%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : HEN006-7 : 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 : n019.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 12:45:45 PM UTC 2026
% Result : Unsatisfiable 1.21s 0.68s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 50 ( 27 unt; 0 nHn; 40 RR)
% Number of literals : 100 ( 5 equ; 53 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 : 96 ( 10 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(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(xQz,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
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_13,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_14,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
cnf(c_0_15,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_13 ).
cnf(c_0_16,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_17,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_14 ).
cnf(c_0_18,hypothesis,
less_equal(xQy,z),
xQyLEz ).
cnf(c_0_19,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_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
quotient(xQy,z,zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,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_19,c_0_20]) ).
cnf(c_0_22,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_23,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_24,hypothesis,
( ~ quotient(X3,X2,xQy)
| ~ quotient(X3,z,X1)
| less_equal(divide(X1,divide(X2,z)),zero) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,hypothesis,
quotient(x,z,xQz),
xQz ).
cnf(c_0_26,plain,
( ~ quotient(X6,X3,X5)
| ~ quotient(X6,X4,X1)
| ~ quotient(X5,X4,X2)
| ~ quotient(X3,X4,zero)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_27,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_28,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_23 ).
cnf(c_0_29,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_30,hypothesis,
( ~ quotient(x,X1,xQy)
| less_equal(divide(xQz,divide(X1,z)),zero) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
quotient(x,y,xQy),
xQy ).
cnf(c_0_32,plain,
( ~ quotient(X4,X3,X1)
| ~ quotient(X4,X2,zero)
| ~ quotient(X2,X3,zero)
| less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_34,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_29 ).
cnf(c_0_35,hypothesis,
less_equal(divide(xQz,divide(y,z)),zero),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_37,plain,
( ~ quotient(X1,X3,zero)
| ~ quotient(X3,X2,zero)
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_38,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_39,hypothesis,
divide(xQz,divide(y,z)) = 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_40,plain,
( ~ quotient(X1,divide(X2,X3),zero)
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,hypothesis,
quotient(xQz,divide(y,z),zero),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_42,hypothesis,
less_equal(divide(xQz,y),zero),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_44,hypothesis,
divide(xQz,y) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_36])]) ).
cnf(c_0_45,negated_conjecture,
~ less_equal(xQz,y),
inference(fof_simplification,[status(thm)],[prove_xQzLEy]) ).
cnf(c_0_46,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_43 ).
cnf(c_0_47,hypothesis,
quotient(xQz,y,zero),
inference(spm,[status(thm)],[c_0_16,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
~ less_equal(xQz,y),
c_0_45 ).
cnf(c_0_49,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:46:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.47 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
% 1.21/0.68 % Version: 3.5.1
% 1.21/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.21/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.21/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.21/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.21/0.68 % Starting sh5l with 300s (1) cores
% 1.21/0.68 % sh5l with pid 897423 completed with status 9
% 1.21/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 897420 completed with status 0
% 1.21/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.21/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.21/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.21/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.21/0.68 % No SInE strategy applied
% 1.21/0.68 % Search class: FHUSM-FFSS22-SFFFFFNN
% 1.21/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.21/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.21/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.21/0.68 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.21/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.21/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.21/0.68 % new_bool_1 with pid 897431 completed with status 0
% 1.21/0.68 % Result found by new_bool_1
% 1.21/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.21/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.21/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.21/0.68 % No SInE strategy applied
% 1.21/0.68 % Search class: FHUSM-FFSS22-SFFFFFNN
% 1.21/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.21/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.21/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.21/0.68 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.21/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.21/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.21/0.68 % Preprocessing time : 0.002 s
% 1.21/0.68 % Presaturation interreduction done
% 1.21/0.68
% 1.21/0.68 % Proof found!
% 1.21/0.68 % SZS status Unsatisfiable
% 1.21/0.68 % SZS output start CNFRefutation
% See solution above
% 1.21/0.68 % Parsed axioms : 17
% 1.21/0.68 % Removed by relevancy pruning/SinE : 0
% 1.21/0.68 % Initial clauses : 17
% 1.21/0.68 % Removed in clause preprocessing : 0
% 1.21/0.68 % Initial clauses in saturation : 17
% 1.21/0.68 % Processed clauses : 2317
% 1.21/0.68 % ...of these trivial : 5
% 1.21/0.68 % ...subsumed : 1425
% 1.21/0.68 % ...remaining for further processing : 887
% 1.21/0.68 % Other redundant clauses eliminated : 0
% 1.21/0.68 % Clauses deleted for lack of memory : 0
% 1.21/0.68 % Backward-subsumed : 44
% 1.21/0.68 % Backward-rewritten : 29
% 1.21/0.68 % Generated clauses : 6261
% 1.21/0.68 % ...of the previous two non-redundant : 3294
% 1.21/0.68 % ...aggressively subsumed : 0
% 1.21/0.68 % Contextual simplify-reflections : 0
% 1.21/0.68 % Paramodulations : 6261
% 1.21/0.68 % Factorizations : 0
% 1.21/0.68 % NegExts : 0
% 1.21/0.68 % Equation resolutions : 0
% 1.21/0.68 % Disequality decompositions : 0
% 1.21/0.68 % Total rewrite steps : 4837
% 1.21/0.68 % ...of those cached : 4555
% 1.21/0.68 % Propositional unsat checks : 0
% 1.21/0.68 % Propositional check models : 0
% 1.21/0.68 % Propositional check unsatisfiable : 0
% 1.21/0.68 % Propositional clauses : 0
% 1.21/0.68 % Propositional clauses after purity: 0
% 1.21/0.68 % Propositional unsat core size : 0
% 1.21/0.68 % Propositional preprocessing time : 0.000
% 1.21/0.68 % Propositional encoding time : 0.000
% 1.21/0.68 % Propositional solver time : 0.000
% 1.21/0.68 % Success case prop preproc time : 0.000
% 1.21/0.68 % Success case prop encoding time : 0.000
% 1.21/0.68 % Success case prop solver time : 0.000
% 1.21/0.68 % Current number of processed clauses : 797
% 1.21/0.68 % Positive orientable unit clauses : 100
% 1.21/0.68 % Positive unorientable unit clauses: 0
% 1.21/0.68 % Negative unit clauses : 1
% 1.21/0.68 % Non-unit-clauses : 696
% 1.21/0.68 % Current number of unprocessed clauses: 916
% 1.21/0.68 % ...number of literals in the above : 2351
% 1.21/0.68 % Current number of archived formulas : 0
% 1.21/0.68 % Current number of archived clauses : 90
% 1.21/0.68 % Clause-clause subsumption calls (NU) : 150838
% 1.21/0.68 % Rec. Clause-clause subsumption calls : 121036
% 1.21/0.68 % Non-unit clause-clause subsumptions : 1469
% 1.21/0.68 % Unit Clause-clause subsumption calls : 13
% 1.21/0.68 % Rewrite failures with RHS unbound : 0
% 1.21/0.68 % BW rewrite match attempts : 153
% 1.21/0.68 % BW rewrite match successes : 28
% 1.21/0.68 % Condensation attempts : 0
% 1.21/0.68 % Condensation successes : 0
% 1.21/0.68 % Termbank termtop insertions : 83386
% 1.21/0.68 % Search garbage collected termcells : 30
% 1.21/0.68
% 1.21/0.68 % -------------------------------------------------
% 1.21/0.68 % User time : 0.162 s
% 1.21/0.68 % System time : 0.007 s
% 1.21/0.68 % Total time : 0.169 s
% 1.21/0.68 % Maximum resident set size: 3608 pages
% 1.21/0.68
% 1.21/0.68 % -------------------------------------------------
% 1.21/0.68 % User time : 0.891 s
% 1.21/0.68 % System time : 0.044 s
% 1.21/0.68 % Total time : 0.936 s
% 1.21/0.68 % Maximum resident set size: 4608 pages
% 1.21/0.68 % E exiting
%------------------------------------------------------------------------------