%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT131+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 : n005.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 02:08:32 PM UTC 2026
% Result : Theorem 10.62s 2.17s
% Output : CNFRefutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 28 ( 12 ~; 10 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 19 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_unanimity__def,axiom,
! [X26] :
( c_Arrow__Order__Mirabelle_Ounanimity(X26)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X33,X34] :
( ! [X13] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X34)),hAPP(X3,X13)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X34)),hAPP(X26,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096) ).
fof(fact__096Q_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(c_0_5,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_6,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X221,X222,X223,X224,X226,X230] :
( ( c_Arrow__Order__Mirabelle_Ounanimity(X226)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X226)),esk10_1(X226))),hAPP(X226,esk8_1(X226)))) )
& ( c_Arrow__Order__Mirabelle_Ounanimity(X226)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X226)),esk10_1(X226))),hAPP(esk8_1(X226),X230))) )
& ( c_Arrow__Order__Mirabelle_Ounanimity(X226)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk8_1(X226)),c_Arrow__Order__Mirabelle_OProf)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X223),X224)),hAPP(X221,X222)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X223),X224)),hAPP(X222,esk7_4(X221,X222,X223,X224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X222),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X221) ) ),
inference(distribute,[status(thm)],[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)],[fact_unanimity__def])])])])])])]) ).
fof(c_0_8,plain,
! [X88] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X88))),
inference(variable_rename,[status(thm)],[fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096]) ).
fof(c_0_9,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X2,esk7_4(X1,X2,X3,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X1))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096Q_A_058_AProf_096]) ).
cnf(c_0_13,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(X1,v_Q____))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_15,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT131+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 % Computer : n005.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 04:33:32 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.56 Running first-order theorem proving
% 0.22/0.56 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
% 10.62/2.17 % Version: 3.5.1
% 10.62/2.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.62/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.62/2.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.62/2.17 % Starting new_bool_3 with 300s (1) cores
% 10.62/2.17 % Starting new_bool_1 with 300s (1) cores
% 10.62/2.17 % Starting sh5l with 300s (1) cores
% 10.62/2.17 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2556009 completed with status 0
% 10.62/2.17 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 10.62/2.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.62/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.62/2.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.62/2.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.62/2.17 % No SInE strategy applied
% 10.62/2.17 % Search class: FGHSM-FSLM33-DFFFFFNN
% 10.62/2.17 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 10.62/2.17 % Starting SubtermCWHack with 136s (1) cores
% 10.62/2.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 10.62/2.17 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.62/2.17 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 10.62/2.17 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 10.62/2.17 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2556017 completed with status 0
% 10.62/2.17 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 10.62/2.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.62/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.62/2.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.62/2.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.62/2.17 % No SInE strategy applied
% 10.62/2.17 % Search class: FGHSM-FSLM33-DFFFFFNN
% 10.62/2.17 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 10.62/2.17 % Starting SubtermCWHack with 136s (1) cores
% 10.62/2.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 10.62/2.17 % Preprocessing time : 0.028 s
% 10.62/2.17 % Presaturation interreduction done
% 10.62/2.17
% 10.62/2.17 % Proof found!
% 10.62/2.17 % SZS status Theorem
% 10.62/2.17 % SZS output start CNFRefutation
% See solution above
% 10.62/2.17 % Parsed axioms : 535
% 10.62/2.17 % Removed by relevancy pruning/SinE : 0
% 10.62/2.17 % Initial clauses : 819
% 10.62/2.17 % Removed in clause preprocessing : 32
% 10.62/2.17 % Initial clauses in saturation : 787
% 10.62/2.17 % Processed clauses : 1763
% 10.62/2.17 % ...of these trivial : 32
% 10.62/2.17 % ...subsumed : 201
% 10.62/2.17 % ...remaining for further processing : 1530
% 10.62/2.17 % Other redundant clauses eliminated : 109
% 10.62/2.17 % Clauses deleted for lack of memory : 0
% 10.62/2.17 % Backward-subsumed : 16
% 10.62/2.17 % Backward-rewritten : 14
% 10.62/2.17 % Generated clauses : 17990
% 10.62/2.17 % ...of the previous two non-redundant : 16436
% 10.62/2.17 % ...aggressively subsumed : 0
% 10.62/2.17 % Contextual simplify-reflections : 0
% 10.62/2.17 % Paramodulations : 17880
% 10.62/2.17 % Factorizations : 0
% 10.62/2.17 % NegExts : 0
% 10.62/2.17 % Equation resolutions : 119
% 10.62/2.17 % Disequality decompositions : 0
% 10.62/2.17 % Total rewrite steps : 3598
% 10.62/2.17 % ...of those cached : 2749
% 10.62/2.17 % Propositional unsat checks : 0
% 10.62/2.17 % Propositional check models : 0
% 10.62/2.17 % Propositional check unsatisfiable : 0
% 10.62/2.17 % Propositional clauses : 0
% 10.62/2.17 % Propositional clauses after purity: 0
% 10.62/2.17 % Propositional unsat core size : 0
% 10.62/2.17 % Propositional preprocessing time : 0.000
% 10.62/2.17 % Propositional encoding time : 0.000
% 10.62/2.17 % Propositional solver time : 0.000
% 10.62/2.17 % Success case prop preproc time : 0.000
% 10.62/2.17 % Success case prop encoding time : 0.000
% 10.62/2.17 % Success case prop solver time : 0.000
% 10.62/2.17 % Current number of processed clauses : 792
% 10.62/2.17 % Positive orientable unit clauses : 207
% 10.62/2.17 % Positive unorientable unit clauses: 8
% 10.62/2.17 % Negative unit clauses : 56
% 10.62/2.17 % Non-unit-clauses : 521
% 10.62/2.17 % Current number of unprocessed clauses: 15806
% 10.62/2.17 % ...number of literals in the above : 44396
% 10.62/2.17 % Current number of archived formulas : 0
% 10.62/2.17 % Current number of archived clauses : 677
% 10.62/2.17 % Clause-clause subsumption calls (NU) : 117431
% 10.62/2.17 % Rec. Clause-clause subsumption calls : 62865
% 10.62/2.17 % Non-unit clause-clause subsumptions : 150
% 10.62/2.17 % Unit Clause-clause subsumption calls : 3861
% 10.62/2.17 % Rewrite failures with RHS unbound : 4
% 10.62/2.17 % BW rewrite match attempts : 1560
% 10.62/2.17 % BW rewrite match successes : 126
% 10.62/2.17 % Condensation attempts : 0
% 10.62/2.17 % Condensation successes : 0
% 10.62/2.17 % Termbank termtop insertions : 559781
% 10.62/2.17 % Search garbage collected termcells : 13188
% 10.62/2.17
% 10.62/2.17 % -------------------------------------------------
% 10.62/2.17 % User time : 1.170 s
% 10.62/2.17 % System time : 0.049 s
% 10.62/2.17 % Total time : 1.219 s
% 10.62/2.17 % Maximum resident set size: 7788 pages
% 10.62/2.17
% 10.62/2.17 % -------------------------------------------------
% 10.62/2.17 % User time : 6.080 s
% 10.62/2.17 % System time : 0.296 s
% 10.62/2.17 % Total time : 6.376 s
% 10.62/2.17 % Maximum resident set size: 5632 pages
% 10.62/2.17 % E exiting
%------------------------------------------------------------------------------