%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN008-1 : 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 : n005.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 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 24 unt; 0 nHn; 37 RR)
% Number of literals : 94 ( 9 equ; 50 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
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(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(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
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(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
cnf(aLEb,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
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(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_0_13,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_14,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_15,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
cnf(c_0_16,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_13 ).
cnf(c_0_17,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_18,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_14 ).
cnf(c_0_19,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_15 ).
cnf(c_0_20,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,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_18,c_0_17]) ).
cnf(c_0_22,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ quotient(X1,X2,X4)
| ~ quotient(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[well_defined]) ).
cnf(c_0_24,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_25,plain,
( ~ quotient(X3,X5,X1)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X4,divide(X5,X6))
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
quotient(b,c,bQc),
bQc ).
cnf(c_0_27,plain,
( ~ quotient(X1,X2,X4)
| ~ quotient(X1,X2,X3)
| X3 = X4 ),
c_0_23 ).
cnf(c_0_28,plain,
quotient(X1,identity,zero),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_29,hypothesis,
( ~ quotient(X2,c,X1)
| ~ quotient(X2,b,divide(c,X3))
| less_equal(divide(X1,bQc),zero) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,hypothesis,
quotient(a,c,aQc),
aQc ).
cnf(c_0_31,plain,
( ~ quotient(X2,identity,X1)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
less_equal(a,b),
aLEb ).
cnf(c_0_33,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_34,hypothesis,
( ~ quotient(a,b,divide(c,X1))
| less_equal(divide(aQc,bQc),zero) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_36,hypothesis,
quotient(a,b,zero),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_37,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_33 ).
cnf(c_0_38,hypothesis,
less_equal(divide(aQc,bQc),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_40,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_41,hypothesis,
divide(aQc,bQc) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
~ less_equal(aQc,bQc),
inference(fof_simplification,[status(thm)],[prove_aQcLEbQc]) ).
cnf(c_0_43,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_40 ).
cnf(c_0_44,hypothesis,
quotient(aQc,bQc,zero),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
~ less_equal(aQc,bQc),
c_0_42 ).
cnf(c_0_46,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : 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 : n005.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 20:46:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 0.13/0.50 % Version: 3.5.1
% 0.13/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.50 % Starting sh5l with 300s (1) cores
% 0.13/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1739107 completed with status 0
% 0.13/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.50 % No SInE strategy applied
% 0.13/0.50 % Search class: FHUSS-FFSS22-SFFFFFNN
% 0.13/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.50 % new_bool_3 with pid 1739114 completed with status 0
% 0.13/0.50 % Result found by new_bool_3
% 0.13/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.50 % No SInE strategy applied
% 0.13/0.50 % Search class: FHUSS-FFSS22-SFFFFFNN
% 0.13/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.50 % Preprocessing time : 0.002 s
% 0.13/0.50 % Presaturation interreduction done
% 0.13/0.50
% 0.13/0.50 % Proof found!
% 0.13/0.50 % SZS status Unsatisfiable
% 0.13/0.50 % SZS output start CNFRefutation
% See solution above
% 0.13/0.50 % Parsed axioms : 13
% 0.13/0.50 % Removed by relevancy pruning/SinE : 0
% 0.13/0.50 % Initial clauses : 13
% 0.13/0.50 % Removed in clause preprocessing : 0
% 0.13/0.50 % Initial clauses in saturation : 13
% 0.13/0.50 % Processed clauses : 192
% 0.13/0.50 % ...of these trivial : 1
% 0.13/0.50 % ...subsumed : 22
% 0.13/0.50 % ...remaining for further processing : 169
% 0.13/0.50 % Other redundant clauses eliminated : 0
% 0.13/0.50 % Clauses deleted for lack of memory : 0
% 0.13/0.50 % Backward-subsumed : 8
% 0.13/0.50 % Backward-rewritten : 3
% 0.13/0.50 % Generated clauses : 351
% 0.13/0.50 % ...of the previous two non-redundant : 207
% 0.13/0.50 % ...aggressively subsumed : 0
% 0.13/0.50 % Contextual simplify-reflections : 0
% 0.13/0.50 % Paramodulations : 351
% 0.13/0.50 % Factorizations : 0
% 0.13/0.50 % NegExts : 0
% 0.13/0.50 % Equation resolutions : 0
% 0.13/0.50 % Disequality decompositions : 0
% 0.13/0.50 % Total rewrite steps : 211
% 0.13/0.50 % ...of those cached : 165
% 0.13/0.50 % Propositional unsat checks : 0
% 0.13/0.50 % Propositional check models : 0
% 0.13/0.50 % Propositional check unsatisfiable : 0
% 0.13/0.50 % Propositional clauses : 0
% 0.13/0.50 % Propositional clauses after purity: 0
% 0.13/0.50 % Propositional unsat core size : 0
% 0.13/0.50 % Propositional preprocessing time : 0.000
% 0.13/0.50 % Propositional encoding time : 0.000
% 0.13/0.50 % Propositional solver time : 0.000
% 0.13/0.50 % Success case prop preproc time : 0.000
% 0.13/0.50 % Success case prop encoding time : 0.000
% 0.13/0.50 % Success case prop solver time : 0.000
% 0.13/0.50 % Current number of processed clauses : 145
% 0.13/0.50 % Positive orientable unit clauses : 25
% 0.13/0.50 % Positive unorientable unit clauses: 0
% 0.13/0.50 % Negative unit clauses : 1
% 0.13/0.50 % Non-unit-clauses : 119
% 0.13/0.50 % Current number of unprocessed clauses: 30
% 0.13/0.50 % ...number of literals in the above : 86
% 0.13/0.50 % Current number of archived formulas : 0
% 0.13/0.50 % Current number of archived clauses : 24
% 0.13/0.50 % Clause-clause subsumption calls (NU) : 2841
% 0.13/0.50 % Rec. Clause-clause subsumption calls : 2308
% 0.13/0.50 % Non-unit clause-clause subsumptions : 30
% 0.13/0.50 % Unit Clause-clause subsumption calls : 8
% 0.13/0.50 % Rewrite failures with RHS unbound : 0
% 0.13/0.50 % BW rewrite match attempts : 10
% 0.13/0.50 % BW rewrite match successes : 2
% 0.13/0.50 % Condensation attempts : 0
% 0.13/0.50 % Condensation successes : 0
% 0.13/0.50 % Termbank termtop insertions : 6005
% 0.13/0.50 % Search garbage collected termcells : 30
% 0.13/0.50
% 0.13/0.50 % -------------------------------------------------
% 0.13/0.50 % User time : 0.027 s
% 0.13/0.50 % System time : 0.002 s
% 0.13/0.50 % Total time : 0.030 s
% 0.13/0.50 % Maximum resident set size: 3644 pages
% 0.13/0.50
% 0.13/0.50 % -------------------------------------------------
% 0.13/0.50 % User time : 0.114 s
% 0.13/0.50 % System time : 0.017 s
% 0.13/0.50 % Total time : 0.131 s
% 0.13/0.50 % Maximum resident set size: 4864 pages
% 0.13/0.50 % E exiting
%------------------------------------------------------------------------------