%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN008-2 : 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 : n014.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 12:45:38 PM UTC 2026
% Result : Unsatisfiable 1.39s 0.68s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 68 ( 33 unt; 0 nHn; 54 RR)
% Number of literals : 140 ( 12 equ; 75 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 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 : 141 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_property,axiom,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(well_defined,axiom,
( ~ quotient(X1,X2,X4)
| ~ quotient(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(transitivity_of_less_equal,axiom,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(less_equal_quotient,axiom,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(aLEb,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(quotient_less_equal,axiom,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_0_17,plain,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
inference(fof_simplification,[status(thm)],[quotient_property]) ).
cnf(c_0_18,plain,
( ~ quotient(X1,X2,X4)
| ~ quotient(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[well_defined]) ).
cnf(c_0_19,plain,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
c_0_17 ).
cnf(c_0_20,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_21,plain,
( ~ quotient(X1,X2,X4)
| ~ quotient(X1,X2,X3)
| X3 = X4 ),
c_0_18 ).
cnf(c_0_22,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_23,plain,
( ~ quotient(X7,X6,X4)
| ~ quotient(X7,X5,X1)
| ~ quotient(X6,X5,X2)
| ~ quotient(X4,X5,X3)
| less_equal(divide(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ quotient(X2,zero,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ quotient(X6,X5,X3)
| ~ quotient(X6,X4,X1)
| ~ quotient(X5,X4,X2)
| less_equal(divide(X1,X2),divide(X3,X4)) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_26,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_27,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_28,hypothesis,
quotient(a,c,aQc),
aQc ).
cnf(c_0_29,plain,
( ~ quotient(X4,X3,X2)
| ~ quotient(X4,X3,X1)
| less_equal(X1,divide(X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,hypothesis,
( ~ quotient(a,c,X1)
| X1 = aQc ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_31,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_32,plain,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity_of_less_equal]) ).
cnf(c_0_33,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_34,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_35,hypothesis,
( ~ quotient(a,c,X1)
| less_equal(aQc,divide(X1,c)) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_36,hypothesis,
divide(a,c) = aQc,
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_37,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_31 ).
cnf(c_0_38,plain,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
c_0_32 ).
cnf(c_0_39,hypothesis,
less_equal(a,b),
aLEb ).
cnf(c_0_40,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
inference(fof_simplification,[status(thm)],[xQyLEz_implies_xQzLEy]) ).
cnf(c_0_41,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_33 ).
cnf(c_0_42,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_43,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_34 ).
cnf(c_0_44,hypothesis,
less_equal(aQc,divide(aQc,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_36]) ).
cnf(c_0_45,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_46,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
cnf(c_0_47,hypothesis,
( ~ less_equal(X1,a)
| less_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,hypothesis,
less_equal(aQc,a),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_49,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
c_0_40 ).
cnf(c_0_50,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_51,plain,
( ~ quotient(X3,X5,X1)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X4,zero)
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_52,hypothesis,
quotient(b,c,bQc),
bQc ).
cnf(c_0_53,hypothesis,
divide(aQc,c) = aQc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_54,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_46 ).
cnf(c_0_55,hypothesis,
less_equal(aQc,b),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
( ~ quotient(X3,X2,X4)
| ~ quotient(X3,X4,X1)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,hypothesis,
( ~ quotient(X2,c,X1)
| ~ quotient(X2,b,zero)
| less_equal(divide(X1,bQc),zero) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,hypothesis,
quotient(aQc,c,aQc),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_59,hypothesis,
quotient(aQc,b,zero),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( ~ quotient(X1,X3,X2)
| less_equal(divide(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_20]) ).
cnf(c_0_61,hypothesis,
less_equal(divide(aQc,bQc),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_62,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_63,negated_conjecture,
~ less_equal(aQc,bQc),
inference(fof_simplification,[status(thm)],[prove_aQcLEbQc]) ).
cnf(c_0_64,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_65,hypothesis,
divide(aQc,bQc) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_61]),c_0_62])]) ).
cnf(c_0_66,negated_conjecture,
~ less_equal(aQc,bQc),
c_0_63 ).
cnf(c_0_67,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_27]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:46:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 1.39/0.68 % Version: 3.5.1
% 1.39/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.39/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.39/0.68 % Starting sh5l with 300s (1) cores
% 1.39/0.68 % new_bool_1 with pid 2327701 completed with status 9
% 1.39/0.68 % new_bool_3 with pid 2327700 completed with status 9
% 1.39/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2327699 completed with status 0
% 1.39/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.39/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.68 % No SInE strategy applied
% 1.39/0.68 % Search class: FHUSM-FFSS22-SFFFFFNN
% 1.39/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.68 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.39/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.39/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.39/0.68 % new_bool_1 with pid 2327711 completed with status 0
% 1.39/0.68 % Result found by new_bool_1
% 1.39/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.39/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.68 % No SInE strategy applied
% 1.39/0.68 % Search class: FHUSM-FFSS22-SFFFFFNN
% 1.39/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.68 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.39/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.39/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.39/0.68 % Preprocessing time : 0.001 s
% 1.39/0.68 % Presaturation interreduction done
% 1.39/0.68
% 1.39/0.68 % Proof found!
% 1.39/0.68 % SZS status Unsatisfiable
% 1.39/0.68 % SZS output start CNFRefutation
% See solution above
% 1.39/0.68 % Parsed axioms : 20
% 1.39/0.68 % Removed by relevancy pruning/SinE : 0
% 1.39/0.68 % Initial clauses : 20
% 1.39/0.68 % Removed in clause preprocessing : 0
% 1.39/0.68 % Initial clauses in saturation : 20
% 1.39/0.68 % Processed clauses : 6245
% 1.39/0.68 % ...of these trivial : 130
% 1.39/0.68 % ...subsumed : 4534
% 1.39/0.68 % ...remaining for further processing : 1581
% 1.39/0.68 % Other redundant clauses eliminated : 0
% 1.39/0.68 % Clauses deleted for lack of memory : 0
% 1.39/0.68 % Backward-subsumed : 37
% 1.39/0.68 % Backward-rewritten : 25
% 1.39/0.68 % Generated clauses : 19066
% 1.39/0.68 % ...of the previous two non-redundant : 9321
% 1.39/0.68 % ...aggressively subsumed : 0
% 1.39/0.68 % Contextual simplify-reflections : 0
% 1.39/0.68 % Paramodulations : 19066
% 1.39/0.68 % Factorizations : 0
% 1.39/0.68 % NegExts : 0
% 1.39/0.68 % Equation resolutions : 0
% 1.39/0.68 % Disequality decompositions : 0
% 1.39/0.68 % Total rewrite steps : 17742
% 1.39/0.68 % ...of those cached : 16772
% 1.39/0.68 % Propositional unsat checks : 0
% 1.39/0.68 % Propositional check models : 0
% 1.39/0.68 % Propositional check unsatisfiable : 0
% 1.39/0.68 % Propositional clauses : 0
% 1.39/0.68 % Propositional clauses after purity: 0
% 1.39/0.68 % Propositional unsat core size : 0
% 1.39/0.68 % Propositional preprocessing time : 0.000
% 1.39/0.68 % Propositional encoding time : 0.000
% 1.39/0.68 % Propositional solver time : 0.000
% 1.39/0.68 % Success case prop preproc time : 0.000
% 1.39/0.68 % Success case prop encoding time : 0.000
% 1.39/0.68 % Success case prop solver time : 0.000
% 1.39/0.68 % Current number of processed clauses : 1499
% 1.39/0.68 % Positive orientable unit clauses : 225
% 1.39/0.68 % Positive unorientable unit clauses: 0
% 1.39/0.68 % Negative unit clauses : 21
% 1.39/0.68 % Non-unit-clauses : 1253
% 1.39/0.68 % Current number of unprocessed clauses: 2996
% 1.39/0.68 % ...number of literals in the above : 7277
% 1.39/0.68 % Current number of archived formulas : 0
% 1.39/0.68 % Current number of archived clauses : 82
% 1.39/0.68 % Clause-clause subsumption calls (NU) : 674495
% 1.39/0.68 % Rec. Clause-clause subsumption calls : 387721
% 1.39/0.68 % Non-unit clause-clause subsumptions : 3739
% 1.39/0.68 % Unit Clause-clause subsumption calls : 5849
% 1.39/0.68 % Rewrite failures with RHS unbound : 0
% 1.39/0.68 % BW rewrite match attempts : 573
% 1.39/0.68 % BW rewrite match successes : 20
% 1.39/0.68 % Condensation attempts : 0
% 1.39/0.68 % Condensation successes : 0
% 1.39/0.68 % Termbank termtop insertions : 232304
% 1.39/0.68 % Search garbage collected termcells : 48
% 1.39/0.68
% 1.39/0.68 % -------------------------------------------------
% 1.39/0.68 % User time : 0.239 s
% 1.39/0.68 % System time : 0.007 s
% 1.39/0.68 % Total time : 0.246 s
% 1.39/0.68 % Maximum resident set size: 3388 pages
% 1.39/0.68
% 1.39/0.68 % -------------------------------------------------
% 1.39/0.68 % User time : 1.259 s
% 1.39/0.68 % System time : 0.080 s
% 1.39/0.68 % Total time : 1.339 s
% 1.39/0.68 % Maximum resident set size: 4608 pages
% 1.39/0.68 % E exiting
%------------------------------------------------------------------------------