%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO542^1 : 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 : 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 08:43:23 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 96 ( 21 ~; 18 |; 25 &; 31 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 32 ( 16 ^; 15 !; 1 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(decl_24,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_25,type,
epred1_0: $o ).
thf(decl_26,type,
esk1_0: $i > $i ).
thf(decl_27,type,
esk2_0: $i > $i ).
thf(conj,conjecture,
! [X3: $o,X2: $i > $i,X4: $i > $i] :
( ( ( if @ X3 @ X2 @ X4 )
= X2 )
| ( ( if @ X3 @ X2 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.thAhtvFutB/E---3.1_1542000.p',conj) ).
thf(ifd,axiom,
( if
= ( ^ [X3: $o,X2: $i > $i,X4: $i > $i] :
( epsii
@ ^ [X5: $i > $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.thAhtvFutB/E---3.1_1542000.p',ifd) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ? [X2: $i > $i] : ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.thAhtvFutB/E---3.1_1542000.p',choiceaxii) ).
thf(c_0_3,negated_conjecture,
~ ! [X3: $o,X2: $i > $i,X4: $i > $i] :
( ( ( if @ X3 @ X2 @ X4 )
= X2 )
| ( ( if @ X3 @ X2 @ X4 )
= X4 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_4,plain,
( if
= ( ^ [Z0: $o,Z1: $i > $i,Z2: $i > $i] :
( epsii
@ ^ [Z3: $i > $i] :
( ( Z0
& ( Z3 = Z1 ) )
| ( ~ Z0
& Z3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifd]) ).
thf(c_0_5,negated_conjecture,
~ ! [X3: $o,X2: $i > $i,X4: $i > $i] :
( ( ( epsii
@ ^ [Z0: $i > $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) )
= X2 )
| ( ( epsii
@ ^ [Z0: $i > $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) )
= X4 ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
( ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
!= esk1_0 )
& ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
!= esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_7,plain,
! [X14: ( $i > $i ) > $o,X15: $i > $i] :
( ~ ( X14 @ X15 )
| ( X14 @ ( epsii @ X14 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxii])])])]) ).
thf(c_0_8,negated_conjecture,
( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ ( epsii @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i > $i] :
( ( epred1_0
& ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
= esk1_0 ) )
| ( ~ epred1_0
& ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
= esk2_0 ) )
| ~ ( ( epred1_0
& ( X2 = esk1_0 ) )
| ( ~ epred1_0
& ( X2 = esk2_0 ) ) ) ),
inference(choice_inst,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk2_0 ) ) ) )
!= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
epred1_0,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10]),c_0_11]),c_0_8])]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10]),c_0_11]),c_0_8])]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO542^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:19:50 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 Running higher-order theorem proving
% 0.23/0.29 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.thAhtvFutB/E---3.1_1542000.p
% 0.23/0.32 % Version: 3.5.1-ho
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % Starting sh5l with 300s (1) cores
% 0.23/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.32 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.32 % new_bool_1 with pid 1542017 completed with status 0
% 0.23/0.32 % Result found by new_bool_1
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % Starting sh5l with 300s (1) cores
% 0.23/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.32 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.32 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.32 % Search class: HHUSF-FFSF22-MHSFFSBC
% 0.23/0.32 % partial match(4): HGUSF-FFSF22-SHHFFSBN
% 0.23/0.32 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.32 % SubtermCWHack with pid 1542023 completed with status 0
% 0.23/0.32 % Result found by SubtermCWHack
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % Starting sh5l with 300s (1) cores
% 0.23/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.32 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.32 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.32 % Search class: HHUSF-FFSF22-MHSFFSBC
% 0.23/0.32 % partial match(4): HGUSF-FFSF22-SHHFFSBN
% 0.23/0.32 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.32 % Preprocessing time : 0.001 s
% 0.23/0.32
% 0.23/0.32 % Proof found!
% 0.23/0.32 % SZS status Theorem
% 0.23/0.32 % SZS output start CNFRefutation
% See solution above
% 0.23/0.32 % Parsed axioms : 5
% 0.23/0.32 % Removed by relevancy pruning/SinE : 2
% 0.23/0.32 % Initial clauses : 3
% 0.23/0.32 % Removed in clause preprocessing : 0
% 0.23/0.32 % Initial clauses in saturation : 3
% 0.23/0.32 % Processed clauses : 6
% 0.23/0.32 % ...of these trivial : 0
% 0.23/0.32 % ...subsumed : 0
% 0.23/0.32 % ...remaining for further processing : 5
% 0.23/0.32 % Other redundant clauses eliminated : 4
% 0.23/0.32 % Clauses deleted for lack of memory : 0
% 0.23/0.32 % Backward-subsumed : 0
% 0.23/0.32 % Backward-rewritten : 0
% 0.23/0.32 % Generated clauses : 16
% 0.23/0.32 % ...of the previous two non-redundant : 8
% 0.23/0.32 % ...aggressively subsumed : 0
% 0.23/0.32 % Contextual simplify-reflections : 0
% 0.23/0.32 % Paramodulations : 0
% 0.23/0.32 % Factorizations : 0
% 0.23/0.32 % NegExts : 0
% 0.23/0.32 % Equation resolutions : 4
% 0.23/0.32 % Disequality decompositions : 0
% 0.23/0.32 % Total rewrite steps : 1
% 0.23/0.32 % ...of those cached : 0
% 0.23/0.32 % Propositional unsat checks : 0
% 0.23/0.32 % Propositional check models : 0
% 0.23/0.32 % Propositional check unsatisfiable : 0
% 0.23/0.32 % Propositional clauses : 0
% 0.23/0.32 % Propositional clauses after purity: 0
% 0.23/0.32 % Propositional unsat core size : 0
% 0.23/0.32 % Propositional preprocessing time : 0.000
% 0.23/0.32 % Propositional encoding time : 0.000
% 0.23/0.32 % Propositional solver time : 0.000
% 0.23/0.32 % Success case prop preproc time : 0.000
% 0.23/0.32 % Success case prop encoding time : 0.000
% 0.23/0.32 % Success case prop solver time : 0.000
% 0.23/0.32 % Current number of processed clauses : 4
% 0.23/0.32 % Positive orientable unit clauses : 1
% 0.23/0.32 % Positive unorientable unit clauses: 0
% 0.23/0.32 % Negative unit clauses : 2
% 0.23/0.32 % Non-unit-clauses : 1
% 0.23/0.32 % Current number of unprocessed clauses: 5
% 0.23/0.32 % ...number of literals in the above : 8
% 0.23/0.32 % Current number of archived formulas : 0
% 0.23/0.32 % Current number of archived clauses : 1
% 0.23/0.32 % Clause-clause subsumption calls (NU) : 1
% 0.23/0.32 % Rec. Clause-clause subsumption calls : 1
% 0.23/0.32 % Non-unit clause-clause subsumptions : 0
% 0.23/0.32 % Unit Clause-clause subsumption calls : 1
% 0.23/0.32 % Rewrite failures with RHS unbound : 0
% 0.23/0.32 % BW rewrite match attempts : 0
% 0.23/0.32 % BW rewrite match successes : 0
% 0.23/0.32 % Condensation attempts : 0
% 0.23/0.32 % Condensation successes : 0
% 0.23/0.32 % Termbank termtop insertions : 2242
% 0.23/0.32 % Search garbage collected termcells : 89
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.003 s
% 0.23/0.32 % System time : 0.003 s
% 0.23/0.32 % Total time : 0.007 s
% 0.23/0.32 % Maximum resident set size: 3636 pages
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.004 s
% 0.23/0.32 % System time : 0.009 s
% 0.23/0.32 % Total time : 0.013 s
% 0.23/0.32 % Maximum resident set size: 4608 pages
% 0.23/0.32 % E exiting
%------------------------------------------------------------------------------