%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW312+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 03:10:16 PM UTC 2026
% Result : Theorem 0.15s 6.02s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 57 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 15 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 8 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_emptyE,axiom,
! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_all__not__in__conv,axiom,
! [X11,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
<=> X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_mem__def,axiom,
! [X11,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
<=> hBOOL(hAPP(X11,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_singleton__conv2,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(conj_5,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(fact_hoare__derivs_Oinsert,axiom,
! [X7,X10,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X10),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7)
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X10),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(conj_3,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(conj_4,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_8,plain,
! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(c_0_9,plain,
! [X11,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
<=> X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(c_0_10,plain,
! [X331,X332] : ~ hBOOL(hAPP(hAPP(c_member(X332),X331),c_Orderings_Obot__class_Obot(tc_fun(X332,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
fof(c_0_11,plain,
! [X671,X672,X673] :
( ( hBOOL(hAPP(hAPP(c_member(X673),X672),X671))
| ~ hBOOL(hAPP(X671,X672)) )
& ( hBOOL(hAPP(X671,X672))
| ~ hBOOL(hAPP(hAPP(c_member(X673),X672),X671)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
fof(c_0_12,plain,
! [X344,X345,X347,X348,X349] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X348),X349),X347))
| X347 != c_Orderings_Obot__class_Obot(tc_fun(X348,tc_HOL_Obool)) )
& ( X344 = c_Orderings_Obot__class_Obot(tc_fun(X345,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X345),esk3_2(X344,X345)),X344)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).
cnf(c_0_13,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),esk3_2(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X1747,X1748] : hAPP(c_Set_OCollect(X1748),hAPP(c_fequal,X1747)) = hAPP(hAPP(c_Set_Oinsert(X1748),X1747),c_Orderings_Obot__class_Obot(tc_fun(X1748,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
cnf(c_0_18,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( hBOOL(hAPP(X1,esk3_2(X1,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(assume_negation,[status(cth)],[conj_5]) ).
fof(c_0_21,plain,
! [X303,X304,X305,X306] :
( c_Hoare__Mirabelle_Ohoare__derivs(X306,X305,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X306)),X304),X303))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X306,X305,X303)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X306,X305,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X306)),X304),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X306),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])])]) ).
cnf(c_0_22,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[conj_3]) ).
fof(c_0_28,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(c_fequal,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)) ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,v_t))),
inference(rw,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,hypothesis,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW312+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.38 % Computer : n011.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 09:46:49 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/6.02 % Version: 3.5.1
% 0.15/6.02 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.15/6.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/6.02 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/6.02 % Starting new_bool_3 with 300s (1) cores
% 0.15/6.02 % Starting new_bool_1 with 300s (1) cores
% 0.15/6.02 % Starting sh5l with 300s (1) cores
% 0.15/6.02 % new_bool_3 with pid 1594971 completed with status 0
% 0.15/6.02 % Result found by new_bool_3
% 0.15/6.02 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.15/6.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/6.02 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/6.02 % Starting new_bool_3 with 300s (1) cores
% 0.15/6.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/6.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/6.02 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.15/6.02 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.15/6.02 % Starting SubtermCWHack with 28s (1) cores
% 0.15/6.02 % SubtermCWHack with pid 1594975 completed with status 0
% 0.15/6.02 % Result found by SubtermCWHack
% 0.15/6.02 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.15/6.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/6.02 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/6.02 % Starting new_bool_3 with 300s (1) cores
% 0.15/6.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/6.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/6.02 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.15/6.02 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.15/6.02 % Starting SubtermCWHack with 28s (1) cores
% 0.15/6.02 % Preprocessing time : 0.013 s
% 0.15/6.02
% 0.15/6.02 % Proof found!
% 0.15/6.02 % SZS status Theorem
% 0.15/6.02 % SZS output start CNFRefutation
% See solution above
% 0.15/6.02 % Parsed axioms : 5245
% 0.15/6.02 % Removed by relevancy pruning/SinE : 4674
% 0.15/6.02 % Initial clauses : 822
% 0.15/6.02 % Removed in clause preprocessing : 33
% 0.15/6.02 % Initial clauses in saturation : 789
% 0.15/6.02 % Processed clauses : 3488
% 0.15/6.02 % ...of these trivial : 93
% 0.15/6.02 % ...subsumed : 2169
% 0.15/6.02 % ...remaining for further processing : 1226
% 0.15/6.02 % Other redundant clauses eliminated : 175
% 0.15/6.02 % Clauses deleted for lack of memory : 0
% 0.15/6.02 % Backward-subsumed : 39
% 0.15/6.02 % Backward-rewritten : 44
% 0.15/6.02 % Generated clauses : 16495
% 0.15/6.02 % ...of the previous two non-redundant : 14027
% 0.15/6.02 % ...aggressively subsumed : 0
% 0.15/6.02 % Contextual simplify-reflections : 2
% 0.15/6.02 % Paramodulations : 16302
% 0.15/6.02 % Factorizations : 8
% 0.15/6.02 % NegExts : 0
% 0.15/6.02 % Equation resolutions : 191
% 0.15/6.02 % Disequality decompositions : 0
% 0.15/6.02 % Total rewrite steps : 4304
% 0.15/6.02 % ...of those cached : 3210
% 0.15/6.02 % Propositional unsat checks : 0
% 0.15/6.02 % Propositional check models : 0
% 0.15/6.02 % Propositional check unsatisfiable : 0
% 0.15/6.02 % Propositional clauses : 0
% 0.15/6.02 % Propositional clauses after purity: 0
% 0.15/6.02 % Propositional unsat core size : 0
% 0.15/6.02 % Propositional preprocessing time : 0.000
% 0.15/6.02 % Propositional encoding time : 0.000
% 0.15/6.02 % Propositional solver time : 0.000
% 0.15/6.02 % Success case prop preproc time : 0.000
% 0.15/6.02 % Success case prop encoding time : 0.000
% 0.15/6.02 % Success case prop solver time : 0.000
% 0.15/6.02 % Current number of processed clauses : 1082
% 0.15/6.02 % Positive orientable unit clauses : 269
% 0.15/6.02 % Positive unorientable unit clauses: 16
% 0.15/6.02 % Negative unit clauses : 107
% 0.15/6.02 % Non-unit-clauses : 690
% 0.15/6.02 % Current number of unprocessed clauses: 11114
% 0.15/6.02 % ...number of literals in the above : 29093
% 0.15/6.02 % Current number of archived formulas : 0
% 0.15/6.02 % Current number of archived clauses : 83
% 0.15/6.02 % Clause-clause subsumption calls (NU) : 55563
% 0.15/6.02 % Rec. Clause-clause subsumption calls : 37877
% 0.15/6.02 % Non-unit clause-clause subsumptions : 1279
% 0.15/6.02 % Unit Clause-clause subsumption calls : 1649
% 0.15/6.02 % Rewrite failures with RHS unbound : 164
% 0.15/6.02 % BW rewrite match attempts : 5503
% 0.15/6.02 % BW rewrite match successes : 136
% 0.15/6.02 % Condensation attempts : 0
% 0.15/6.02 % Condensation successes : 0
% 0.15/6.02 % Termbank termtop insertions : 528266
% 0.15/6.02 % Search garbage collected termcells : 54722
% 0.15/6.02
% 0.15/6.02 % -------------------------------------------------
% 0.15/6.02 % User time : 0.255 s
% 0.15/6.02 % System time : 0.033 s
% 0.15/6.02 % Total time : 0.288 s
% 0.15/6.02 % Maximum resident set size: 13220 pages
% 0.15/6.02
% 0.15/6.02 % -------------------------------------------------
% 0.15/6.02 % User time : 0.520 s
% 0.15/6.02 % System time : 0.055 s
% 0.15/6.02 % Total time : 0.575 s
% 0.15/6.02 % Maximum resident set size: 12288 pages
% 0.15/6.02 % E exiting
%------------------------------------------------------------------------------