%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:45:38 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 16 unt; 0 nHn; 28 RR)
% Number of literals : 64 ( 6 equ; 37 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 54 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(c_0_9,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
inference(fof_simplification,[status(thm)],[xQyLEz_implies_xQzLEy]) ).
cnf(c_0_10,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_11,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
c_0_9 ).
cnf(c_0_12,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_13,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_10 ).
cnf(c_0_14,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_15,plain,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
inference(fof_simplification,[status(thm)],[xLEy_implies_zQyLEzQx]) ).
cnf(c_0_16,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_17,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_18,hypothesis,
( ~ less_equal(X2,idQ_idQa)
| ~ quotient(identity,X1,X2)
| less_equal(idQ__idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
idQa != idQ__idQ_idQa,
inference(fof_simplification,[status(thm)],[prove_one_inversion_equals_three]) ).
cnf(c_0_21,plain,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
c_0_15 ).
cnf(c_0_22,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_23,hypothesis,
( ~ less_equal(X2,idQa)
| ~ quotient(identity,X1,X2)
| less_equal(idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_24,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_17 ).
cnf(c_0_25,hypothesis,
less_equal(idQ__idQ_idQa,idQa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_19])]) ).
cnf(c_0_26,negated_conjecture,
idQa != idQ__idQ_idQa,
c_0_20 ).
cnf(c_0_27,hypothesis,
( ~ less_equal(X2,a)
| ~ quotient(identity,X2,X1)
| less_equal(idQa,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
less_equal(idQ_idQa,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_19])]) ).
cnf(c_0_29,hypothesis,
~ less_equal(idQa,idQ__idQ_idQa),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_12]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 % Computer : n016.cluster.edu
% 0.14/0.44 % Model : x86_64 x86_64
% 0.14/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.44 % Memory : 8046.5625MB
% 0.14/0.44 % OS : Linux 6.8.0-71-generic
% 0.14/0.44 % CPULimit : 300
% 0.14/0.44 % WCLimit : 300
% 0.14/0.44 % DateTime : Sun Sep 20 20:51:23 UTC 2026
% 0.14/0.44 % CPUTime :
% 0.14/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 % Version: 3.5.1
% 0.19/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 % Starting sh5l with 300s (1) cores
% 0.19/0.51 % new_bool_1 with pid 783426 completed with status 0
% 0.19/0.51 % Result found by new_bool_1
% 0.19/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FHUSM-FFSS00-SFFFFFNN
% 0.19/0.51 % partial match(2): FHUNF-FFSS00-SFFFFFNN
% 0.19/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.51 % SubtermCWHack with pid 783432 completed with status 0
% 0.19/0.51 % Result found by SubtermCWHack
% 0.19/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FHUSM-FFSS00-SFFFFFNN
% 0.19/0.51 % partial match(2): FHUNF-FFSS00-SFFFFFNN
% 0.19/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.51 % Preprocessing time : 0.001 s
% 0.19/0.51
% 0.19/0.51 % Proof found!
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
% 0.19/0.51 % Parsed axioms : 21
% 0.19/0.51 % Removed by relevancy pruning/SinE : 1
% 0.19/0.51 % Initial clauses : 20
% 0.19/0.51 % Removed in clause preprocessing : 0
% 0.19/0.51 % Initial clauses in saturation : 20
% 0.19/0.51 % Processed clauses : 176
% 0.19/0.51 % ...of these trivial : 0
% 0.19/0.51 % ...subsumed : 60
% 0.19/0.51 % ...remaining for further processing : 116
% 0.19/0.51 % Other redundant clauses eliminated : 0
% 0.19/0.51 % Clauses deleted for lack of memory : 0
% 0.19/0.51 % Backward-subsumed : 13
% 0.19/0.51 % Backward-rewritten : 0
% 0.19/0.51 % Generated clauses : 418
% 0.19/0.51 % ...of the previous two non-redundant : 322
% 0.19/0.51 % ...aggressively subsumed : 0
% 0.19/0.51 % Contextual simplify-reflections : 0
% 0.19/0.51 % Paramodulations : 418
% 0.19/0.51 % Factorizations : 0
% 0.19/0.51 % NegExts : 0
% 0.19/0.51 % Equation resolutions : 0
% 0.19/0.51 % Disequality decompositions : 0
% 0.19/0.51 % Total rewrite steps : 123
% 0.19/0.51 % ...of those cached : 94
% 0.19/0.51 % Propositional unsat checks : 0
% 0.19/0.51 % Propositional check models : 0
% 0.19/0.51 % Propositional check unsatisfiable : 0
% 0.19/0.51 % Propositional clauses : 0
% 0.19/0.51 % Propositional clauses after purity: 0
% 0.19/0.51 % Propositional unsat core size : 0
% 0.19/0.51 % Propositional preprocessing time : 0.000
% 0.19/0.51 % Propositional encoding time : 0.000
% 0.19/0.51 % Propositional solver time : 0.000
% 0.19/0.51 % Success case prop preproc time : 0.000
% 0.19/0.51 % Success case prop encoding time : 0.000
% 0.19/0.51 % Success case prop solver time : 0.000
% 0.19/0.51 % Current number of processed clauses : 103
% 0.19/0.51 % Positive orientable unit clauses : 14
% 0.19/0.51 % Positive unorientable unit clauses: 0
% 0.19/0.51 % Negative unit clauses : 12
% 0.19/0.51 % Non-unit-clauses : 77
% 0.19/0.51 % Current number of unprocessed clauses: 137
% 0.19/0.51 % ...number of literals in the above : 387
% 0.19/0.51 % Current number of archived formulas : 0
% 0.19/0.51 % Current number of archived clauses : 13
% 0.19/0.51 % Clause-clause subsumption calls (NU) : 542
% 0.19/0.51 % Rec. Clause-clause subsumption calls : 526
% 0.19/0.51 % Non-unit clause-clause subsumptions : 50
% 0.19/0.51 % Unit Clause-clause subsumption calls : 96
% 0.19/0.51 % Rewrite failures with RHS unbound : 0
% 0.19/0.51 % BW rewrite match attempts : 11
% 0.19/0.51 % BW rewrite match successes : 0
% 0.19/0.51 % Condensation attempts : 0
% 0.19/0.51 % Condensation successes : 0
% 0.19/0.51 % Termbank termtop insertions : 4269
% 0.19/0.51 % Search garbage collected termcells : 57
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.007 s
% 0.19/0.51 % System time : 0.000 s
% 0.19/0.51 % Total time : 0.008 s
% 0.19/0.51 % Maximum resident set size: 3644 pages
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.008 s
% 0.19/0.51 % System time : 0.005 s
% 0.19/0.51 % Total time : 0.013 s
% 0.19/0.51 % Maximum resident set size: 4864 pages
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------