%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:50:12 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 39 ~; 5 |; 1 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
nat: $tType ).
tff(decl_23,type,
x: nat ).
tff(decl_24,type,
y: nat ).
tff(decl_25,type,
pl: ( nat * nat ) > nat ).
tff(decl_26,type,
n_1: nat ).
tff(decl_27,type,
esk1_3: ( nat * ( nat * nat ) ) > nat ).
tff(decl_28,type,
esk2_1: nat > nat ).
tff(decl_29,type,
esk3_0: nat ).
tff(satz25,conjecture,
( ~ ~ ! [X1: nat] : ( y != pl(pl(x,n_1),X1) )
=> ( y = pl(x,n_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz25) ).
tff(satz19a,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ~ ! [X1: nat] : ( X3 != pl(X4,X1) )
=> ~ ! [X1: nat] : ( pl(X3,X5) != pl(pl(X4,X5),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
tff(satz6,axiom,
! [X3: nat,X4: nat] : ( pl(X3,X4) = pl(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
tff(satz24,axiom,
! [X3: nat] :
( ~ ~ ! [X1: nat] : ( X3 != pl(n_1,X1) )
=> ( X3 = n_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24) ).
tff(m,axiom,
~ ! [X1: nat] : ( y != pl(x,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(c_0_5,negated_conjecture,
~ ( ~ ~ ! [X1: nat] : ( y != pl(pl(x,n_1),X1) )
=> ( y = pl(x,n_1) ) ),
inference(assume_negation,[status(cth)],[satz25]) ).
tff(c_0_6,negated_conjecture,
~ ( ~ ~ ! [X1: nat] : ( y != pl(pl(x,n_1),X1) )
=> ( y = pl(x,n_1) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
tff(c_0_7,plain,
! [X3: nat,X4: nat,X5: nat] :
( ~ ! [X1: nat] : ( X3 != pl(X4,X1) )
=> ~ ! [X1: nat] : ( pl(X3,X5) != pl(pl(X4,X5),X1) ) ),
inference(fof_simplification,[status(thm)],[satz19a]) ).
tff(c_0_8,negated_conjecture,
! [X6: nat] :
( ( y != pl(x,n_1) )
& ( y != pl(pl(x,n_1),X6) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
tff(c_0_9,plain,
! [X12: nat,X13: nat] : ( pl(X12,X13) = pl(X13,X12) ),
inference(variable_rename,[status(thm)],[satz6]) ).
tff(c_0_10,plain,
! [X7: nat,X8: nat,X9: nat,X10: nat] :
( ( pl(X7,X10) = pl(pl(X8,X10),esk1_3(X7,X8,X10)) )
| ( X7 != pl(X8,X9) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
tcf(c_0_11,negated_conjecture,
! [X1: nat] : y != pl(pl(x,n_1),X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,plain,
! [X3: nat,X1: nat] : pl(X1,X3) = pl(X3,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_13,plain,
! [X1: nat,X3: nat,X5: nat,X4: nat] :
( ( X1 != pl(X3,X4) )
| ( pl(X1,X5) = pl(pl(X3,X5),esk1_3(X1,X3,X5)) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_14,plain,
! [X3: nat] :
( ~ ~ ! [X1: nat] : ( X3 != pl(n_1,X1) )
=> ( X3 = n_1 ) ),
inference(fof_simplification,[status(thm)],[satz24]) ).
tcf(c_0_15,negated_conjecture,
! [X1: nat] : pl(pl(n_1,x),X1) != y,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_16,plain,
! [X1: nat,X4: nat,X3: nat] : pl(pl(X1,X3),esk1_3(pl(X1,X4),X1,X3)) = pl(pl(X1,X4),X3),
inference(er,[status(thm)],[c_0_13]) ).
tff(c_0_17,plain,
! [X14: nat] :
( ( X14 = n_1 )
| ( X14 = pl(n_1,esk2_1(X14)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
tff(c_0_18,plain,
~ ! [X1: nat] : ( y != pl(x,X1) ),
inference(fof_simplification,[status(thm)],[m]) ).
tcf(c_0_19,negated_conjecture,
! [X1: nat] : pl(x,pl(n_1,X1)) != y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]) ).
tcf(c_0_20,plain,
! [X1: nat] :
( ( X1 = n_1 )
| ( X1 = pl(n_1,esk2_1(X1)) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tff(c_0_21,plain,
y = pl(x,esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
tcf(c_0_22,negated_conjecture,
! [X1: nat] :
( ( pl(x,X1) != y )
| ( X1 = n_1 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
tcf(c_0_23,plain,
y = pl(x,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_24,negated_conjecture,
y != pl(x,n_1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_25,negated_conjecture,
esk3_0 = n_1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
tcf(c_0_26,negated_conjecture,
pl(n_1,x) != y,
inference(rw,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_27,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_25]),c_0_12]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:57:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % new_bool_1 with pid 3255099 completed with status 0
% 0.11/0.44 % Result found by new_bool_1
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGUPF-FFSF32-SFFFFFNN
% 0.11/0.44 % partial match(1): FGUPF-FFSM32-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 3255103 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGUPF-FFSF32-SFFFFFNN
% 0.11/0.44 % partial match(1): FGUPF-FFSM32-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 11
% 0.11/0.44 % Removed by relevancy pruning/SinE : 6
% 0.11/0.44 % Initial clauses : 6
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 6
% 0.11/0.44 % Processed clauses : 19
% 0.11/0.44 % ...of these trivial : 0
% 0.11/0.44 % ...subsumed : 6
% 0.11/0.44 % ...remaining for further processing : 13
% 0.11/0.44 % Other redundant clauses eliminated : 1
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 2
% 0.11/0.44 % Generated clauses : 24
% 0.11/0.44 % ...of the previous two non-redundant : 25
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 23
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 1
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 5
% 0.11/0.44 % ...of those cached : 1
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 10
% 0.11/0.44 % Positive orientable unit clauses : 2
% 0.11/0.44 % Positive unorientable unit clauses: 1
% 0.11/0.44 % Negative unit clauses : 5
% 0.11/0.44 % Non-unit-clauses : 2
% 0.11/0.44 % Current number of unprocessed clauses: 12
% 0.11/0.44 % ...number of literals in the above : 16
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 2
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.44 % Non-unit clause-clause subsumptions : 0
% 0.11/0.44 % Unit Clause-clause subsumption calls : 6
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 5
% 0.11/0.44 % BW rewrite match successes : 5
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 629
% 0.11/0.44 % Search garbage collected termcells : 106
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.004 s
% 0.11/0.44 % System time : 0.002 s
% 0.11/0.44 % Total time : 0.006 s
% 0.11/0.44 % Maximum resident set size: 3636 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.006 s
% 0.11/0.44 % System time : 0.006 s
% 0.11/0.44 % Total time : 0.012 s
% 0.11/0.44 % Maximum resident set size: 4608 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------