%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:45:36 PM UTC 2026
% Result : Unsatisfiable 2.22s 0.76s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 20 unt; 0 nHn; 38 RR)
% Number of literals : 90 ( 4 equ; 50 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 : 86 ( 7 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/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(xQyLEz,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).
cnf(xQz,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(xQy,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(transitivity_of_less_equal,axiom,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(less_equal_quotient,axiom,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(prove_xQzLEy,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).
cnf(c_0_12,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_13,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
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) ),
c_0_12 ).
cnf(c_0_15,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_16,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_13 ).
cnf(c_0_17,hypothesis,
less_equal(xQy,z),
xQyLEz ).
cnf(c_0_18,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_14,c_0_15]) ).
cnf(c_0_19,hypothesis,
quotient(xQy,z,zero),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
( ~ quotient(X4,X3,xQy)
| ~ quotient(X4,z,X1)
| ~ quotient(X3,z,X2)
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
( ~ quotient(X3,X2,xQy)
| ~ quotient(X3,z,X1)
| less_equal(divide(X1,divide(X2,z)),zero) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_22,hypothesis,
quotient(x,z,xQz),
xQz ).
cnf(c_0_23,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_24,hypothesis,
( ~ quotient(x,X1,xQy)
| less_equal(divide(xQz,divide(X1,z)),zero) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
quotient(x,y,xQy),
xQy ).
cnf(c_0_26,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_27,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_23 ).
cnf(c_0_28,hypothesis,
less_equal(divide(xQz,divide(y,z)),zero),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_30,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_31,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_26 ).
cnf(c_0_32,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_33,hypothesis,
divide(xQz,divide(y,z)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
c_0_30 ).
cnf(c_0_35,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_36,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_32 ).
cnf(c_0_37,hypothesis,
quotient(xQz,divide(y,z),zero),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
~ less_equal(xQz,y),
inference(fof_simplification,[status(thm)],[prove_xQzLEy]) ).
cnf(c_0_39,plain,
( ~ less_equal(X1,divide(X2,X3))
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,hypothesis,
less_equal(xQz,divide(y,z)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
~ less_equal(xQz,y),
c_0_38 ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:45:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.22/0.76 % Version: 3.5.1
% 2.22/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.22/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.22/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.22/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.22/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.22/0.76 % Starting sh5l with 300s (1) cores
% 2.22/0.76 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1738255 completed with status 0
% 2.22/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.22/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.22/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.22/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.22/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.22/0.76 % No SInE strategy applied
% 2.22/0.76 % Search class: FHUSM-FFSS22-SFFFFFNN
% 2.22/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.22/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.22/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.22/0.76 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.22/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.22/0.76 % Starting new_bool_1 with 136s (1) cores
% 2.22/0.76 % new_bool_3 with pid 1738264 completed with status 0
% 2.22/0.76 % Result found by new_bool_3
% 2.22/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.22/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.22/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.22/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.22/0.76 % No SInE strategy applied
% 2.22/0.76 % Search class: FHUSM-FFSS22-SFFFFFNN
% 2.22/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.22/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.22/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.22/0.76 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.22/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.22/0.76 % Preprocessing time : 0.001 s
% 2.22/0.76 % Presaturation interreduction done
% 2.22/0.76
% 2.22/0.76 % Proof found!
% 2.22/0.76 % SZS status Unsatisfiable
% 2.22/0.76 % SZS output start CNFRefutation
% See solution above
% 2.22/0.76 % Parsed axioms : 18
% 2.22/0.76 % Removed by relevancy pruning/SinE : 0
% 2.22/0.76 % Initial clauses : 18
% 2.22/0.76 % Removed in clause preprocessing : 0
% 2.22/0.76 % Initial clauses in saturation : 18
% 2.22/0.76 % Processed clauses : 4390
% 2.22/0.76 % ...of these trivial : 67
% 2.22/0.76 % ...subsumed : 3165
% 2.22/0.76 % ...remaining for further processing : 1158
% 2.22/0.76 % Other redundant clauses eliminated : 0
% 2.22/0.76 % Clauses deleted for lack of memory : 0
% 2.22/0.76 % Backward-subsumed : 45
% 2.22/0.76 % Backward-rewritten : 14
% 2.22/0.76 % Generated clauses : 13875
% 2.22/0.76 % ...of the previous two non-redundant : 6625
% 2.22/0.76 % ...aggressively subsumed : 0
% 2.22/0.76 % Contextual simplify-reflections : 0
% 2.22/0.76 % Paramodulations : 13875
% 2.22/0.76 % Factorizations : 0
% 2.22/0.76 % NegExts : 0
% 2.22/0.76 % Equation resolutions : 0
% 2.22/0.76 % Disequality decompositions : 0
% 2.22/0.76 % Total rewrite steps : 14015
% 2.22/0.76 % ...of those cached : 13487
% 2.22/0.76 % Propositional unsat checks : 0
% 2.22/0.76 % Propositional check models : 0
% 2.22/0.76 % Propositional check unsatisfiable : 0
% 2.22/0.76 % Propositional clauses : 0
% 2.22/0.76 % Propositional clauses after purity: 0
% 2.22/0.76 % Propositional unsat core size : 0
% 2.22/0.76 % Propositional preprocessing time : 0.000
% 2.22/0.76 % Propositional encoding time : 0.000
% 2.22/0.76 % Propositional solver time : 0.000
% 2.22/0.76 % Success case prop preproc time : 0.000
% 2.22/0.76 % Success case prop encoding time : 0.000
% 2.22/0.76 % Success case prop solver time : 0.000
% 2.22/0.76 % Current number of processed clauses : 1081
% 2.22/0.76 % Positive orientable unit clauses : 150
% 2.22/0.76 % Positive unorientable unit clauses: 0
% 2.22/0.76 % Negative unit clauses : 1
% 2.22/0.76 % Non-unit-clauses : 930
% 2.22/0.76 % Current number of unprocessed clauses: 2170
% 2.22/0.76 % ...number of literals in the above : 5092
% 2.22/0.76 % Current number of archived formulas : 0
% 2.22/0.76 % Current number of archived clauses : 77
% 2.22/0.76 % Clause-clause subsumption calls (NU) : 274867
% 2.22/0.76 % Rec. Clause-clause subsumption calls : 203132
% 2.22/0.76 % Non-unit clause-clause subsumptions : 3210
% 2.22/0.76 % Unit Clause-clause subsumption calls : 10
% 2.22/0.76 % Rewrite failures with RHS unbound : 0
% 2.22/0.76 % BW rewrite match attempts : 372
% 2.22/0.76 % BW rewrite match successes : 14
% 2.22/0.76 % Condensation attempts : 0
% 2.22/0.76 % Condensation successes : 0
% 2.22/0.76 % Termbank termtop insertions : 174989
% 2.22/0.76 % Search garbage collected termcells : 34
% 2.22/0.76
% 2.22/0.76 % -------------------------------------------------
% 2.22/0.76 % User time : 0.314 s
% 2.22/0.76 % System time : 0.009 s
% 2.22/0.76 % Total time : 0.324 s
% 2.22/0.76 % Maximum resident set size: 3644 pages
% 2.22/0.76
% 2.22/0.76 % -------------------------------------------------
% 2.22/0.76 % User time : 1.495 s
% 2.22/0.76 % System time : 0.051 s
% 2.22/0.76 % Total time : 1.546 s
% 2.22/0.76 % Maximum resident set size: 4864 pages
% 2.22/0.76 % E exiting
%------------------------------------------------------------------------------