumed : 5
% 0.10/0.48 % Backward-rewritten : 32
% 0.10/0.48 % Generated clauses : 3599
% 0.10/0.48 % ...of the previous two non-redundant : 1271
% 0.10/0.48 % ...aggressively subsumed : 0
% 0.10/0.48 % Contextual simplify-reflections : 1
% 0.10/0.48 % Paramodulations : 3599
% 0.10/0.48 % Factorizations : 0
% 0.10/0.48 % NegExts : 0
% 0.10/0.48 % Equation resolutions : 0
% 0.10/0.48 % Disequality decompositions : 0
% 0.10/0.48 % Total rewrite steps : 7387
% 0.10/0.48 % ...of those cached : 6599
% 0.10/0.48 % Propositional unsat checks : 0
% 0.10/0.48 % Propositional check models : 0
% 0.10/0.48 % Propositional check unsatisfiable : 0
% 0.10/0.48 % Propositional clauses : 0
% 0.10/0.48 % Propositional clauses after purity: 0
% 0.10/0.48 % Propositional unsat core size : 0
% 0.10/0.48 % Propositional preprocessing time : 0.000
% 0.10/0.48 % Propositional encoding time : 0.000
% 0.10/0.48 % Propositional solver time : 0.000
% 0.10/0.48 % Success case prop preproc time : 0.000
% 0.10/0.48 % Success case prop encoding time : 0.000
% 0.10/0.48 % Success case prop solver time : 0.000
% 0.10/0.48 % Current number of processed clauses : 62
% 0.10/0.48 % Positive orientable unit clauses : 32
% 0.10/0.48 % Positive unorientable unit clauses: 1
% 0.10/0.48 % Negative unit clauses : 2
% 0.10/0.48 % Non-unit-clauses : 27
% 0.10/0.48 % Current number of unprocessed clauses: 899
% 0.10/0.48 % ...number of literals in the above : 1169
% 0.10/0.48 % Current number of archived formulas : 0
% 0.10/0.48 % Current number of archived clauses : 45
% 0.10/0.48 % Clause-clause subsumption calls (NU) : 378
% 0.10/0.48 % Rec. Clause-clause subsumption calls : 378
% 0.10/0.48 % Non-unit clause-clause subsumptions : 114
% 0.10/0.48 % Unit Clause-clause subsumption calls : 21
% 0.10/0.48 % Rewrite failures with RHS unbound : 0
% 0.10/0.48 % BW rewrite match attempts : 150
% 0.10/0.48 % BW rewrite match successes : 30
% 0.10/0.48 % Condensation attempts : 0
% 0.10/0.48 % Condensation successes : 0
% 0.10/0.48 % Termbank termtop insertions : 44671
% 0.10/0.48 % Search garbage collected termcells : 10
% 0.10/0.48
% 0.10/0.48 % -------------------------------------------------
% 0.10/0.48 % User time : 0.033 s
% 0.10/0.48 % System time : 0.005 s
% 0.10/0.48 % Total time : 0.038 s
% 0.10/0.48 % Maximum resident set size: 3640 pages
% 0.10/0.48
% 0.10/0.48 % -------------------------------------------------
% 0.10/0.48 % User time : 0.158 s
% 0.10/0.48 % System time : 0.024 s
% 0.10/0.48 % Total time : 0.182 s
% 0.10/0.48 % Maximum resident set size: 4608 pages
% 0.10/0.48 % E exiting
%------------------------------------------------------------------------------