%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : QUA005^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:21:19 AM UTC 2026
% Result : Theorem 1.30s 0.43s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 38 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 93 ( 9 ~; 0 |; 10 &; 74 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 23 ^; 20 !; 10 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
emptyset: $i > $o ).
thf(decl_25,type,
singleton: $i > $i > $o ).
thf(decl_26,type,
zero: $i ).
thf(decl_27,type,
sup: ( $i > $o ) > $i ).
thf(decl_32,type,
multiplication: $i > $i > $i ).
thf(decl_33,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
one: $i ).
thf(decl_35,type,
esk1_0: $i ).
thf(crossmult_def,axiom,
( crossmult
= ( ^ [X10: $i > $o,X3: $i > $o,X11: $i] :
? [X8: $i,X12: $i] :
( ( X10 @ X8 )
& ( X3 @ X12 )
& ( X11
= ( multiplication @ X8 @ X12 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',crossmult_def) ).
thf(emptyset_def,axiom,
( emptyset
= ( ^ [X1: $i] : ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',emptyset_def) ).
thf(singleton_def,axiom,
( singleton
= ( ^ [X1: $i,X4: $i] : ( X4 = X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',singleton_def) ).
thf(multiplication_def,axiom,
! [X13: $i > $o,X3: $i > $o] :
( ( multiplication @ ( sup @ X13 ) @ ( sup @ X3 ) )
= ( sup @ ( crossmult @ X13 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',multiplication_def) ).
thf(sup_es,axiom,
( ( sup @ emptyset )
= zero ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',sup_es) ).
thf(sup_singleset,axiom,
! [X1: $i] :
( ( sup @ ( singleton @ X1 ) )
= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',sup_singleset) ).
thf(multiplication_neutral_left,axiom,
! [X1: $i] :
( ( multiplication @ one @ X1 )
= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',multiplication_neutral_left) ).
thf(multiplication_anni,conjecture,
! [X8: $i] :
( ( multiplication @ X8 @ zero )
= zero ),
file('/export/starexec/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p',multiplication_anni) ).
thf(c_0_8,plain,
( crossmult
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
? [X8: $i,X12: $i] :
( ( Z0 @ X8 )
& ( Z1 @ X12 )
& ( Z2
= ( multiplication @ X8 @ X12 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[crossmult_def]) ).
thf(c_0_9,plain,
( emptyset
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[emptyset_def]) ).
thf(c_0_10,plain,
( singleton
= ( ^ [Z0: $i,Z1: $i] : Z1 ) ),
inference(fof_simplification,[status(thm)],[singleton_def]) ).
thf(c_0_11,plain,
! [X13: $i > $o,X3: $i > $o] :
( ( multiplication @ ( sup @ X13 ) @ ( sup @ X3 ) )
= ( sup
@ ^ [Z0: $i] :
? [X25: $i,X26: $i] :
( ( X13 @ X25 )
& ( X3 @ X26 )
& ( Z0
= ( multiplication @ X25 @ X26 ) ) ) ) ),
inference(apply_def,[status(thm)],[multiplication_def,c_0_8]) ).
thf(c_0_12,plain,
( ( sup
@ ^ [Z0: $i] : ~ $true )
= zero ),
inference(apply_def,[status(thm)],[sup_es,c_0_9]) ).
thf(c_0_13,plain,
! [X1: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= X1 ),
inference(apply_def,[status(thm)],[sup_singleset,c_0_10]) ).
thf(c_0_14,plain,
! [X35: $i > $o,X36: $i > $o] :
( ( multiplication @ ( sup @ X35 ) @ ( sup @ X36 ) )
= ( sup
@ ^ [Z0: $i] :
? [X25: $i,X26: $i] :
( ( X35 @ X25 )
& ( X36 @ X26 )
& ( Z0
= ( multiplication @ X25 @ X26 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( ( sup
@ ^ [Z0: $i] : ~ $true )
= zero ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X38: $i] :
( ( multiplication @ one @ X38 )
= X38 ),
inference(variable_rename,[status(thm)],[multiplication_neutral_left]) ).
thf(c_0_17,plain,
! [X29: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X29 ) )
= X29 ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
~ ! [X8: $i] :
( ( multiplication @ X8 @ zero )
= zero ),
inference(assume_negation,[status(cth)],[multiplication_anni]) ).
thf(c_0_19,plain,
! [X2: $i > $o,X3: $i > $o] :
( ( multiplication @ ( sup @ X2 ) @ ( sup @ X3 ) )
= ( sup
@ ^ [Z0: $i] :
? [X105: $i,X106: $i] :
( ( X2 @ X105 )
& ( X3 @ X106 )
& ( Z0
= ( multiplication @ X105 @ X106 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
( ( sup
@ ^ [Z0: $i] : ~ $true )
= zero ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X1: $i] :
( ( multiplication @ one @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
! [X1: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
( ( multiplication @ esk1_0 @ zero )
!= zero ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
thf(c_0_24,plain,
! [X2: $i > $o] :
( ( multiplication @ ( sup @ X2 ) @ zero )
= ( sup
@ ^ [Z0: $i] : ~ $true ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_25,plain,
! [X1: $i] :
( ( sup
@ ^ [Z0: $i] :
( Z0
= ( multiplication @ one @ X1 ) ) )
= X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,negated_conjecture,
( ( multiplication @ esk1_0 @ zero )
!= zero ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,plain,
! [X1: $i] :
( ( multiplication @ X1 @ zero )
= zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA005^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:34:50 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.KqvyRFpdlB/E---3.1_1235212.p
% 1.30/0.43 % Version: 3.5.1-ho
% 1.30/0.43 % Preprocessing class: HSSSSMSSSLSCHFN.
% 1.30/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.43 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 1.30/0.43 % Starting sh2lt with 300s (1) cores
% 1.30/0.43 % Starting sh5l with 300s (1) cores
% 1.30/0.43 % Starting pre_casc_6 with 300s (1) cores
% 1.30/0.43 % ehoh_best2_full_lfho with pid 1235225 completed with status 0
% 1.30/0.43 % Result found by ehoh_best2_full_lfho
% 1.30/0.43 % Preprocessing class: HSSSSMSSSLSCHFN.
% 1.30/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.43 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 1.30/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.30/0.43 % No SInE strategy applied
% 1.30/0.43 % Search class: HHUSM-FFSF21-DHFFMFBN
% 1.30/0.43 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 1.30/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.43 % Starting SubtermCWHack with 136s (1) cores
% 1.30/0.43 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 1.30/0.43 % Starting sh5l with 136s (1) cores
% 1.30/0.43 % Starting new_bool_1 with 136s (1) cores
% 1.30/0.43 % Starting new_bool_2 with 136s (1) cores
% 1.30/0.43 % SubtermCWHack with pid 1235229 completed with status 10
% 1.30/0.43 % Starting new_bool_9 with 136s (1) cores
% 1.30/0.43 % new_bool_9 with pid 1235238 completed with status 0
% 1.30/0.43 % Result found by new_bool_9
% 1.30/0.43 % Preprocessing class: HSSSSMSSSLSCHFN.
% 1.30/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.43 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 1.30/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.30/0.43 % No SInE strategy applied
% 1.30/0.43 % Search class: HHUSM-FFSF21-DHFFMFBN
% 1.30/0.43 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 1.30/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.43 % Starting SubtermCWHack with 136s (1) cores
% 1.30/0.43 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 1.30/0.43 % Starting sh5l with 136s (1) cores
% 1.30/0.43 % Starting new_bool_1 with 136s (1) cores
% 1.30/0.43 % Starting new_bool_2 with 136s (1) cores
% 1.30/0.43 % SubtermCWHack with pid 1235229 completed with status 10
% 1.30/0.43 % Starting new_bool_9 with 136s (1) cores
% 1.30/0.43 % Preprocessing time : 0.001 s
% 1.30/0.43 % Presaturation interreduction done
% 1.30/0.43
% 1.30/0.43 % Proof found!
% 1.30/0.43 % SZS status Theorem
% 1.30/0.43 % SZS output start CNFRefutation
% See solution above
% 1.30/0.43 % Parsed axioms : 27
% 1.30/0.43 % Removed by relevancy pruning/SinE : 0
% 1.30/0.43 % Initial clauses : 22
% 1.30/0.43 % Removed in clause preprocessing : 12
% 1.30/0.43 % Initial clauses in saturation : 10
% 1.30/0.43 % Processed clauses : 459
% 1.30/0.43 % ...of these trivial : 9
% 1.30/0.43 % ...subsumed : 233
% 1.30/0.43 % ...remaining for further processing : 217
% 1.30/0.43 % Other redundant clauses eliminated : 71
% 1.30/0.43 % Clauses deleted for lack of memory : 0
% 1.30/0.43 % Backward-subsumed : 0
% 1.30/0.43 % Backward-rewritten : 3
% 1.30/0.43 % Generated clauses : 4097
% 1.30/0.43 % ...of the previous two non-redundant : 3923
% 1.30/0.43 % ...aggressively subsumed : 0
% 1.30/0.43 % Contextual simplify-reflections : 11
% 1.30/0.43 % Paramodulations : 3254
% 1.30/0.43 % Factorizations : 17
% 1.30/0.43 % NegExts : 43
% 1.30/0.43 % Equation resolutions : 83
% 1.30/0.43 % Disequality decompositions : 0
% 1.30/0.43 % Total rewrite steps : 287
% 1.30/0.43 % ...of those cached : 258
% 1.30/0.43 % Propositional unsat checks : 0
% 1.30/0.43 % Propositional check models : 0
% 1.30/0.43 % Propositional check unsatisfiable : 0
% 1.30/0.43 % Propositional clauses : 0
% 1.30/0.43 % Propositional clauses after purity: 0
% 1.30/0.43 % Propositional unsat core size : 0
% 1.30/0.43 % Propositional preprocessing time : 0.000
% 1.30/0.43 % Propositional encoding time : 0.000
% 1.30/0.43 % Propositional solver time : 0.000
% 1.30/0.43 % Success case prop preproc time : 0.000
% 1.30/0.43 % Success case prop encoding time : 0.000
% 1.30/0.43 % Success case prop solver time : 0.000
% 1.30/0.43 % Current number of processed clauses : 192
% 1.30/0.43 % Positive orientable unit clauses : 4
% 1.30/0.43 % Positive unorientable unit clauses: 22
% 1.30/0.43 % Negative unit clauses : 0
% 1.30/0.43 % Non-unit-clauses : 166
% 1.30/0.43 % Current number of unprocessed clauses: 3484
% 1.30/0.43 % ...number of literals in the above : 7240
% 1.30/0.43 % Current number of archived formulas : 0
% 1.30/0.43 % Current number of archived clauses : 25
% 1.30/0.43 % Clause-clause subsumption calls (NU) : 12593
% 1.30/0.43 % Rec. Clause-clause subsumption calls : 7387
% 1.30/0.43 % Non-unit clause-clause subsumptions : 237
% 1.30/0.43 % Unit Clause-clause subsumption calls : 23
% 1.30/0.43 % Rewrite failures with RHS unbound : 1
% 1.30/0.43 % BW rewrite match attempts : 755
% 1.30/0.43 % BW rewrite match successes : 412
% 1.30/0.43 % Condensation attempts : 0
% 1.30/0.43 % Condensation successes : 0
% 1.30/0.43 % Termbank termtop insertions : 402740
% 1.30/0.43 % Search garbage collected termcells : 184
% 1.30/0.43
% 1.30/0.43 % -------------------------------------------------
% 1.30/0.43 % User time : 0.184 s
% 1.30/0.43 % System time : 0.008 s
% 1.30/0.43 % Total time : 0.192 s
% 1.30/0.43 % Maximum resident set size: 3652 pages
% 1.30/0.43
% 1.30/0.43 % -------------------------------------------------
% 1.30/0.43 % User time : 0.817 s
% 1.30/0.43 % System time : 0.048 s
% 1.30/0.43 % Total time : 0.865 s
% 1.30/0.43 % Maximum resident set size: 4608 pages
% 1.30/0.43 % E exiting
%------------------------------------------------------------------------------