%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MSC025^2 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 : Wed Sep 30 08:15:34 AM UTC 2026
% Result : Theorem 196.06s 28.62s
% Output : CNFRefutation 196.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 63 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 47 ~; 28 |; 12 &; 48 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
one: $i ).
thf(decl_24,type,
two: $i ).
thf(decl_25,type,
b1: $o > $i ).
thf(decl_26,type,
b2: $o > $i ).
thf(decl_27,type,
esk1_0: $o > $i ).
thf(decl_28,type,
esk2_0: $o ).
thf(decl_29,type,
esk3_0: $o ).
thf(goal,conjecture,
! [X4: $o > $i] :
( ! [X5: $o] :
( ( X4 @ X5 )
!= ( X4 @ ~ X5 ) )
=> ( ( X4 = b1 )
| ( X4 = b2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.asQNEPprdN/E---3.1_4150918.p',goal) ).
thf(b1,axiom,
! [X2: $o] :
( ( X2
=> ( ( b1 @ X2 )
= one ) )
& ( ~ X2
=> ( ( b1 @ X2 )
= two ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.asQNEPprdN/E---3.1_4150918.p',b1) ).
thf(binarity_exhaust,axiom,
! [X1: $i] :
( ( X1 = one )
| ( X1 = two ) ),
file('/export/starexec/sandbox2/tmp/tmp.asQNEPprdN/E---3.1_4150918.p',binarity_exhaust) ).
thf(b2,axiom,
! [X3: $o] :
( ( X3
=> ( ( b2 @ X3 )
= two ) )
& ( ~ X3
=> ( ( b2 @ X3 )
= one ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.asQNEPprdN/E---3.1_4150918.p',b2) ).
thf(binarity_distinc,axiom,
one != two,
file('/export/starexec/sandbox2/tmp/tmp.asQNEPprdN/E---3.1_4150918.p',binarity_distinc) ).
thf(c_0_5,negated_conjecture,
~ ! [X4: $o > $i] :
( ! [X5: $o] :
( ( X4 @ X5 )
!= ( X4 @ ~ X5 ) )
=> ( ( X4 = b1 )
| ( X4 = b2 ) ) ),
inference(assume_negation,[status(cth)],[goal]) ).
thf(c_0_6,negated_conjecture,
~ ! [X4: $o > $i] :
( ! [X5: $o] :
~ ( ( X5
| ( ( X4 @ X5 )
= ( X4 @ $true ) ) )
& ( ~ X5
| ( ( X4 @ X5 )
= ( X4 @ $false ) ) ) )
=> ( ( X4 = b1 )
| ( X4 = b2 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_5])]) ).
thf(c_0_7,negated_conjecture,
! [X12: $o] :
( ( X12
| ~ X12 )
& ( ( ( esk1_0 @ X12 )
!= ( esk1_0 @ $false ) )
| ~ X12 )
& ( X12
| ( ( esk1_0 @ X12 )
!= ( esk1_0 @ $true ) ) )
& ( ( ( esk1_0 @ X12 )
!= ( esk1_0 @ $false ) )
| ( ( esk1_0 @ X12 )
!= ( esk1_0 @ $true ) ) )
& ( esk1_0 != b1 )
& ( esk1_0 != b2 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
thf(c_0_8,plain,
! [X2: $o] :
( ( X2
=> ( ( b1 @ X2 )
= one ) )
& ( ~ X2
=> ( ( b1 @ X2 )
= two ) ) ),
inference(fof_simplification,[status(thm)],[b1]) ).
thf(c_0_9,negated_conjecture,
esk1_0 != b1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X14: $o] :
( ( ~ X14
| ( ( b1 @ X14 )
= one ) )
& ( X14
| ( ( b1 @ X14 )
= two ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_11,plain,
! [X15: $i] :
( ( X15 = one )
| ( X15 = two ) ),
inference(variable_rename,[status(thm)],[binarity_exhaust]) ).
thf(c_0_12,negated_conjecture,
( ( b1 @ esk2_0 )
!= ( esk1_0 @ esk2_0 ) ),
inference(neg_ext,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( ( b1 @ $true )
= one ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10])])]) ).
thf(c_0_14,plain,
! [X1: $i] :
( ( X1 = one )
| ( X1 = two ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( ( b1 @ ~ $true )
= two ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10])])]) ).
thf(c_0_16,plain,
! [X3: $o] :
( ( X3
=> ( ( b2 @ X3 )
= two ) )
& ( ~ X3
=> ( ( b2 @ X3 )
= one ) ) ),
inference(fof_simplification,[status(thm)],[b2]) ).
thf(c_0_17,plain,
( ( ( esk1_0 @ esk2_0 )
!= one )
| ~ esk2_0 ),
inference(ext_sup,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
! [X10: $i,X1: $i] :
( ( X1 = one )
| ( X10 = one )
| ( X10 = X1 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
thf(c_0_19,plain,
( esk2_0
| ( ( esk1_0 @ esk2_0 )
!= two ) ),
inference(ext_sup,[status(thm)],[c_0_12,c_0_15]) ).
thf(c_0_20,negated_conjecture,
esk1_0 != b2,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_21,plain,
! [X13: $o] :
( ( ~ X13
| ( ( b2 @ X13 )
= two ) )
& ( X13
| ( ( b2 @ X13 )
= one ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
thf(c_0_22,negated_conjecture,
( ( esk1_0 @ $true )
!= ( esk1_0 @ ~ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7])])]) ).
thf(c_0_23,plain,
! [X1: $i] :
( ( ( esk1_0 @ $true )
= X1 )
| ( X1 = one )
| ~ esk2_0 ),
inference(local_rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_24,plain,
( ( ( esk1_0 @ ~ $true )
= one )
| esk2_0 ),
inference(local_rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14])]) ).
thf(c_0_25,negated_conjecture,
( ( b2 @ esk3_0 )
!= ( esk1_0 @ esk3_0 ) ),
inference(neg_ext,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
( ( b2 @ $true )
= two ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).
thf(c_0_27,plain,
( ( b2 @ ~ $true )
= one ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).
thf(c_0_28,negated_conjecture,
( ( esk1_0 @ ~ $true )
= one ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
thf(c_0_29,plain,
( ( ( esk1_0 @ esk3_0 )
!= two )
| ~ esk3_0 ),
inference(ext_sup,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,plain,
one != two,
inference(fof_simplification,[status(thm)],[binarity_distinc]) ).
thf(c_0_31,plain,
( esk3_0
| ( ( esk1_0 @ esk3_0 )
!= one ) ),
inference(ext_sup,[status(thm)],[c_0_25,c_0_27]) ).
thf(c_0_32,negated_conjecture,
( ( esk1_0 @ $true )
!= one ),
inference(rw,[status(thm)],[c_0_22,c_0_28]) ).
thf(c_0_33,plain,
( ( ( esk1_0 @ $true )
= one )
| ~ esk3_0 ),
inference(local_rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14])]) ).
thf(c_0_34,plain,
one != two,
inference(fof_nnf,[status(thm)],[c_0_30]) ).
thf(c_0_35,plain,
! [X1: $i] :
( ( ( esk1_0 @ ~ $true )
= X1 )
| ( X1 = one )
| esk3_0 ),
inference(local_rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_18])]) ).
thf(c_0_36,plain,
~ esk3_0,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_37,plain,
one != two,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_38,plain,
! [X1: $i] : ( one = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_28])]),c_0_36]) ).
thf(c_0_39,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC025^2 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n011.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 11:23:16 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.29 Running higher-order theorem proving
% 0.08/0.30 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.asQNEPprdN/E---3.1_4150918.p
% 196.06/28.62 % Version: 3.5.1-ho
% 196.06/28.62 % Preprocessing class: HSSSSMSSSSSNSSA.
% 196.06/28.62 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 196.06/28.62 % Starting post_as_ho12 with 300s (1) cores
% 196.06/28.62 % Starting new_bool_9 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho1 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho4 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho2 with 300s (1) cores
% 196.06/28.62 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 196.06/28.62 % Starting full_lambda_10 with 300s (1) cores
% 196.06/28.62 % Starting new_ho_8 with 300s (1) cores
% 196.06/28.62 % full_lambda_10 with pid 4150937 completed with status 0
% 196.06/28.62 % Result found by full_lambda_10
% 196.06/28.62 % Preprocessing class: HSSSSMSSSSSNSSA.
% 196.06/28.62 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 196.06/28.62 % Starting post_as_ho12 with 300s (1) cores
% 196.06/28.62 % Starting new_bool_9 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho1 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho4 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho2 with 300s (1) cores
% 196.06/28.62 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 196.06/28.62 % Starting full_lambda_10 with 300s (1) cores
% 196.06/28.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 196.06/28.62 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 196.06/28.62 % Search class: HGHPF-FFSS11-SSSFFFBN
% 196.06/28.62 % partial match(3): HGHNF-FFSF11-SSSFFMBN
% 196.06/28.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 196.06/28.62 % Starting SubtermCWHack with 28s (1) cores
% 196.06/28.62 % SubtermCWHack with pid 4150946 completed with status 8
% 196.06/28.62 % Starting full_lambda_10 with 31s (1) cores
% 196.06/28.62 % full_lambda_10 with pid 4151043 completed with status 0
% 196.06/28.62 % Result found by full_lambda_10
% 196.06/28.62 % Preprocessing class: HSSSSMSSSSSNSSA.
% 196.06/28.62 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 196.06/28.62 % Starting post_as_ho12 with 300s (1) cores
% 196.06/28.62 % Starting new_bool_9 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho1 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho4 with 300s (1) cores
% 196.06/28.62 % Starting post_as_ho2 with 300s (1) cores
% 196.06/28.62 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 196.06/28.62 % Starting full_lambda_10 with 300s (1) cores
% 196.06/28.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 196.06/28.62 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 196.06/28.62 % Search class: HGHPF-FFSS11-SSSFFFBN
% 196.06/28.62 % partial match(3): HGHNF-FFSF11-SSSFFMBN
% 196.06/28.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 196.06/28.62 % Starting SubtermCWHack with 28s (1) cores
% 196.06/28.62 % SubtermCWHack with pid 4150946 completed with status 8
% 196.06/28.62 % Starting full_lambda_10 with 31s (1) cores
% 196.06/28.62 % Preprocessing time : 0.001 s
% 196.06/28.62 % Presaturation interreduction done
% 196.06/28.62
% 196.06/28.62 % Proof found!
% 196.06/28.62 % SZS status Theorem
% 196.06/28.62 % SZS output start CNFRefutation
% See solution above
% 196.06/28.62 % Parsed axioms : 9
% 196.06/28.62 % Removed by relevancy pruning/SinE : 4
% 196.06/28.62 % Initial clauses : 12
% 196.06/28.62 % Removed in clause preprocessing : 1
% 196.06/28.62 % Initial clauses in saturation : 11
% 196.06/28.62 % Processed clauses : 80
% 196.06/28.62 % ...of these trivial : 0
% 196.06/28.62 % ...subsumed : 32
% 196.06/28.62 % ...remaining for further processing : 48
% 196.06/28.62 % Other redundant clauses eliminated : 22
% 196.06/28.62 % Clauses deleted for lack of memory : 0
% 196.06/28.62 % Backward-subsumed : 10
% 196.06/28.62 % Backward-rewritten : 24
% 196.06/28.62 % Generated clauses : 304
% 196.06/28.62 % ...of the previous two non-redundant : 200
% 196.06/28.62 % ...aggressively subsumed : 0
% 196.06/28.62 % Contextual simplify-reflections : 1
% 196.06/28.62 % Paramodulations : 238
% 196.06/28.62 % Factorizations : 34
% 196.06/28.62 % NegExts : 2
% 196.06/28.62 % Equation resolutions : 23
% 196.06/28.62 % Disequality decompositions : 0
% 196.06/28.62 % Total rewrite steps : 38
% 196.06/28.62 % ...of those cached : 22
% 196.06/28.62 % Propositional unsat checks : 0
% 196.06/28.62 % Propositional check models : 0
% 196.06/28.62 % Propositional check unsatisfiable : 0
% 196.06/28.62 % Propositional clauses : 0
% 196.06/28.62 % Propositional clauses after purity: 0
% 196.06/28.62 % Propositional unsat core size : 0
% 196.06/28.62 % Propositional preprocessing time : 0.000
% 196.06/28.62 % Propositional encoding time : 0.000
% 196.06/28.62 % Propositional solver time : 0.000
% 196.06/28.62 % Success case prop preproc time : 0.000
% 196.06/28.62 % Success case prop encoding time : 0.000
% 196.06/28.62 % Success case prop solver time : 0.000
% 196.06/28.62 % Current number of processed clauses : 4
% 196.06/28.62 % Positive orientable unit clauses : 0
% 196.06/28.62 % Positive unorientable unit clauses: 1
% 196.06/28.62 % Negative unit clauses : 3
% 196.06/28.62 % Non-unit-clauses : 0
% 196.06/28.62 % Current number of unprocessed clauses: 140
% 196.06/28.62 % ...number of literals in the above : 429
% 196.06/28.62 % Current number of archived formulas : 0
% 196.06/28.62 % Current number of archived clauses : 44
% 196.06/28.62 % Clause-clause subsumption calls (NU) : 79
% 196.06/28.62 % Rec. Clause-clause subsumption calls : 64
% 196.06/28.62 % Non-unit clause-clause subsumptions : 25
% 196.06/28.62 % Unit Clause-clause subsumption calls : 18
% 196.06/28.62 % Rewrite failures with RHS unbound : 0
% 196.06/28.62 % BW rewrite match attempts : 21
% 196.06/28.62 % BW rewrite match successes : 14
% 196.06/28.62 % Condensation attempts : 80
% 196.06/28.62 % Condensation successes : 6
% 196.06/28.62 % Termbank termtop insertions : 2223
% 196.06/28.62 % Search garbage collected termcells : 161
% 196.06/28.62
% 196.06/28.62 % -------------------------------------------------
% 196.06/28.62 % User time : 27.575 s
% 196.06/28.62 % System time : 0.498 s
% 196.06/28.62 % Total time : 28.074 s
% 196.06/28.62 % Maximum resident set size: 3892 pages
% 196.06/28.62
% 196.06/28.62 % -------------------------------------------------
% 196.06/28.62 % User time : 27.577 s
% 196.06/28.62 % System time : 0.504 s
% 196.06/28.62 % Total time : 28.081 s
% 196.06/28.62 % Maximum resident set size: 4864 pages
% 196.06/28.62 % E exiting
%------------------------------------------------------------------------------