%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM670_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Thu Sep 24 01:50:04 PM UTC 2026
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% 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)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
nat: $tType ).
tff(decl_23,type,
x: nat ).
tff(decl_24,type,
y: nat ).
tff(decl_25,type,
z: nat ).
tff(decl_26,type,
pl: ( nat * nat ) > nat ).
tff(decl_27,type,
esk1_0: nat ).
tff(satz19a,conjecture,
~ ! [X1: nat] : ( pl(x,z) != pl(pl(y,z),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
tff(satz5,axiom,
! [X3: nat,X4: nat,X5: nat] : ( pl(pl(X3,X4),X5) = pl(X3,pl(X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
tff(m,axiom,
~ ! [X1: nat] : ( x != pl(y,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(satz6,axiom,
! [X3: nat,X4: nat] : ( pl(X3,X4) = pl(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(c_0_4,negated_conjecture,
~ ~ ! [X1: nat] : ( pl(x,z) != pl(pl(y,z),X1) ),
inference(assume_negation,[status(cth)],[satz19a]) ).
tff(c_0_5,negated_conjecture,
~ ~ ! [X1: nat] : ( pl(x,z) != pl(pl(y,z),X1) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
tff(c_0_6,negated_conjecture,
! [X6: nat] : ( pl(x,z) != pl(pl(y,z),X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
tff(c_0_7,plain,
! [X9: nat,X10: nat,X11: nat] : ( pl(pl(X9,X10),X11) = pl(X9,pl(X10,X11)) ),
inference(variable_rename,[status(thm)],[satz5]) ).
tff(c_0_8,plain,
~ ! [X1: nat] : ( x != pl(y,X1) ),
inference(fof_simplification,[status(thm)],[m]) ).
tcf(c_0_9,negated_conjecture,
! [X1: nat] : pl(x,z) != pl(pl(y,z),X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(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]) ).
tff(c_0_11,plain,
! [X7: nat,X8: nat] : ( pl(X7,X8) = pl(X8,X7) ),
inference(variable_rename,[status(thm)],[satz6]) ).
tff(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])])]) ).
tcf(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]) ).
tcf(c_0_14,plain,
! [X3: nat,X1: nat] : pl(X1,X3) = pl(X3,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_15,plain,
x = pl(y,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(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]) ).
tcf(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]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM670_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 % Computer : n018.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Mon Sep 21 02:53:58 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.54 Running first-order theorem proving
% 0.20/0.55 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.57 % Version: 3.5.1
% 0.20/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.57 % Starting sh5l with 300s (1) cores
% 0.20/0.57 % new_bool_3 with pid 808672 completed with status 0
% 0.20/0.57 % Result found by new_bool_3
% 0.20/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.57 % Search class: FUUPS-FFSF22-SFFFFFNN
% 0.20/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.57 % SubtermCWHack with pid 808676 completed with status 0
% 0.20/0.57 % Result found by SubtermCWHack
% 0.20/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.57 % Search class: FUUPS-FFSF22-SFFFFFNN
% 0.20/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.57 % Preprocessing time : 0.002 s
% 0.20/0.57
% 0.20/0.57 % Proof found!
% 0.20/0.57 % SZS status Theorem
% 0.20/0.57 % SZS output start CNFRefutation
% See solution above
% 0.20/0.57 % Parsed axioms : 10
% 0.20/0.57 % Removed by relevancy pruning/SinE : 6
% 0.20/0.57 % Initial clauses : 4
% 0.20/0.57 % Removed in clause preprocessing : 0
% 0.20/0.57 % Initial clauses in saturation : 4
% 0.20/0.57 % Processed clauses : 12
% 0.20/0.57 % ...of these trivial : 0
% 0.20/0.57 % ...subsumed : 3
% 0.20/0.57 % ...remaining for further processing : 9
% 0.20/0.57 % Other redundant clauses eliminated : 0
% 0.20/0.57 % Clauses deleted for lack of memory : 0
% 0.20/0.57 % Backward-subsumed : 0
% 0.20/0.57 % Backward-rewritten : 1
% 0.20/0.57 % Generated clauses : 27
% 0.20/0.57 % ...of the previous two non-redundant : 25
% 0.20/0.57 % ...aggressively subsumed : 0
% 0.20/0.57 % Contextual simplify-reflections : 0
% 0.20/0.57 % Paramodulations : 27
% 0.20/0.57 % Factorizations : 0
% 0.20/0.57 % NegExts : 0
% 0.20/0.57 % Equation resolutions : 0
% 0.20/0.57 % Disequality decompositions : 0
% 0.20/0.57 % Total rewrite steps : 15
% 0.20/0.57 % ...of those cached : 5
% 0.20/0.57 % Propositional unsat checks : 0
% 0.20/0.57 % Propositional check models : 0
% 0.20/0.57 % Propositional check unsatisfiable : 0
% 0.20/0.57 % Propositional clauses : 0
% 0.20/0.57 % Propositional clauses after purity: 0
% 0.20/0.57 % Propositional unsat core size : 0
% 0.20/0.57 % Propositional preprocessing time : 0.000
% 0.20/0.57 % Propositional encoding time : 0.000
% 0.20/0.57 % Propositional solver time : 0.000
% 0.20/0.57 % Success case prop preproc time : 0.000
% 0.20/0.57 % Success case prop encoding time : 0.000
% 0.20/0.57 % Success case prop solver time : 0.000
% 0.20/0.57 % Current number of processed clauses : 8
% 0.20/0.57 % Positive orientable unit clauses : 3
% 0.20/0.57 % Positive unorientable unit clauses: 1
% 0.20/0.57 % Negative unit clauses : 4
% 0.20/0.57 % Non-unit-clauses : 0
% 0.20/0.57 % Current number of unprocessed clauses: 14
% 0.20/0.57 % ...number of literals in the above : 14
% 0.20/0.57 % Current number of archived formulas : 0
% 0.20/0.57 % Current number of archived clauses : 1
% 0.20/0.57 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.57 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.57 % Non-unit clause-clause subsumptions : 0
% 0.20/0.57 % Unit Clause-clause subsumption calls : 5
% 0.20/0.57 % Rewrite failures with RHS unbound : 0
% 0.20/0.57 % BW rewrite match attempts : 3
% 0.20/0.57 % BW rewrite match successes : 3
% 0.20/0.57 % Condensation attempts : 0
% 0.20/0.57 % Condensation successes : 0
% 0.20/0.57 % Termbank termtop insertions : 495
% 0.20/0.57 % Search garbage collected termcells : 25
% 0.20/0.57
% 0.20/0.57 % -------------------------------------------------
% 0.20/0.57 % User time : 0.002 s
% 0.20/0.57 % System time : 0.006 s
% 0.20/0.57 % Total time : 0.008 s
% 0.20/0.57 % Maximum resident set size: 3636 pages
% 0.20/0.57
% 0.20/0.57 % -------------------------------------------------
% 0.20/0.57 % User time : 0.002 s
% 0.20/0.57 % System time : 0.014 s
% 0.20/0.57 % Total time : 0.016 s
% 0.20/0.57 % Maximum resident set size: 4608 pages
% 0.20/0.57 % E exiting
%------------------------------------------------------------------------------