%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM670^1 : 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 : n001.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 08:17:23 AM UTC 2026
% Result : Theorem 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 108 ( 16 ~; 0 |; 0 &; 92 @)
% ( 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 : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% 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(satz19a,conjecture,
~ ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.IhmkbHkZFE/E---3.1_1178750.p',satz19a) ).
thf(satz5,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ( pl @ ( pl @ X3 @ X4 ) @ X5 )
= ( pl @ X3 @ ( pl @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IhmkbHkZFE/E---3.1_1178750.p',satz5) ).
thf(m,axiom,
~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.IhmkbHkZFE/E---3.1_1178750.p',m) ).
thf(satz6,axiom,
! [X3: nat,X4: nat] :
( ( pl @ X3 @ X4 )
= ( pl @ X4 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.IhmkbHkZFE/E---3.1_1178750.p',satz6) ).
thf(c_0_4,negated_conjecture,
~ ~ ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
inference(assume_negation,[status(cth)],[satz19a]) ).
thf(c_0_5,negated_conjecture,
~ ~ ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X20: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_7,plain,
! [X17: nat,X18: nat,X19: nat] :
( ( pl @ ( pl @ X17 @ X18 ) @ X19 )
= ( pl @ X17 @ ( pl @ X18 @ X19 ) ) ),
inference(variable_rename,[status(thm)],[satz5]) ).
thf(c_0_8,plain,
~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_9,negated_conjecture,
! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: nat,X3: nat,X4: nat] :
( ( pl @ ( pl @ X1 @ X3 ) @ X4 )
= ( pl @ X1 @ ( pl @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X15: nat,X16: nat] :
( ( pl @ X15 @ X16 )
= ( pl @ X16 @ X15 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_12,plain,
( x
= ( pl @ y @ esk1_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: nat] :
( ( pl @ y @ ( pl @ z @ X1 ) )
!= ( pl @ x @ z ) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X3: nat,X1: nat] :
( ( pl @ X1 @ X3 )
= ( pl @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( x
= ( pl @ y @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: nat] :
( ( pl @ y @ ( pl @ X1 @ z ) )
!= ( pl @ x @ z ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
! [X1: nat] :
( ( pl @ y @ ( pl @ esk1_0 @ X1 ) )
= ( pl @ x @ X1 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM670^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n001.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 12:40:35 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 Running higher-order theorem proving
% 0.08/0.20 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.IhmkbHkZFE/E---3.1_1178750.p
% 0.08/0.22 % Version: 3.5.1-ho
% 0.08/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.22 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.22 % Starting sh4l with 300s (1) cores
% 0.08/0.22 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.22 % ehoh_best_nonlift_rwall with pid 1178766 completed with status 0
% 0.08/0.22 % Result found by ehoh_best_nonlift_rwall
% 0.08/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.22 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.22 % Starting sh4l with 300s (1) cores
% 0.08/0.22 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.22 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.08/0.22 % No SInE strategy applied
% 0.08/0.22 % Search class: HUUPS-FFSF22-SFFFFFNN
% 0.08/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.22 % SubtermCWHack with pid 1178767 completed with status 0
% 0.08/0.22 % Result found by SubtermCWHack
% 0.08/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.22 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.22 % Starting sh4l with 300s (1) cores
% 0.08/0.22 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.22 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.08/0.22 % No SInE strategy applied
% 0.08/0.22 % Search class: HUUPS-FFSF22-SFFFFFNN
% 0.08/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.22 % Preprocessing time : 0.001 s
% 0.08/0.22
% 0.08/0.22 % Proof found!
% 0.08/0.22 % SZS status Theorem
% 0.08/0.22 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22 % Parsed axioms : 10
% 0.08/0.22 % Removed by relevancy pruning/SinE : 0
% 0.08/0.22 % Initial clauses : 10
% 0.08/0.22 % Removed in clause preprocessing : 6
% 0.08/0.22 % Initial clauses in saturation : 4
% 0.08/0.22 % Processed clauses : 12
% 0.08/0.22 % ...of these trivial : 0
% 0.08/0.22 % ...subsumed : 3
% 0.08/0.22 % ...remaining for further processing : 9
% 0.08/0.22 % Other redundant clauses eliminated : 0
% 0.08/0.22 % Clauses deleted for lack of memory : 0
% 0.08/0.22 % Backward-subsumed : 0
% 0.08/0.22 % Backward-rewritten : 1
% 0.08/0.22 % Generated clauses : 27
% 0.08/0.22 % ...of the previous two non-redundant : 25
% 0.08/0.22 % ...aggressively subsumed : 0
% 0.08/0.22 % Contextual simplify-reflections : 0
% 0.08/0.22 % Paramodulations : 27
% 0.08/0.22 % Factorizations : 0
% 0.08/0.22 % NegExts : 0
% 0.08/0.22 % Equation resolutions : 0
% 0.08/0.22 % Disequality decompositions : 0
% 0.08/0.22 % Total rewrite steps : 15
% 0.08/0.22 % ...of those cached : 5
% 0.08/0.22 % Propositional unsat checks : 0
% 0.08/0.22 % Propositional check models : 0
% 0.08/0.22 % Propositional check unsatisfiable : 0
% 0.08/0.22 % Propositional clauses : 0
% 0.08/0.22 % Propositional clauses after purity: 0
% 0.08/0.22 % Propositional unsat core size : 0
% 0.08/0.22 % Propositional preprocessing time : 0.000
% 0.08/0.22 % Propositional encoding time : 0.000
% 0.08/0.22 % Propositional solver time : 0.000
% 0.08/0.22 % Success case prop preproc time : 0.000
% 0.08/0.22 % Success case prop encoding time : 0.000
% 0.08/0.22 % Success case prop solver time : 0.000
% 0.08/0.22 % Current number of processed clauses : 8
% 0.08/0.22 % Positive orientable unit clauses : 3
% 0.08/0.22 % Positive unorientable unit clauses: 1
% 0.08/0.22 % Negative unit clauses : 4
% 0.08/0.22 % Non-unit-clauses : 0
% 0.08/0.22 % Current number of unprocessed clauses: 14
% 0.08/0.22 % ...number of literals in the above : 14
% 0.08/0.22 % Current number of archived formulas : 0
% 0.08/0.22 % Current number of archived clauses : 1
% 0.08/0.22 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.22 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.22 % Non-unit clause-clause subsumptions : 0
% 0.08/0.22 % Unit Clause-clause subsumption calls : 5
% 0.08/0.22 % Rewrite failures with RHS unbound : 0
% 0.08/0.22 % BW rewrite match attempts : 3
% 0.08/0.22 % BW rewrite match successes : 3
% 0.08/0.22 % Condensation attempts : 0
% 0.08/0.22 % Condensation successes : 0
% 0.08/0.22 % Termbank termtop insertions : 629
% 0.08/0.22 % Search garbage collected termcells : 50
% 0.08/0.22
% 0.08/0.22 % -------------------------------------------------
% 0.08/0.22 % User time : 0.001 s
% 0.08/0.22 % System time : 0.003 s
% 0.08/0.22 % Total time : 0.004 s
% 0.08/0.22 % Maximum resident set size: 3580 pages
% 0.08/0.22
% 0.08/0.22 % -------------------------------------------------
% 0.08/0.22 % User time : 0.002 s
% 0.08/0.22 % System time : 0.007 s
% 0.08/0.22 % Total time : 0.010 s
% 0.08/0.22 % Maximum resident set size: 4608 pages
% 0.08/0.22 % E exiting
%------------------------------------------------------------------------------