%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM662^1 : 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 : n012.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 08:16:45 AM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 77 ( 19 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
z: nat ).
thf(decl_26,type,
pl: nat > nat > nat ).
thf(decl_27,type,
esk1_0: nat ).
thf(decl_28,type,
esk2_0: nat ).
thf(satz15,conjecture,
~ ! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vs47xFWUuM/E---3.1_34780.p',satz15) ).
thf(l,axiom,
~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vs47xFWUuM/E---3.1_34780.p',l) ).
thf(satz5,axiom,
! [X2: nat,X4: nat,X5: nat] :
( ( pl @ ( pl @ X2 @ X4 ) @ X5 )
= ( pl @ X2 @ ( pl @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vs47xFWUuM/E---3.1_34780.p',satz5) ).
thf(k,axiom,
~ ! [X2: nat] :
( z
!= ( pl @ y @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vs47xFWUuM/E---3.1_34780.p',k) ).
thf(c_0_4,negated_conjecture,
~ ~ ! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
inference(assume_negation,[status(cth)],[satz15]) ).
thf(c_0_5,plain,
~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ),
inference(fof_simplification,[status(thm)],[l]) ).
thf(c_0_6,negated_conjecture,
~ ~ ! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X15: nat,X16: nat,X17: nat] :
( ( pl @ ( pl @ X15 @ X16 ) @ X17 )
= ( pl @ X15 @ ( pl @ X16 @ X17 ) ) ),
inference(variable_rename,[status(thm)],[satz5]) ).
thf(c_0_8,plain,
( y
= ( pl @ x @ esk1_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_9,plain,
~ ! [X2: nat] :
( z
!= ( pl @ y @ X2 ) ),
inference(fof_simplification,[status(thm)],[k]) ).
thf(c_0_10,negated_conjecture,
! [X18: nat] :
( z
!= ( pl @ x @ X18 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_11,plain,
! [X1: nat,X2: nat,X4: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X4 )
= ( pl @ X1 @ ( pl @ X2 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
( y
= ( pl @ x @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
( z
= ( pl @ y @ esk2_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: nat] :
( ( pl @ x @ ( pl @ esk1_0 @ X1 ) )
= ( pl @ y @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
( z
= ( pl @ y @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X1: nat] :
( ( pl @ y @ X1 )
!= z ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,plain,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM662^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:32:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 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.vs47xFWUuM/E---3.1_34780.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % Starting sh4l with 300s (1) cores
% 0.08/0.14 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.14 % ho_unfolding_6 with pid 34804 completed with status 0
% 0.08/0.14 % Result found by ho_unfolding_6
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HUUPF-FFSF22-SFFFFFNN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % SubtermCWHack with pid 34809 completed with status 0
% 0.08/0.14 % Result found by SubtermCWHack
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HUUPF-FFSF22-SFFFFFNN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % Preprocessing time : 0.001 s
% 0.08/0.14
% 0.08/0.14 % Proof found!
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14 % SZS output start CNFRefutation
% See solution above
% 0.08/0.14 % Parsed axioms : 10
% 0.08/0.14 % Removed by relevancy pruning/SinE : 0
% 0.08/0.14 % Initial clauses : 10
% 0.08/0.14 % Removed in clause preprocessing : 6
% 0.08/0.14 % Initial clauses in saturation : 4
% 0.08/0.14 % Processed clauses : 8
% 0.08/0.14 % ...of these trivial : 0
% 0.08/0.14 % ...subsumed : 0
% 0.08/0.14 % ...remaining for further processing : 8
% 0.08/0.14 % Other redundant clauses eliminated : 0
% 0.08/0.14 % Clauses deleted for lack of memory : 0
% 0.08/0.14 % Backward-subsumed : 0
% 0.08/0.14 % Backward-rewritten : 0
% 0.08/0.14 % Generated clauses : 9
% 0.08/0.14 % ...of the previous two non-redundant : 4
% 0.08/0.14 % ...aggressively subsumed : 0
% 0.08/0.14 % Contextual simplify-reflections : 0
% 0.08/0.14 % Paramodulations : 8
% 0.08/0.14 % Factorizations : 0
% 0.08/0.14 % NegExts : 0
% 0.08/0.14 % Equation resolutions : 0
% 0.08/0.14 % Disequality decompositions : 0
% 0.08/0.14 % Total rewrite steps : 9
% 0.08/0.14 % ...of those cached : 0
% 0.08/0.14 % Propositional unsat checks : 0
% 0.08/0.14 % Propositional check models : 0
% 0.08/0.14 % Propositional check unsatisfiable : 0
% 0.08/0.14 % Propositional clauses : 0
% 0.08/0.14 % Propositional clauses after purity: 0
% 0.08/0.14 % Propositional unsat core size : 0
% 0.08/0.14 % Propositional preprocessing time : 0.000
% 0.08/0.14 % Propositional encoding time : 0.000
% 0.08/0.14 % Propositional solver time : 0.000
% 0.08/0.14 % Success case prop preproc time : 0.000
% 0.08/0.14 % Success case prop encoding time : 0.000
% 0.08/0.14 % Success case prop solver time : 0.000
% 0.08/0.14 % Current number of processed clauses : 7
% 0.08/0.14 % Positive orientable unit clauses : 4
% 0.08/0.14 % Positive unorientable unit clauses: 0
% 0.08/0.14 % Negative unit clauses : 3
% 0.08/0.14 % Non-unit-clauses : 0
% 0.08/0.14 % Current number of unprocessed clauses: 0
% 0.08/0.14 % ...number of literals in the above : 0
% 0.08/0.14 % Current number of archived formulas : 0
% 0.08/0.14 % Current number of archived clauses : 1
% 0.08/0.14 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.14 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.14 % Non-unit clause-clause subsumptions : 0
% 0.08/0.14 % Unit Clause-clause subsumption calls : 2
% 0.08/0.14 % Rewrite failures with RHS unbound : 0
% 0.08/0.14 % BW rewrite match attempts : 0
% 0.08/0.14 % BW rewrite match successes : 0
% 0.08/0.14 % Condensation attempts : 0
% 0.08/0.14 % Condensation successes : 0
% 0.08/0.14 % Termbank termtop insertions : 429
% 0.08/0.14 % Search garbage collected termcells : 60
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.003 s
% 0.08/0.14 % System time : 0.000 s
% 0.08/0.14 % Total time : 0.003 s
% 0.08/0.14 % Maximum resident set size: 3632 pages
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.004 s
% 0.08/0.14 % System time : 0.003 s
% 0.08/0.14 % Total time : 0.007 s
% 0.08/0.14 % Maximum resident set size: 4864 pages
% 0.08/0.14 % E exiting
%------------------------------------------------------------------------------