%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN012-3 : 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 : n008.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 12:45:41 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 18 unt; 0 nHn; 13 RR)
% Number of literals : 39 ( 13 equ; 15 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(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(prove_a_LE_a,negated_conjecture,
~ less_equal(a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_LE_a) ).
cnf(c_0_7,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_8,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_7 ).
cnf(c_0_9,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_10,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_11,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_13,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_14,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_16,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_17,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_13 ).
cnf(c_0_18,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_16 ).
cnf(c_0_20,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12])]) ).
cnf(c_0_21,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
~ less_equal(a,a),
inference(fof_simplification,[status(thm)],[prove_a_LE_a]) ).
cnf(c_0_23,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_12])]) ).
cnf(c_0_24,negated_conjecture,
~ less_equal(a,a),
c_0_22 ).
cnf(c_0_25,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:47:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3580980 completed with status 0
% 0.13/0.43 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.13/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.43 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with pid 3580987 completed with status 0
% 0.13/0.43 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43 % Presaturation interreduction done
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 8
% 0.13/0.43 % Removed by relevancy pruning/SinE : 0
% 0.13/0.43 % Initial clauses : 8
% 0.13/0.43 % Removed in clause preprocessing : 0
% 0.13/0.43 % Initial clauses in saturation : 8
% 0.13/0.43 % Processed clauses : 35
% 0.13/0.43 % ...of these trivial : 2
% 0.13/0.43 % ...subsumed : 2
% 0.13/0.43 % ...remaining for further processing : 31
% 0.13/0.43 % Other redundant clauses eliminated : 0
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 0
% 0.13/0.43 % Backward-rewritten : 5
% 0.13/0.43 % Generated clauses : 117
% 0.13/0.43 % ...of the previous two non-redundant : 45
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 0
% 0.13/0.43 % Paramodulations : 117
% 0.13/0.43 % Factorizations : 0
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 0
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 147
% 0.13/0.43 % ...of those cached : 106
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 18
% 0.13/0.43 % Positive orientable unit clauses : 12
% 0.13/0.43 % Positive unorientable unit clauses: 0
% 0.13/0.43 % Negative unit clauses : 0
% 0.13/0.43 % Non-unit-clauses : 6
% 0.13/0.43 % Current number of unprocessed clauses: 25
% 0.13/0.43 % ...number of literals in the above : 30
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 13
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 4
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 4
% 0.13/0.43 % Non-unit clause-clause subsumptions : 2
% 0.13/0.43 % Unit Clause-clause subsumption calls : 2
% 0.13/0.43 % Rewrite failures with RHS unbound : 0
% 0.13/0.43 % BW rewrite match attempts : 26
% 0.13/0.43 % BW rewrite match successes : 4
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 1153
% 0.13/0.43 % Search garbage collected termcells : 10
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.005 s
% 0.13/0.43 % System time : 0.003 s
% 0.13/0.43 % Total time : 0.007 s
% 0.13/0.43 % Maximum resident set size: 3380 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.016 s
% 0.13/0.43 % System time : 0.015 s
% 0.13/0.43 % Total time : 0.031 s
% 0.13/0.43 % Maximum resident set size: 4608 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------