%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PHI008^4 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Wed Sep 30 08:20:11 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 11 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 246 ( 39 ~; 32 |; 7 &; 162 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-5 aty)
% Number of variables : 89 ( 8 ^; 80 !; 1 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
qML_mu: $tType ).
thf(decl_sort2,type,
qML_i: $tType ).
thf(decl_23,type,
scott_G: qML_mu > qML_i > $o ).
thf(decl_26,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(decl_28,type,
esk1_1: qML_i > qML_mu ).
thf(decl_29,type,
epred2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_30,type,
esk2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_i ).
thf(decl_31,type,
esk3_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu ).
thf(decl_37,type,
esk8_0: qML_i ).
thf(decl_38,type,
epred4_0: qML_i > $o ).
thf(decl_39,type,
esk9_0: qML_i ).
thf(decl_75,type,
esk42_0: qML_mu ).
thf(decl_76,type,
esk43_0: qML_i ).
thf(decl_81,type,
esk48_0: qML_i ).
thf(fact_4_ess__def,axiom,
( scott_ess_QML_mu
= ( ^ [X9: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ( X9 @ X1 @ X2 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X9 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bEvBt4Y4Ym/E---3.1_84762.p',fact_4_ess__def) ).
thf(fact_9_T2,axiom,
! [X4: qML_i,X19: qML_mu] :
( ( scott_G @ X19 @ X4 )
=> ( scott_ess_QML_mu @ scott_G @ X19 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.bEvBt4Y4Ym/E---3.1_84762.p',fact_9_T2) ).
thf(fact_2_T3,axiom,
! [X4: qML_i,X7: qML_i] :
? [X8: qML_mu] : ( scott_G @ X8 @ X7 ),
file('/export/starexec/sandbox/tmp/tmp.bEvBt4Y4Ym/E---3.1_84762.p',fact_2_T3) ).
thf(conj_0,conjecture,
! [X20: qML_i,X21: qML_i > $o] :
( ~ ( X21 @ X20 )
| ! [X13: qML_i] : ( X21 @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.bEvBt4Y4Ym/E---3.1_84762.p',conj_0) ).
thf(c_0_4,plain,
! [X46: qML_mu > qML_i > $o,X47: qML_mu,X48: qML_i] :
( ( scott_ess_QML_mu @ X46 @ X47 @ X48 )
<=> ( ( X46 @ X47 @ X48 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X47 @ X48 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X46 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_4_ess__def])]) ).
thf(c_0_5,plain,
! [X63: qML_mu > qML_i > $o,X64: qML_mu,X65: qML_i,X66: qML_mu > qML_i > $o,X67: qML_i,X68: qML_mu,X69: qML_mu > qML_i > $o,X70: qML_mu,X71: qML_i] :
( ( ( X63 @ X64 @ X65 )
| ~ ( scott_ess_QML_mu @ X63 @ X64 @ X65 ) )
& ( ~ ( X66 @ X64 @ X65 )
| ~ ( X63 @ X68 @ X67 )
| ( X66 @ X68 @ X67 )
| ~ ( scott_ess_QML_mu @ X63 @ X64 @ X65 ) )
& ( ( epred2_3 @ X69 @ X70 @ X71 @ X70 @ X71 )
| ~ ( X69 @ X70 @ X71 )
| ( scott_ess_QML_mu @ X69 @ X70 @ X71 ) )
& ( ( X69 @ ( esk3_3 @ X69 @ X70 @ X71 ) @ ( esk2_3 @ X69 @ X70 @ X71 ) )
| ~ ( X69 @ X70 @ X71 )
| ( scott_ess_QML_mu @ X69 @ X70 @ X71 ) )
& ( ~ ( epred2_3 @ X69 @ X70 @ X71 @ ( esk3_3 @ X69 @ X70 @ X71 ) @ ( esk2_3 @ X69 @ X70 @ X71 ) )
| ~ ( X69 @ X70 @ X71 )
| ( scott_ess_QML_mu @ X69 @ X70 @ X71 ) ) ),
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)],[c_0_4])])])])])])]) ).
thf(c_0_6,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ X1 @ X2 )
| ~ ( scott_ess_QML_mu @ X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X85: qML_i,X86: qML_mu] :
( ~ ( scott_G @ X86 @ X85 )
| ( scott_ess_QML_mu @ scott_G @ X86 @ X85 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_T2])])]) ).
thf(c_0_8,plain,
! [X1: qML_mu,X2: qML_i] :
~ ( scott_ess_QML_mu
@ ^ [Z0: qML_mu,Z1: qML_i] : ~ $true
@ X1
@ X2 ),
inference(primitive_enumeration,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: qML_mu,X2: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X1 @ X2 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: qML_mu,X2: qML_i] :
( ( ( ^ [Z0: qML_mu,Z1: qML_i] : ~ $true )
!= scott_G )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_8,c_0_9])])]) ).
thf(c_0_11,plain,
! [X60: qML_i] : ( scott_G @ ( esk1_1 @ X60 ) @ X60 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_2_T3])])]) ).
thf(c_0_12,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X8: qML_mu,X5: qML_mu > qML_i > $o,X4: qML_i,X2: qML_i] :
( ( X3 @ X8 @ X4 )
| ~ ( X3 @ X1 @ X2 )
| ~ ( X5 @ X8 @ X4 )
| ~ ( scott_ess_QML_mu @ X5 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,plain,
! [X1: qML_mu,X2: qML_i] :
( ( ( ^ [Z0: qML_i] : ~ $true )
!= ( scott_G @ esk42_0 ) )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(neg_ext,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X1: qML_mu,X2: qML_i] :
( ( scott_G @ esk42_0 @ esk43_0 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(neg_ext,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X2: qML_i] : ( scott_G @ ( esk1_1 @ X2 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: qML_mu,X2: qML_i,X3: qML_mu > qML_i > $o,X8: qML_mu,X4: qML_i] :
( ( X1 = X8 )
| ~ ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X8 @ X4 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_12]) ).
thf(c_0_17,plain,
! [X1: qML_mu,X2: qML_i] :
( ( scott_G @ esk42_0 @ esk48_0 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
scott_G @ esk42_0 @ esk43_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
! [X1: qML_mu,X2: qML_i,X8: qML_mu,X4: qML_i] :
( ( X1 = X8 )
| ~ ( scott_G @ X8 @ X2 )
| ~ ( scott_G @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
thf(c_0_20,plain,
scott_G @ esk42_0 @ esk48_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,plain,
! [X1: qML_mu,X2: qML_i] :
( ( X1 = esk42_0 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,plain,
! [X1: qML_mu,X2: qML_i,X3: qML_mu > qML_i > $o,X8: qML_mu,X4: qML_i] :
( ( X2 = X4 )
| ~ ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X8 @ X4 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_12]) ).
thf(c_0_23,plain,
! [X2: qML_i] :
( ( esk1_1 @ X2 )
= esk42_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
thf(c_0_24,negated_conjecture,
~ ! [X20: qML_i,X21: qML_i > $o] :
( ~ ( X21 @ X20 )
| ! [X13: qML_i] : ( X21 @ X13 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_25,plain,
! [X1: qML_mu,X8: qML_mu,X4: qML_i,X2: qML_i] :
( ( X2 = X4 )
| ~ ( scott_G @ X1 @ X4 )
| ~ ( scott_G @ X8 @ X2 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
thf(c_0_26,plain,
! [X2: qML_i] : ( scott_G @ esk42_0 @ X2 ),
inference(rw,[status(thm)],[c_0_15,c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ( epred4_0 @ esk8_0 )
& ~ ( epred4_0 @ esk9_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_28,plain,
! [X1: qML_mu,X4: qML_i,X2: qML_i] :
( ( X2 = X4 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
~ ( epred4_0 @ esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
! [X2: qML_i,X4: qML_i] : ( X2 = X4 ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
thf(c_0_31,negated_conjecture,
epred4_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PHI008^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:19:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.bEvBt4Y4Ym/E---3.1_84762.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.08/0.15 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.08/0.15 % ho_unfolding_3 with pid 84775 completed with status 0
% 0.08/0.15 % Result found by ho_unfolding_3
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGHNS-FFMF32-SHSFFSBN
% 0.08/0.15 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.15 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.15 % Starting ho_unfolding_3 with 901s (1) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_rwall with 151s (1) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.08/0.15 % Starting ehoh_best8_lambda with 146s (1) cores
% 0.08/0.15 % ehoh_best_nonlift_rwall with pid 84784 completed with status 0
% 0.08/0.15 % Result found by ehoh_best_nonlift_rwall
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGHNS-FFMF32-SHSFFSBN
% 0.08/0.15 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.15 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.15 % Starting ho_unfolding_3 with 901s (1) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_rwall with 151s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15 % Presaturation interreduction done
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 18
% 0.08/0.15 % Removed by relevancy pruning/SinE : 0
% 0.08/0.15 % Initial clauses : 30
% 0.08/0.15 % Removed in clause preprocessing : 6
% 0.08/0.15 % Initial clauses in saturation : 24
% 0.08/0.15 % Processed clauses : 161
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 14
% 0.08/0.15 % ...remaining for further processing : 147
% 0.08/0.15 % Other redundant clauses eliminated : 11
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 7
% 0.08/0.15 % Backward-rewritten : 21
% 0.08/0.15 % Generated clauses : 269
% 0.08/0.15 % ...of the previous two non-redundant : 190
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 0
% 0.08/0.15 % Paramodulations : 146
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 49
% 0.08/0.15 % Equation resolutions : 11
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 15
% 0.08/0.15 % ...of those cached : 0
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 79
% 0.08/0.15 % Positive orientable unit clauses : 7
% 0.08/0.15 % Positive unorientable unit clauses: 1
% 0.08/0.15 % Negative unit clauses : 14
% 0.08/0.15 % Non-unit-clauses : 57
% 0.08/0.15 % Current number of unprocessed clauses: 67
% 0.08/0.15 % ...number of literals in the above : 170
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 68
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 828
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 649
% 0.08/0.15 % Non-unit clause-clause subsumptions : 19
% 0.08/0.15 % Unit Clause-clause subsumption calls : 134
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 312
% 0.08/0.15 % BW rewrite match successes : 41
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 8824
% 0.08/0.15 % Search garbage collected termcells : 670
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.007 s
% 0.08/0.15 % System time : 0.005 s
% 0.08/0.15 % Total time : 0.012 s
% 0.08/0.15 % Maximum resident set size: 3656 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.037 s
% 0.08/0.15 % System time : 0.012 s
% 0.08/0.15 % Total time : 0.050 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------