%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : HEN006-4 : 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 : 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 12:45:45 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 23 RR)
% Number of literals : 49 ( 12 equ; 23 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 6 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(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(a_divide_b_LE_d,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_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(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(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(prove_a_divide_d_LE_b,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
cnf(c_0_9,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_10,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_11,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_9 ).
cnf(c_0_12,hypothesis,
less_equal(divide(a,b),d),
a_divide_b_LE_d ).
cnf(c_0_13,plain,
( ~ less_equal(X2,X3)
| ~ less_equal(X1,X2)
| less_equal(X1,X3) ),
c_0_10 ).
cnf(c_0_14,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_15,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_16,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_17,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_18,hypothesis,
divide(divide(a,b),d) = zero,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( ~ less_equal(X1,divide(X2,X3))
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_15 ).
cnf(c_0_21,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_16 ).
cnf(c_0_22,hypothesis,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_24,negated_conjecture,
~ less_equal(divide(a,d),b),
inference(fof_simplification,[status(thm)],[prove_a_divide_d_LE_b]) ).
cnf(c_0_25,plain,
( divide(X1,divide(X2,X3)) != zero
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
divide(divide(a,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
~ less_equal(divide(a,d),b),
c_0_24 ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.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 20:46:38 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % sh5l with pid 3578509 completed with status 0
% 0.11/0.44 % Result found by sh5l
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.44 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 3578513 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.44 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Unsatisfiable
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 14
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 14
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 14
% 0.11/0.44 % Processed clauses : 80
% 0.11/0.44 % ...of these trivial : 1
% 0.11/0.44 % ...subsumed : 26
% 0.11/0.44 % ...remaining for further processing : 53
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 3
% 0.11/0.44 % Generated clauses : 457
% 0.11/0.44 % ...of the previous two non-redundant : 210
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 457
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 454
% 0.11/0.44 % ...of those cached : 359
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 50
% 0.11/0.44 % Positive orientable unit clauses : 25
% 0.11/0.44 % Positive unorientable unit clauses: 0
% 0.11/0.44 % Negative unit clauses : 3
% 0.11/0.44 % Non-unit-clauses : 22
% 0.11/0.44 % Current number of unprocessed clauses: 123
% 0.11/0.44 % ...number of literals in the above : 189
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 3
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 55
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 55
% 0.11/0.44 % Non-unit clause-clause subsumptions : 26
% 0.11/0.44 % Unit Clause-clause subsumption calls : 0
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 21
% 0.11/0.44 % BW rewrite match successes : 3
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 4250
% 0.11/0.44 % Search garbage collected termcells : 14
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.004 s
% 0.11/0.44 % System time : 0.002 s
% 0.11/0.44 % Total time : 0.006 s
% 0.11/0.44 % Maximum resident set size: 3640 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.007 s
% 0.11/0.44 % System time : 0.006 s
% 0.11/0.44 % Total time : 0.012 s
% 0.11/0.44 % Maximum resident set size: 4608 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------