%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM677^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:16:48 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 101 ( 10 ~; 5 |; 0 &; 84 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 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,
u: nat ).
thf(decl_27,type,
more: nat > nat > $o ).
thf(decl_28,type,
pl: nat > nat > nat ).
thf(satz19h,conjecture,
more @ ( pl @ z @ x ) @ ( pl @ u @ y ),
file('/export/starexec/sandbox/tmp/tmp.6aTlNBhkpE/E---3.1_651857.p',satz19h) ).
thf(satz6,axiom,
! [X1: nat,X2: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.6aTlNBhkpE/E---3.1_651857.p',satz6) ).
thf(satz19g,axiom,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( X1 = X2 )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6aTlNBhkpE/E---3.1_651857.p',satz19g) ).
thf(i,axiom,
x = y,
file('/export/starexec/sandbox/tmp/tmp.6aTlNBhkpE/E---3.1_651857.p',i) ).
thf(m,axiom,
more @ z @ u,
file('/export/starexec/sandbox/tmp/tmp.6aTlNBhkpE/E---3.1_651857.p',m) ).
thf(c_0_5,negated_conjecture,
~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ),
inference(assume_negation,[status(cth)],[satz19h]) ).
thf(c_0_6,negated_conjecture,
~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X15: nat,X16: nat] :
( ( pl @ X15 @ X16 )
= ( pl @ X16 @ X15 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_9,plain,
! [X11: nat,X12: nat,X13: nat,X14: nat] :
( ( X11 != X12 )
| ~ ( more @ X13 @ X14 )
| ( more @ ( pl @ X11 @ X13 ) @ ( pl @ X12 @ X14 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz19g])])]) ).
thf(c_0_10,negated_conjecture,
~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X2: nat,X1: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
x = y,
inference(split_conjunct,[status(thm)],[i]) ).
thf(c_0_13,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) )
| ( X1 != X2 )
| ~ ( more @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_11]) ).
thf(c_0_15,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X1 @ X3 ) )
| ~ ( more @ X2 @ X3 ) ),
inference(er,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
more @ z @ u,
inference(split_conjunct,[status(thm)],[m]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM677^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n006.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 12:35:24 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.6aTlNBhkpE/E---3.1_651857.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.24 % Starting sh4l with 300s (1) cores
% 0.09/0.24 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.09/0.24 % ho_unfolding_6 with pid 651871 completed with status 0
% 0.09/0.24 % Result found by ho_unfolding_6
% 0.09/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HHUSF-FFSF22-SFFFFFNN
% 0.09/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 651874 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HHUSF-FFSF22-SFFFFFNN
% 0.09/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 12
% 0.09/0.24 % Removed by relevancy pruning/SinE : 0
% 0.09/0.24 % Initial clauses : 12
% 0.09/0.24 % Removed in clause preprocessing : 7
% 0.09/0.24 % Initial clauses in saturation : 5
% 0.09/0.24 % Processed clauses : 6
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 6
% 0.09/0.24 % Other redundant clauses eliminated : 1
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 6
% 0.09/0.24 % ...of the previous two non-redundant : 1
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 5
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 1
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 4
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 5
% 0.09/0.24 % Positive orientable unit clauses : 2
% 0.09/0.24 % Positive unorientable unit clauses: 1
% 0.09/0.24 % Negative unit clauses : 1
% 0.09/0.24 % Non-unit-clauses : 1
% 0.09/0.24 % Current number of unprocessed clauses: 0
% 0.09/0.24 % ...number of literals in the above : 0
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 0
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 0
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 420
% 0.09/0.24 % Search garbage collected termcells : 42
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.002 s
% 0.09/0.24 % System time : 0.002 s
% 0.09/0.24 % Total time : 0.004 s
% 0.09/0.24 % Maximum resident set size: 3632 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.003 s
% 0.09/0.24 % System time : 0.007 s
% 0.09/0.24 % Total time : 0.010 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------