%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN010-4 : 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 : n010.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 12:45:40 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 21 unt; 0 nHn; 15 RR)
% Number of literals : 46 ( 19 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 4 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(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(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(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
cnf(one_inversion_equals_three,axiom,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
cnf(c_0_9,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_10,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_11,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[property_of_divide1]) ).
cnf(c_0_12,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_9 ).
cnf(c_0_13,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_14,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_10 ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
c_0_11 ).
cnf(c_0_17,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ less_equal(X1,zero)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
divide(X1,divide(X1,zero)) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_22,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_23,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_24,plain,
( ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2)))
| divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_25,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_22]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(fof_simplification,[status(thm)],[prove_property_of_inversion]) ).
cnf(c_0_27,plain,
divide(divide(X1,X2),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_25]),c_0_25]),c_0_23])]) ).
cnf(c_0_28,axiom,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
one_inversion_equals_three ).
cnf(c_0_29,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
c_0_26 ).
cnf(c_0_30,plain,
divide(divide(identity,X1),divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n010.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 20:46:41 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3490608 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 3490615 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42 % Presaturation interreduction done
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 17
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 17
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 17
% 0.13/0.42 % Processed clauses : 112
% 0.13/0.42 % ...of these trivial : 4
% 0.13/0.42 % ...subsumed : 37
% 0.13/0.42 % ...remaining for further processing : 71
% 0.13/0.42 % Other redundant clauses eliminated : 1
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 2
% 0.13/0.42 % Backward-rewritten : 11
% 0.13/0.42 % Generated clauses : 703
% 0.13/0.42 % ...of the previous two non-redundant : 257
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 0
% 0.13/0.42 % Paramodulations : 702
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 1
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 825
% 0.13/0.42 % ...of those cached : 675
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 41
% 0.13/0.42 % Positive orientable unit clauses : 20
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 0
% 0.13/0.42 % Non-unit-clauses : 21
% 0.13/0.42 % Current number of unprocessed clauses: 169
% 0.13/0.42 % ...number of literals in the above : 209
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 30
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 75
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 75
% 0.13/0.42 % Non-unit clause-clause subsumptions : 39
% 0.13/0.42 % Unit Clause-clause subsumption calls : 15
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 44
% 0.13/0.42 % BW rewrite match successes : 7
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 6750
% 0.13/0.42 % Search garbage collected termcells : 19
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.005 s
% 0.13/0.42 % System time : 0.002 s
% 0.13/0.42 % Total time : 0.007 s
% 0.13/0.42 % Maximum resident set size: 3640 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.029 s
% 0.13/0.42 % System time : 0.010 s
% 0.13/0.42 % Total time : 0.040 s
% 0.13/0.42 % Maximum resident set size: 4608 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------