%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.14s 5.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 54 ( 35 unt; 0 nHn; 27 RR)
% Number of literals : 76 ( 30 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 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 : 78 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_divide3,axiom,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).
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(property_of_divide1,axiom,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
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_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(x_divide_zero_is_x,axiom,
divide(a,zero) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
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(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(prove_this,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_12,plain,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
inference(fof_simplification,[status(thm)],[property_of_divide3]) ).
cnf(c_0_13,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_14,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[property_of_divide1]) ).
cnf(c_0_15,plain,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
c_0_12 ).
cnf(c_0_16,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_17,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_13 ).
cnf(c_0_18,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_19,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
c_0_14 ).
cnf(c_0_20,plain,
less_equal(divide(X1,X2),divide(identity,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_22,plain,
( ~ less_equal(X1,zero)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
less_equal(divide(X1,divide(identity,X2)),X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_21 ).
cnf(c_0_25,plain,
divide(X1,divide(identity,zero)) = zero,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_27,axiom,
divide(a,zero) = a,
x_divide_zero_is_x ).
cnf(c_0_28,plain,
( ~ less_equal(identity,X1)
| identity = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_29,plain,
less_equal(X1,divide(identity,zero)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
less_equal(divide(divide(X1,zero),a),divide(divide(X1,a),zero)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
divide(identity,zero) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_33,plain,
less_equal(divide(identity,a),divide(divide(identity,a),zero)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_35,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_36,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_37,plain,
divide(divide(identity,a),zero) = divide(identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_34])]) ).
cnf(c_0_38,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_35 ).
cnf(c_0_39,plain,
less_equal(divide(identity,a),divide(divide(identity,a),a)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_41,plain,
divide(divide(identity,a),a) = divide(identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_39]),c_0_34])]) ).
cnf(c_0_42,plain,
divide(divide(divide(identity,a),divide(X1,a)),divide(divide(divide(identity,a),X1),a)) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
divide(divide(X1,divide(identity,X2)),X2) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_44,plain,
divide(divide(identity,a),divide(divide(divide(identity,a),divide(X1,divide(identity,a))),a)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_37]) ).
cnf(c_0_45,plain,
less_equal(divide(identity,a),divide(divide(divide(identity,a),divide(X1,divide(identity,a))),a)),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_46,plain,
( ~ less_equal(X1,divide(X1,X2))
| divide(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_47,plain,
divide(divide(divide(identity,a),divide(X1,divide(identity,a))),a) = divide(identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_45]),c_0_20])]) ).
cnf(c_0_48,plain,
divide(divide(identity,a),divide(X1,divide(identity,a))) = divide(identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_34])]) ).
cnf(c_0_49,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(fof_simplification,[status(thm)],[prove_this]) ).
cnf(c_0_50,plain,
( ~ less_equal(X2,divide(X1,divide(identity,X2)))
| divide(X1,divide(identity,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_51,plain,
less_equal(divide(identity,a),divide(identity,divide(X1,divide(identity,a)))),
inference(spm,[status(thm)],[c_0_20,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
c_0_49 ).
cnf(c_0_53,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 20:47:23 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 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
% 0.14/5.47 % Version: 3.5.1
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % Starting sh5l with 300s (1) cores
% 0.14/5.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1200310 completed with status 0
% 0.14/5.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.47 % No SInE strategy applied
% 0.14/5.47 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.14/5.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/5.47 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.14/5.47 % Starting new_bool_3 with 136s (1) cores
% 0.14/5.47 % new_bool_3 with pid 1200318 completed with status 0
% 0.14/5.47 % Result found by new_bool_3
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.47 % No SInE strategy applied
% 0.14/5.47 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.14/5.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/5.47 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.14/5.47 % Starting new_bool_3 with 136s (1) cores
% 0.14/5.47 % Preprocessing time : 0.001 s
% 0.14/5.47 % Presaturation interreduction done
% 0.14/5.47
% 0.14/5.47 % Proof found!
% 0.14/5.47 % SZS status Unsatisfiable
% 0.14/5.47 % SZS output start CNFRefutation
% See solution above
% 0.14/5.47 % Parsed axioms : 16
% 0.14/5.47 % Removed by relevancy pruning/SinE : 0
% 0.14/5.47 % Initial clauses : 16
% 0.14/5.47 % Removed in clause preprocessing : 0
% 0.14/5.47 % Initial clauses in saturation : 16
% 0.14/5.47 % Processed clauses : 291
% 0.14/5.47 % ...of these trivial : 10
% 0.14/5.47 % ...subsumed : 134
% 0.14/5.47 % ...remaining for further processing : 147
% 0.14/5.47 % Other redundant clauses eliminated : 2
% 0.14/5.47 % Clauses deleted for lack of memory : 0
% 0.14/5.47 % Backward-subsumed : 4
% 0.14/5.47 % Backward-rewritten : 52
% 0.14/5.47 % Generated clauses : 3736
% 0.14/5.47 % ...of the previous two non-redundant : 1590
% 0.14/5.47 % ...aggressively subsumed : 0
% 0.14/5.47 % Contextual simplify-reflections : 0
% 0.14/5.47 % Paramodulations : 3734
% 0.14/5.47 % Factorizations : 0
% 0.14/5.47 % NegExts : 0
% 0.14/5.47 % Equation resolutions : 2
% 0.14/5.47 % Disequality decompositions : 0
% 0.14/5.47 % Total rewrite steps : 5184
% 0.14/5.47 % ...of those cached : 4309
% 0.14/5.47 % Propositional unsat checks : 0
% 0.14/5.47 % Propositional check models : 0
% 0.14/5.47 % Propositional check unsatisfiable : 0
% 0.14/5.47 % Propositional clauses : 0
% 0.14/5.47 % Propositional clauses after purity: 0
% 0.14/5.47 % Propositional unsat core size : 0
% 0.14/5.47 % Propositional preprocessing time : 0.000
% 0.14/5.47 % Propositional encoding time : 0.000
% 0.14/5.47 % Propositional solver time : 0.000
% 0.14/5.47 % Success case prop preproc time : 0.000
% 0.14/5.47 % Success case prop encoding time : 0.000
% 0.14/5.47 % Success case prop solver time : 0.000
% 0.14/5.47 % Current number of processed clauses : 75
% 0.14/5.47 % Positive orientable unit clauses : 43
% 0.14/5.47 % Positive unorientable unit clauses: 0
% 0.14/5.47 % Negative unit clauses : 1
% 0.14/5.47 % Non-unit-clauses : 31
% 0.14/5.47 % Current number of unprocessed clauses: 1262
% 0.14/5.47 % ...number of literals in the above : 1571
% 0.14/5.47 % Current number of archived formulas : 0
% 0.14/5.47 % Current number of archived clauses : 72
% 0.14/5.47 % Clause-clause subsumption calls (NU) : 352
% 0.14/5.47 % Rec. Clause-clause subsumption calls : 352
% 0.14/5.47 % Non-unit clause-clause subsumptions : 138
% 0.14/5.47 % Unit Clause-clause subsumption calls : 29
% 0.14/5.47 % Rewrite failures with RHS unbound : 0
% 0.14/5.47 % BW rewrite match attempts : 173
% 0.14/5.47 % BW rewrite match successes : 35
% 0.14/5.47 % Condensation attempts : 0
% 0.14/5.47 % Condensation successes : 0
% 0.14/5.47 % Termbank termtop insertions : 50152
% 0.14/5.47 % Search garbage collected termcells : 19
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.022 s
% 0.14/5.47 % System time : 0.005 s
% 0.14/5.47 % Total time : 0.027 s
% 0.14/5.47 % Maximum resident set size: 3640 pages
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.120 s
% 0.14/5.47 % System time : 0.018 s
% 0.14/5.47 % Total time : 0.138 s
% 0.14/5.47 % Maximum resident set size: 4608 pages
% 0.14/5.47 % E exiting
%------------------------------------------------------------------------------