%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM635^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:17:15 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 13 ~; 3 |; 1 &; 18 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
succ: $i > $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(decl_27,type,
esk3_0: $i ).
thf(satz1,conjecture,
! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.c5RM0zw1Ny/E---3.1_3054554.p',satz1) ).
thf(succ_injective,axiom,
! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.c5RM0zw1Ny/E---3.1_3054554.p',succ_injective) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(assume_negation,[status(cth)],[satz1]) ).
thf(c_0_3,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
thf(c_0_4,plain,
! [X13: $i,X14: $i] :
( ( ( succ @ X13 )
!= ( succ @ X14 ) )
| ( X13 = X14 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[succ_injective])])]) ).
thf(c_0_5,negated_conjecture,
( ( esk2_0 != esk3_0 )
& ( ( succ @ esk2_0 )
= ( succ @ esk3_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
thf(c_0_6,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
( ( succ @ esk2_0 )
= ( succ @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ( X1 = esk3_0 )
| ( ( succ @ X1 )
!= ( succ @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM635^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n008.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 12:01:39 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running higher-order theorem proving
% 0.24/0.32 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.c5RM0zw1Ny/E---3.1_3054554.p
% 0.24/0.35 % Version: 3.5.1-ho
% 0.24/0.35 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.24/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.35 % Starting new_ho_14 with 1500s (5) cores
% 0.24/0.35 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.35 % Starting new_ho_13 with 300s (1) cores
% 0.24/0.35 % Starting ho_unfolding_3 with 300s (1) cores
% 0.24/0.35 % ho_unfolding_3 with pid 3054574 completed with status 0
% 0.24/0.35 % Result found by ho_unfolding_3
% 0.24/0.35 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.24/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.35 % Starting new_ho_14 with 1500s (5) cores
% 0.24/0.35 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.35 % Starting new_ho_13 with 300s (1) cores
% 0.24/0.35 % Starting ho_unfolding_3 with 300s (1) cores
% 0.24/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.35 % No SInE strategy applied
% 0.24/0.35 % Search class: HGUSF-FFSF11-SSFFFSBN
% 0.24/0.35 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.35 % SubtermCWHack with pid 3054576 completed with status 0
% 0.24/0.35 % Result found by SubtermCWHack
% 0.24/0.35 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.24/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.35 % Starting new_ho_14 with 1500s (5) cores
% 0.24/0.35 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.35 % Starting new_ho_13 with 300s (1) cores
% 0.24/0.35 % Starting ho_unfolding_3 with 300s (1) cores
% 0.24/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.35 % No SInE strategy applied
% 0.24/0.35 % Search class: HGUSF-FFSF11-SSFFFSBN
% 0.24/0.35 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.35 % Preprocessing time : 0.002 s
% 0.24/0.35
% 0.24/0.35 % Proof found!
% 0.24/0.35 % SZS status Theorem
% 0.24/0.35 % SZS output start CNFRefutation
% See solution above
% 0.24/0.35 % Parsed axioms : 6
% 0.24/0.35 % Removed by relevancy pruning/SinE : 0
% 0.24/0.35 % Initial clauses : 8
% 0.24/0.35 % Removed in clause preprocessing : 2
% 0.24/0.35 % Initial clauses in saturation : 6
% 0.24/0.35 % Processed clauses : 8
% 0.24/0.35 % ...of these trivial : 0
% 0.24/0.35 % ...subsumed : 1
% 0.24/0.35 % ...remaining for further processing : 7
% 0.24/0.35 % Other redundant clauses eliminated : 0
% 0.24/0.35 % Clauses deleted for lack of memory : 0
% 0.24/0.35 % Backward-subsumed : 0
% 0.24/0.35 % Backward-rewritten : 0
% 0.24/0.35 % Generated clauses : 5
% 0.24/0.35 % ...of the previous two non-redundant : 3
% 0.24/0.35 % ...aggressively subsumed : 0
% 0.24/0.35 % Contextual simplify-reflections : 0
% 0.24/0.35 % Paramodulations : 3
% 0.24/0.35 % Factorizations : 0
% 0.24/0.35 % NegExts : 0
% 0.24/0.35 % Equation resolutions : 2
% 0.24/0.35 % Disequality decompositions : 0
% 0.24/0.35 % Total rewrite steps : 0
% 0.24/0.35 % ...of those cached : 0
% 0.24/0.35 % Propositional unsat checks : 0
% 0.24/0.35 % Propositional check models : 0
% 0.24/0.35 % Propositional check unsatisfiable : 0
% 0.24/0.35 % Propositional clauses : 0
% 0.24/0.35 % Propositional clauses after purity: 0
% 0.24/0.35 % Propositional unsat core size : 0
% 0.24/0.35 % Propositional preprocessing time : 0.000
% 0.24/0.35 % Propositional encoding time : 0.000
% 0.24/0.35 % Propositional solver time : 0.000
% 0.24/0.35 % Success case prop preproc time : 0.000
% 0.24/0.35 % Success case prop encoding time : 0.000
% 0.24/0.35 % Success case prop solver time : 0.000
% 0.24/0.35 % Current number of processed clauses : 7
% 0.24/0.35 % Positive orientable unit clauses : 1
% 0.24/0.35 % Positive unorientable unit clauses: 0
% 0.24/0.35 % Negative unit clauses : 2
% 0.24/0.35 % Non-unit-clauses : 4
% 0.24/0.35 % Current number of unprocessed clauses: 1
% 0.24/0.35 % ...number of literals in the above : 2
% 0.24/0.35 % Current number of archived formulas : 0
% 0.24/0.35 % Current number of archived clauses : 0
% 0.24/0.35 % Clause-clause subsumption calls (NU) : 2
% 0.24/0.35 % Rec. Clause-clause subsumption calls : 2
% 0.24/0.35 % Non-unit clause-clause subsumptions : 0
% 0.24/0.35 % Unit Clause-clause subsumption calls : 0
% 0.24/0.35 % Rewrite failures with RHS unbound : 0
% 0.24/0.35 % BW rewrite match attempts : 0
% 0.24/0.35 % BW rewrite match successes : 0
% 0.24/0.35 % Condensation attempts : 0
% 0.24/0.35 % Condensation successes : 0
% 0.24/0.35 % Termbank termtop insertions : 502
% 0.24/0.35 % Search garbage collected termcells : 138
% 0.24/0.35
% 0.24/0.35 % -------------------------------------------------
% 0.24/0.35 % User time : 0.006 s
% 0.24/0.35 % System time : 0.002 s
% 0.24/0.35 % Total time : 0.008 s
% 0.24/0.35 % Maximum resident set size: 3632 pages
% 0.24/0.35
% 0.24/0.35 % -------------------------------------------------
% 0.24/0.35 % User time : 0.009 s
% 0.24/0.35 % System time : 0.005 s
% 0.24/0.35 % Total time : 0.015 s
% 0.24/0.35 % Maximum resident set size: 4864 pages
% 0.24/0.35 % E exiting
%------------------------------------------------------------------------------