%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM687^1 : 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 : n019.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 08:16:49 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 146 ( 17 ~; 11 |; 0 &; 112 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% 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(satz22a,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox/tmp/tmp.pxEsVn8O4n/E---3.1_697246.p',satz22a) ).
thf(m,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.pxEsVn8O4n/E---3.1_697246.p',m) ).
thf(satz21,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ X2 @ X3 )
=> ( ( more @ X4 @ X5 )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pxEsVn8O4n/E---3.1_697246.p',satz21) ).
thf(n,axiom,
more @ z @ u,
file('/export/starexec/sandbox/tmp/tmp.pxEsVn8O4n/E---3.1_697246.p',n) ).
thf(satz19g,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( X2 = X3 )
=> ( ( more @ X4 @ X5 )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pxEsVn8O4n/E---3.1_697246.p',satz19g) ).
thf(c_0_5,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(assume_negation,[status(cth)],[satz22a]) ).
thf(c_0_6,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_8,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X19: nat,X20: nat,X21: nat,X22: nat] :
( ~ ( more @ X19 @ X20 )
| ~ ( more @ X21 @ X22 )
| ( more @ ( pl @ X19 @ X21 ) @ ( pl @ X20 @ X22 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz21])])]) ).
thf(c_0_10,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) )
| ~ ( more @ X2 @ X3 )
| ~ ( more @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
more @ z @ u,
inference(split_conjunct,[status(thm)],[n]) ).
thf(c_0_14,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ( more @ x @ y ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
thf(c_0_16,plain,
! [X15: nat,X16: nat,X17: nat,X18: nat] :
( ( X15 != X16 )
| ~ ( more @ X17 @ X18 )
| ( more @ ( pl @ X15 @ X17 ) @ ( pl @ X16 @ X18 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz19g])])]) ).
thf(c_0_17,plain,
x = y,
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) )
| ( X2 != X3 )
| ~ ( more @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
~ ( more @ ( pl @ y @ z ) @ ( pl @ y @ u ) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
thf(c_0_20,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X2 @ X4 ) )
| ~ ( more @ X3 @ X4 ) ),
inference(er,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM687^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:39:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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.pxEsVn8O4n/E---3.1_697246.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % Starting sh4l with 300s (1) cores
% 0.22/0.27 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.27 % ho_unfolding_6 with pid 697277 completed with status 0
% 0.22/0.27 % Result found by ho_unfolding_6
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUSF-FFSF22-SFFFFFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 697281 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUSF-FFSF22-SFFFFFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 13
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 13
% 0.22/0.27 % Removed in clause preprocessing : 8
% 0.22/0.27 % Initial clauses in saturation : 5
% 0.22/0.27 % Processed clauses : 10
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 10
% 0.22/0.27 % Other redundant clauses eliminated : 1
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 1
% 0.22/0.27 % Generated clauses : 6
% 0.22/0.27 % ...of the previous two non-redundant : 5
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 4
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 1
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 3
% 0.22/0.27 % ...of those cached : 1
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 7
% 0.22/0.27 % Positive orientable unit clauses : 2
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 3
% 0.22/0.27 % Non-unit-clauses : 2
% 0.22/0.27 % Current number of unprocessed clauses: 0
% 0.22/0.27 % ...number of literals in the above : 0
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 2
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 3
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 3
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 1
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 1
% 0.22/0.27 % BW rewrite match successes : 1
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 590
% 0.22/0.27 % Search garbage collected termcells : 83
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.003 s
% 0.22/0.27 % System time : 0.002 s
% 0.22/0.27 % Total time : 0.005 s
% 0.22/0.27 % Maximum resident set size: 3636 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.003 s
% 0.22/0.27 % System time : 0.009 s
% 0.22/0.27 % Total time : 0.012 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------