%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 0.29s 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 30 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 36 ( 5 ~; 7 |; 0 &; 24 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 32 ( 25 ^; 7 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_25,type,
singleton: $i > $i > $o ).
thf(decl_27,type,
sup: ( $i > $o ) > $i ).
thf(decl_30,type,
addition: $i > $i > $i ).
thf(decl_35,type,
esk1_0: $i ).
thf(addition_def,axiom,
( addition
= ( ^ [X1: $i,X7: $i] : ( sup @ ( union @ ( singleton @ X1 ) @ ( singleton @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.knOc2AeJNX/E---3.1_3515416.p',addition_def) ).
thf(singleton_def,axiom,
( singleton
= ( ^ [X1: $i,X4: $i] : ( X4 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.knOc2AeJNX/E---3.1_3515416.p',singleton_def) ).
thf(union_def,axiom,
( union
= ( ^ [X2: $i > $o,X3: $i > $o,X4: $i] :
( ( X2 @ X4 )
| ( X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.knOc2AeJNX/E---3.1_3515416.p',union_def) ).
thf(addition_idemp,conjecture,
! [X8: $i] :
( ( addition @ X8 @ X8 )
= X8 ),
file('/export/starexec/sandbox/tmp/tmp.knOc2AeJNX/E---3.1_3515416.p',addition_idemp) ).
thf(sup_singleset,axiom,
! [X1: $i] :
( ( sup @ ( singleton @ X1 ) )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.knOc2AeJNX/E---3.1_3515416.p',sup_singleset) ).
thf(c_0_5,plain,
( addition
= ( ^ [Z0: $i,Z1: $i] :
( sup
@ ^ [Z2: $i] :
( ( Z2 = Z0 )
| Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[addition_def]) ).
thf(c_0_6,plain,
( singleton
= ( ^ [Z0: $i,Z1: $i] : Z1 ) ),
inference(fof_simplification,[status(thm)],[singleton_def]) ).
thf(c_0_7,plain,
( union
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[union_def]) ).
thf(c_0_8,negated_conjecture,
~ ! [X8: $i] :
( ( addition @ X8 @ X8 )
= X8 ),
inference(assume_negation,[status(cth)],[addition_idemp]) ).
thf(c_0_9,plain,
( addition
= ( ^ [Z0: $i,Z1: $i] :
( sup
@ ^ [Z2: $i] :
( ( Z2 = Z0 )
| Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ! [X8: $i] :
( ( sup
@ ^ [Z0: $i] :
( ( Z0 = X8 )
| ( Z0 = X8 ) ) )
= X8 ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( sup
@ ^ [Z0: $i] :
( ( Z0 = esk1_0 )
| ( Z0 = esk1_0 ) ) )
!= esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
thf(c_0_12,plain,
! [X1: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= X1 ),
inference(apply_def,[status(thm)],[sup_singleset,c_0_6]) ).
thf(c_0_13,negated_conjecture,
( ( sup
@ ^ [Z0: $i] :
( ( Z0 = esk1_0 )
| ( Z0 = esk1_0 ) ) )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
! [X30: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X30 ) )
= X30 ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
( ( sup
@ ^ [Z0: $i] : ( Z0 = esk1_0 ) )
!= esk1_0 ),
inference(cn,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( sup
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 13:32:25 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.25 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.knOc2AeJNX/E---3.1_3515416.p
% 0.29/0.29 % Version: 3.5.1-ho
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSCHFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.29 % Starting sh2lt with 300s (1) cores
% 0.29/0.29 % Starting sh5l with 300s (1) cores
% 0.29/0.29 % Starting pre_casc_6 with 300s (1) cores
% 0.29/0.29 % sh5l with pid 3515431 completed with status 0
% 0.29/0.29 % Result found by sh5l
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSCHFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.29 % Starting sh2lt with 300s (1) cores
% 0.29/0.29 % Starting sh5l with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.29/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.29/0.29 % Search class: HHUSM-FFSF21-DHFFMFBN
% 0.29/0.29 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.29/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.29/0.29 % SubtermCWHack with pid 3515436 completed with status 0
% 0.29/0.29 % Result found by SubtermCWHack
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSCHFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.29 % Starting sh2lt with 300s (1) cores
% 0.29/0.29 % Starting sh5l with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.29/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.29/0.29 % Search class: HHUSM-FFSF21-DHFFMFBN
% 0.29/0.29 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.29/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.29/0.29 % Preprocessing time : 0.001 s
% 0.29/0.29
% 0.29/0.29 % Proof found!
% 0.29/0.29 % SZS status Theorem
% 0.29/0.29 % SZS output start CNFRefutation
% See solution above
% 0.29/0.29 % Parsed axioms : 27
% 0.29/0.29 % Removed by relevancy pruning/SinE : 14
% 0.29/0.29 % Initial clauses : 8
% 0.29/0.29 % Removed in clause preprocessing : 0
% 0.29/0.29 % Initial clauses in saturation : 8
% 0.29/0.29 % Processed clauses : 4
% 0.29/0.29 % ...of these trivial : 0
% 0.29/0.29 % ...subsumed : 0
% 0.29/0.29 % ...remaining for further processing : 4
% 0.29/0.29 % Other redundant clauses eliminated : 0
% 0.29/0.29 % Clauses deleted for lack of memory : 0
% 0.29/0.29 % Backward-subsumed : 0
% 0.29/0.29 % Backward-rewritten : 0
% 0.29/0.29 % Generated clauses : 1
% 0.29/0.29 % ...of the previous two non-redundant : 0
% 0.29/0.29 % ...aggressively subsumed : 0
% 0.29/0.29 % Contextual simplify-reflections : 0
% 0.29/0.29 % Paramodulations : 1
% 0.29/0.29 % Factorizations : 0
% 0.29/0.29 % NegExts : 0
% 0.29/0.29 % Equation resolutions : 0
% 0.29/0.29 % Disequality decompositions : 0
% 0.29/0.29 % Total rewrite steps : 0
% 0.29/0.29 % ...of those cached : 0
% 0.29/0.29 % Propositional unsat checks : 0
% 0.29/0.29 % Propositional check models : 0
% 0.29/0.29 % Propositional check unsatisfiable : 0
% 0.29/0.29 % Propositional clauses : 0
% 0.29/0.29 % Propositional clauses after purity: 0
% 0.29/0.29 % Propositional unsat core size : 0
% 0.29/0.29 % Propositional preprocessing time : 0.000
% 0.29/0.29 % Propositional encoding time : 0.000
% 0.29/0.29 % Propositional solver time : 0.000
% 0.29/0.29 % Success case prop preproc time : 0.000
% 0.29/0.29 % Success case prop encoding time : 0.000
% 0.29/0.29 % Success case prop solver time : 0.000
% 0.29/0.29 % Current number of processed clauses : 4
% 0.29/0.29 % Positive orientable unit clauses : 3
% 0.29/0.29 % Positive unorientable unit clauses: 0
% 0.29/0.29 % Negative unit clauses : 1
% 0.29/0.29 % Non-unit-clauses : 0
% 0.29/0.29 % Current number of unprocessed clauses: 4
% 0.29/0.29 % ...number of literals in the above : 6
% 0.29/0.29 % Current number of archived formulas : 0
% 0.29/0.29 % Current number of archived clauses : 0
% 0.29/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.29/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.29/0.29 % Non-unit clause-clause subsumptions : 0
% 0.29/0.29 % Unit Clause-clause subsumption calls : 0
% 0.29/0.29 % Rewrite failures with RHS unbound : 0
% 0.29/0.29 % BW rewrite match attempts : 0
% 0.29/0.29 % BW rewrite match successes : 0
% 0.29/0.29 % Condensation attempts : 0
% 0.29/0.29 % Condensation successes : 0
% 0.29/0.29 % Termbank termtop insertions : 887
% 0.29/0.29 % Search garbage collected termcells : 191
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.002 s
% 0.29/0.29 % System time : 0.004 s
% 0.29/0.29 % Total time : 0.006 s
% 0.29/0.29 % Maximum resident set size: 3652 pages
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.004 s
% 0.29/0.29 % System time : 0.009 s
% 0.29/0.29 % Total time : 0.013 s
% 0.29/0.29 % Maximum resident set size: 4864 pages
% 0.29/0.29 % E exiting
%------------------------------------------------------------------------------