%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN009-6 : 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 : n013.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 0.16s 15.55s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 52 ( 34 unt; 0 nHn; 31 RR)
% Number of literals : 73 ( 25 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal2,axiom,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_a_is_b) ).
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_b_is_c) ).
cnf(property_of_divide3,axiom,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(id_divide_c_is_d,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_c_is_d) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(prove_b_equals_d,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_d) ).
cnf(c_0_14,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_15,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_16,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[property_of_divide1]) ).
cnf(c_0_17,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_14 ).
cnf(c_0_18,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_19,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_15 ).
cnf(c_0_20,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_21,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
c_0_16 ).
cnf(c_0_22,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,hypothesis,
divide(identity,a) = b,
id_divide_a_is_b ).
cnf(c_0_24,plain,
( ~ less_equal(X1,zero)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_27,hypothesis,
( ~ less_equal(b,X1)
| less_equal(divide(identity,X1),a) ),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_28,hypothesis,
divide(identity,b) = c,
id_divide_b_is_c ).
cnf(c_0_29,plain,
divide(X1,divide(X1,zero)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
inference(fof_simplification,[status(thm)],[property_of_divide3]) ).
cnf(c_0_31,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_32,hypothesis,
divide(identity,c) = d,
id_divide_c_is_d ).
cnf(c_0_33,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_26 ).
cnf(c_0_34,hypothesis,
less_equal(c,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_28]) ).
cnf(c_0_35,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_36,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_37,plain,
( ~ less_equal(X1,X2)
| less_equal(divide(X1,X3),divide(X2,X3)) ),
c_0_30 ).
cnf(c_0_38,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_39,hypothesis,
less_equal(divide(divide(identity,X1),divide(c,X1)),divide(d,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,hypothesis,
divide(c,a) = zero,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
less_equal(divide(X1,X2),divide(identity,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
( ~ less_equal(c,X1)
| less_equal(divide(identity,X1),b) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_44,negated_conjecture,
b != d,
inference(fof_simplification,[status(thm)],[prove_b_equals_d]) ).
cnf(c_0_45,hypothesis,
less_equal(b,divide(d,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_41]) ).
cnf(c_0_46,hypothesis,
less_equal(divide(X1,a),b),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_47,hypothesis,
less_equal(d,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_22]),c_0_32]) ).
cnf(c_0_48,negated_conjecture,
b != d,
c_0_44 ).
cnf(c_0_49,hypothesis,
divide(d,a) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_45]),c_0_46])]) ).
cnf(c_0_50,hypothesis,
~ less_equal(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_47]),c_0_48]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/15.40 % Computer : n013.cluster.edu
% 0.04/15.40 % Model : x86_64 x86_64
% 0.04/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.40 % Memory : 8046.5625MB
% 0.04/15.40 % OS : Linux 6.8.0-71-generic
% 0.04/15.40 % CPULimit : 300
% 0.04/15.40 % WCLimit : 300
% 0.04/15.40 % DateTime : Sun Sep 20 20:46:07 UTC 2026
% 0.04/15.40 % CPUTime :
% 0.04/15.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/15.48 Running first-order theorem proving
% 0.04/15.48 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
% 0.16/15.55 % Version: 3.5.1
% 0.16/15.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.55 % Starting new_bool_3 with 300s (1) cores
% 0.16/15.55 % Starting new_bool_1 with 300s (1) cores
% 0.16/15.55 % Starting sh5l with 300s (1) cores
% 0.16/15.55 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3384558 completed with status 0
% 0.16/15.55 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/15.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/15.55 % No SInE strategy applied
% 0.16/15.55 % Search class: FHUSM-FFSS22-MFFFFFNN
% 0.16/15.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/15.55 % Starting SubtermCWHack with 136s (1) cores
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/15.55 % Starting new_bool_3 with 136s (1) cores
% 0.16/15.55 % Starting new_bool_1 with 136s (1) cores
% 0.16/15.55 % new_bool_3 with pid 3384565 completed with status 0
% 0.16/15.55 % Result found by new_bool_3
% 0.16/15.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/15.55 % No SInE strategy applied
% 0.16/15.55 % Search class: FHUSM-FFSS22-MFFFFFNN
% 0.16/15.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/15.55 % Starting SubtermCWHack with 136s (1) cores
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/15.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/15.55 % Starting new_bool_3 with 136s (1) cores
% 0.16/15.55 % Preprocessing time : 0.002 s
% 0.16/15.55 % Presaturation interreduction done
% 0.16/15.55
% 0.16/15.55 % Proof found!
% 0.16/15.55 % SZS status Unsatisfiable
% 0.16/15.55 % SZS output start CNFRefutation
% See solution above
% 0.16/15.55 % Parsed axioms : 17
% 0.16/15.55 % Removed by relevancy pruning/SinE : 0
% 0.16/15.55 % Initial clauses : 17
% 0.16/15.55 % Removed in clause preprocessing : 0
% 0.16/15.55 % Initial clauses in saturation : 17
% 0.16/15.55 % Processed clauses : 162
% 0.16/15.55 % ...of these trivial : 2
% 0.16/15.55 % ...subsumed : 58
% 0.16/15.55 % ...remaining for further processing : 102
% 0.16/15.55 % Other redundant clauses eliminated : 1
% 0.16/15.55 % Clauses deleted for lack of memory : 0
% 0.16/15.55 % Backward-subsumed : 1
% 0.16/15.55 % Backward-rewritten : 9
% 0.16/15.55 % Generated clauses : 1116
% 0.16/15.55 % ...of the previous two non-redundant : 512
% 0.16/15.55 % ...aggressively subsumed : 0
% 0.16/15.55 % Contextual simplify-reflections : 0
% 0.16/15.55 % Paramodulations : 1115
% 0.16/15.55 % Factorizations : 0
% 0.16/15.55 % NegExts : 0
% 0.16/15.55 % Equation resolutions : 1
% 0.16/15.55 % Disequality decompositions : 0
% 0.16/15.55 % Total rewrite steps : 1524
% 0.16/15.55 % ...of those cached : 1231
% 0.16/15.55 % Propositional unsat checks : 0
% 0.16/15.55 % Propositional check models : 0
% 0.16/15.55 % Propositional check unsatisfiable : 0
% 0.16/15.55 % Propositional clauses : 0
% 0.16/15.55 % Propositional clauses after purity: 0
% 0.16/15.55 % Propositional unsat core size : 0
% 0.16/15.55 % Propositional preprocessing time : 0.000
% 0.16/15.55 % Propositional encoding time : 0.000
% 0.16/15.55 % Propositional solver time : 0.000
% 0.16/15.55 % Success case prop preproc time : 0.000
% 0.16/15.55 % Success case prop encoding time : 0.000
% 0.16/15.55 % Success case prop solver time : 0.000
% 0.16/15.55 % Current number of processed clauses : 76
% 0.16/15.55 % Positive orientable unit clauses : 45
% 0.16/15.55 % Positive unorientable unit clauses: 0
% 0.16/15.55 % Negative unit clauses : 2
% 0.16/15.55 % Non-unit-clauses : 29
% 0.16/15.55 % Current number of unprocessed clauses: 379
% 0.16/15.55 % ...number of literals in the above : 420
% 0.16/15.55 % Current number of archived formulas : 0
% 0.16/15.55 % Current number of archived clauses : 26
% 0.16/15.55 % Clause-clause subsumption calls (NU) : 87
% 0.16/15.55 % Rec. Clause-clause subsumption calls : 87
% 0.16/15.55 % Non-unit clause-clause subsumptions : 54
% 0.16/15.55 % Unit Clause-clause subsumption calls : 20
% 0.16/15.55 % Rewrite failures with RHS unbound : 0
% 0.16/15.55 % BW rewrite match attempts : 32
% 0.16/15.55 % BW rewrite match successes : 7
% 0.16/15.55 % Condensation attempts : 0
% 0.16/15.55 % Condensation successes : 0
% 0.16/15.55 % Termbank termtop insertions : 11021
% 0.16/15.55 % Search garbage collected termcells : 16
% 0.16/15.55
% 0.16/15.55 % -------------------------------------------------
% 0.16/15.55 % User time : 0.019 s
% 0.16/15.55 % System time : 0.002 s
% 0.16/15.55 % Total time : 0.020 s
% 0.16/15.55 % Maximum resident set size: 3640 pages
% 0.16/15.55
% 0.16/15.55 % -------------------------------------------------
% 0.16/15.55 % User time : 0.082 s
% 0.16/15.55 % System time : 0.016 s
% 0.16/15.55 % Total time : 0.098 s
% 0.16/15.55 % Maximum resident set size: 4864 pages
% 0.16/15.55 % E exiting
%------------------------------------------------------------------------------