%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM696^1 : 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 : n007.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 08:16:52 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 175 ( 39 ~; 5 |; 1 &; 123 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 43 ( 0 ^; 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
pl: nat > nat > nat ).
thf(decl_26,type,
n_1: nat ).
thf(decl_27,type,
esk1_0: nat ).
thf(decl_28,type,
esk2_1: nat > nat ).
thf(decl_29,type,
esk3_3: nat > nat > nat > nat ).
thf(satz25,conjecture,
( ~ ~ ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.W5XVIjRvbA/E---3.1_3298970.p',satz25) ).
thf(satz19a,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ~ ! [X1: nat] :
( X3
!= ( pl @ X4 @ X1 ) )
=> ~ ! [X1: nat] :
( ( pl @ X3 @ X5 )
!= ( pl @ ( pl @ X4 @ X5 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.W5XVIjRvbA/E---3.1_3298970.p',satz19a) ).
thf(satz6,axiom,
! [X3: nat,X4: nat] :
( ( pl @ X3 @ X4 )
= ( pl @ X4 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.W5XVIjRvbA/E---3.1_3298970.p',satz6) ).
thf(satz24,axiom,
! [X3: nat] :
( ~ ~ ! [X1: nat] :
( X3
!= ( pl @ n_1 @ X1 ) )
=> ( X3 = n_1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.W5XVIjRvbA/E---3.1_3298970.p',satz24) ).
thf(m,axiom,
~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.W5XVIjRvbA/E---3.1_3298970.p',m) ).
thf(c_0_5,negated_conjecture,
~ ( ~ ~ ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(assume_negation,[status(cth)],[satz25]) ).
thf(c_0_6,negated_conjecture,
~ ( ~ ~ ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X3: nat,X4: nat,X5: nat] :
( ~ ! [X1: nat] :
( X3
!= ( pl @ X4 @ X1 ) )
=> ~ ! [X1: nat] :
( ( pl @ X3 @ X5 )
!= ( pl @ ( pl @ X4 @ X5 ) @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[satz19a]) ).
thf(c_0_8,negated_conjecture,
! [X28: nat] :
( ( y
!= ( pl @ ( pl @ x @ n_1 ) @ X28 ) )
& ( y
!= ( pl @ x @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
thf(c_0_9,plain,
! [X26: nat,X27: nat] :
( ( pl @ X26 @ X27 )
= ( pl @ X27 @ X26 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_10,plain,
! [X21: nat,X22: nat,X23: nat,X24: nat] :
( ( X21
!= ( pl @ X22 @ X23 ) )
| ( ( pl @ X21 @ X24 )
= ( pl @ ( pl @ X22 @ X24 ) @ ( esk3_3 @ X21 @ X22 @ X24 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X3: nat,X1: nat] :
( ( pl @ X1 @ X3 )
= ( pl @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X1: nat,X3: nat,X5: nat,X4: nat] :
( ( ( pl @ X1 @ X5 )
= ( pl @ ( pl @ X3 @ X5 ) @ ( esk3_3 @ X1 @ X3 @ X5 ) ) )
| ( X1
!= ( pl @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X3: nat] :
( ~ ~ ! [X1: nat] :
( X3
!= ( pl @ n_1 @ X1 ) )
=> ( X3 = n_1 ) ),
inference(fof_simplification,[status(thm)],[satz24]) ).
thf(c_0_15,negated_conjecture,
! [X1: nat] :
( ( pl @ ( pl @ n_1 @ x ) @ X1 )
!= y ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
! [X1: nat,X4: nat,X3: nat] :
( ( pl @ ( pl @ X1 @ X3 ) @ ( esk3_3 @ ( pl @ X1 @ X4 ) @ X1 @ X3 ) )
= ( pl @ ( pl @ X1 @ X4 ) @ X3 ) ),
inference(er,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X19: nat] :
( ( X19
= ( pl @ n_1 @ ( esk2_1 @ X19 ) ) )
| ( X19 = n_1 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
thf(c_0_18,plain,
~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_19,negated_conjecture,
! [X1: nat] :
( ( pl @ x @ ( pl @ n_1 @ X1 ) )
!= y ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]) ).
thf(c_0_20,plain,
! [X1: nat] :
( ( X1
= ( pl @ n_1 @ ( esk2_1 @ X1 ) ) )
| ( X1 = n_1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
( y
= ( pl @ x @ esk1_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
thf(c_0_22,negated_conjecture,
! [X1: nat] :
( ( X1 = n_1 )
| ( ( pl @ x @ X1 )
!= y ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,plain,
( y
= ( pl @ x @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
( y
!= ( pl @ x @ n_1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_25,negated_conjecture,
esk1_0 = n_1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
( ( pl @ n_1 @ x )
!= y ),
inference(rw,[status(thm)],[c_0_24,c_0_12]) ).
thf(c_0_27,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_25]),c_0_12]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:38:55 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.W5XVIjRvbA/E---3.1_3298970.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % Starting sh4l with 300s (1) cores
% 0.07/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.07/0.25 % new_ho_10 with pid 3298983 completed with status 0
% 0.07/0.25 % Result found by new_ho_10
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGUPF-FFSF32-SFFFFFNN
% 0.07/0.25 % partial match(2): FGUPF-FFSM32-SFFFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting new_ho_10 with 151s (1) cores
% 0.07/0.25 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.07/0.25 % Starting new_bool_3 with 136s (1) cores
% 0.07/0.25 % Starting new_bool_1 with 136s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 3298987 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGUPF-FFSF32-SFFFFFNN
% 0.07/0.25 % partial match(2): FGUPF-FFSM32-SFFFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 11
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 12
% 0.07/0.25 % Removed in clause preprocessing : 6
% 0.07/0.25 % Initial clauses in saturation : 6
% 0.07/0.25 % Processed clauses : 19
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 6
% 0.07/0.25 % ...remaining for further processing : 13
% 0.07/0.25 % Other redundant clauses eliminated : 1
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 2
% 0.07/0.25 % Generated clauses : 24
% 0.07/0.25 % ...of the previous two non-redundant : 25
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 23
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 1
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 5
% 0.07/0.25 % ...of those cached : 1
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 10
% 0.07/0.25 % Positive orientable unit clauses : 2
% 0.07/0.25 % Positive unorientable unit clauses: 1
% 0.07/0.25 % Negative unit clauses : 5
% 0.07/0.25 % Non-unit-clauses : 2
% 0.07/0.25 % Current number of unprocessed clauses: 12
% 0.07/0.25 % ...number of literals in the above : 16
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 2
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 6
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 5
% 0.07/0.25 % BW rewrite match successes : 5
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 780
% 0.07/0.25 % Search garbage collected termcells : 150
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.003 s
% 0.07/0.25 % Total time : 0.007 s
% 0.07/0.25 % Maximum resident set size: 3636 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.009 s
% 0.07/0.25 % System time : 0.011 s
% 0.07/0.25 % Total time : 0.019 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------