%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM651_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 : n016.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 01:49:57 PM UTC 2026
% Result : Theorem 0.14s 5.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 104 ( 56 ~; 26 |; 7 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?; 45 :)
% 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,
esk1_0: nat ).
tff(decl_27,type,
esk2_0: nat ).
tff(decl_28,type,
esk3_0: nat ).
tff(decl_29,type,
esk4_0: nat ).
tff(satz7,axiom,
! [X1: nat,X2: nat] : ( X2 != pl(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz7) ).
tff(satz9b,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] : ( x != pl(y,X5) ) )
=> ~ ~ ( ( ~ ! [X5: nat] : ( x != pl(y,X5) )
=> ~ ~ ! [X5: nat] : ( y != pl(x,X5) ) )
=> ~ ( ~ ! [X5: nat] : ( y != pl(x,X5) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz9b) ).
tff(satz5,axiom,
! [X1: nat,X2: nat,X4: nat] : ( pl(pl(X1,X2),X4) = pl(X1,pl(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
tff(satz6,axiom,
! [X1: nat,X2: nat] : ( pl(X1,X2) = pl(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(c_0_4,plain,
! [X1: nat,X2: nat] : ( X2 != pl(X1,X2) ),
inference(fof_simplification,[status(thm)],[satz7]) ).
tff(c_0_5,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] : ( x != pl(y,X5) ) )
=> ~ ~ ( ( ~ ! [X5: nat] : ( x != pl(y,X5) )
=> ~ ~ ! [X5: nat] : ( y != pl(x,X5) ) )
=> ~ ( ~ ! [X5: nat] : ( y != pl(x,X5) )
=> ( x != y ) ) ) ),
inference(assume_negation,[status(cth)],[satz9b]) ).
tff(c_0_6,plain,
! [X10: nat,X11: nat] : ( X11 != pl(X10,X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_4])]) ).
tff(c_0_7,plain,
! [X14: nat,X15: nat,X16: nat] : ( pl(pl(X14,X15),X16) = pl(X14,pl(X15,X16)) ),
inference(variable_rename,[status(thm)],[satz5]) ).
tff(c_0_8,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] : ( x != pl(y,X5) ) )
=> ~ ~ ( ( ~ ! [X5: nat] : ( x != pl(y,X5) )
=> ~ ~ ! [X5: nat] : ( y != pl(x,X5) ) )
=> ~ ( ~ ! [X5: nat] : ( y != pl(x,X5) )
=> ( x != y ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
tcf(c_0_9,plain,
! [X2: nat,X1: nat] : X1 != pl(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_10,plain,
! [X1: nat,X2: nat,X4: nat] : pl(pl(X1,X2),X4) = pl(X1,pl(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tff(c_0_11,plain,
! [X12: nat,X13: nat] : ( pl(X12,X13) = pl(X13,X12) ),
inference(variable_rename,[status(thm)],[satz6]) ).
tff(c_0_12,negated_conjecture,
( ( ( x = pl(y,esk1_0) )
| ( y = pl(x,esk3_0) )
| ( x = y ) )
& ( ( x = pl(y,esk1_0) )
| ( y = pl(x,esk3_0) )
| ( y = pl(x,esk4_0) ) )
& ( ( x = pl(y,esk1_0) )
| ( x = pl(y,esk2_0) )
| ( x = y ) )
& ( ( x = pl(y,esk1_0) )
| ( x = pl(y,esk2_0) )
| ( y = pl(x,esk4_0) ) )
& ( ( x = y )
| ( y = pl(x,esk3_0) )
| ( x = y ) )
& ( ( x = y )
| ( y = pl(x,esk3_0) )
| ( y = pl(x,esk4_0) ) )
& ( ( x = y )
| ( x = pl(y,esk2_0) )
| ( x = y ) )
& ( ( x = y )
| ( x = pl(y,esk2_0) )
| ( y = pl(x,esk4_0) ) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
tcf(c_0_13,plain,
! [X1: nat,X2: nat,X4: nat] : pl(X1,pl(X2,X4)) != X4,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
tcf(c_0_14,plain,
! [X2: nat,X1: nat] : pl(X1,X2) = pl(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_15,negated_conjecture,
( ( x = y )
| ( x = pl(y,esk2_0) )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_16,plain,
! [X1: nat,X4: nat,X2: nat] : pl(X1,pl(X2,X4)) != X2,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
tcf(c_0_17,negated_conjecture,
( ( x = pl(y,esk2_0) )
| ( y = x ) ),
inference(cn,[status(thm)],[c_0_15]) ).
tcf(c_0_18,negated_conjecture,
! [X1: nat] :
( ( pl(X1,x) != y )
| ( x = y ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_19,negated_conjecture,
( ( x = y )
| ( y = pl(x,esk3_0) )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_20,negated_conjecture,
! [X1: nat] :
( ( pl(x,X1) != y )
| ( x = y ) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
tcf(c_0_21,negated_conjecture,
( ( y = pl(x,esk3_0) )
| ( y = x ) ),
inference(cn,[status(thm)],[c_0_19]) ).
tcf(c_0_22,negated_conjecture,
( ( x = pl(y,esk1_0) )
| ( x = pl(y,esk2_0) )
| ( y = pl(x,esk4_0) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_23,negated_conjecture,
x = y,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
tcf(c_0_24,plain,
! [X2: nat,X1: nat] : pl(X1,X2) != X1,
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_24]),c_0_24]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.37 % Computer : n016.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 02:53:43 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.44 % Version: 3.5.1
% 0.14/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.44 % Starting sh5l with 300s (1) cores
% 0.14/5.44 % new_bool_3 with pid 1400830 completed with status 0
% 0.14/5.44 % Result found by new_bool_3
% 0.14/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.44 % Search class: FGUPS-FFSM22-SFFFFFNN
% 0.14/5.44 % partial match(2): FGUSS-FFSF22-SFFFFFNN
% 0.14/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.44 % SubtermCWHack with pid 1400836 completed with status 0
% 0.14/5.44 % Result found by SubtermCWHack
% 0.14/5.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.44 % Search class: FGUPS-FFSM22-SFFFFFNN
% 0.14/5.44 % partial match(2): FGUSS-FFSF22-SFFFFFNN
% 0.14/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.44 % Preprocessing time : 0.001 s
% 0.14/5.44
% 0.14/5.44 % Proof found!
% 0.14/5.44 % SZS status Theorem
% 0.14/5.44 % SZS output start CNFRefutation
% See solution above
% 0.14/5.44 % Parsed axioms : 9
% 0.14/5.44 % Removed by relevancy pruning/SinE : 5
% 0.14/5.44 % Initial clauses : 11
% 0.14/5.44 % Removed in clause preprocessing : 0
% 0.14/5.44 % Initial clauses in saturation : 11
% 0.14/5.44 % Processed clauses : 55
% 0.14/5.44 % ...of these trivial : 1
% 0.14/5.44 % ...subsumed : 28
% 0.14/5.44 % ...remaining for further processing : 25
% 0.14/5.44 % Other redundant clauses eliminated : 0
% 0.14/5.44 % Clauses deleted for lack of memory : 0
% 0.14/5.44 % Backward-subsumed : 0
% 0.14/5.44 % Backward-rewritten : 13
% 0.14/5.44 % Generated clauses : 90
% 0.14/5.44 % ...of the previous two non-redundant : 87
% 0.14/5.44 % ...aggressively subsumed : 0
% 0.14/5.44 % Contextual simplify-reflections : 0
% 0.14/5.44 % Paramodulations : 90
% 0.14/5.44 % Factorizations : 0
% 0.14/5.44 % NegExts : 0
% 0.14/5.44 % Equation resolutions : 0
% 0.14/5.44 % Disequality decompositions : 0
% 0.14/5.44 % Total rewrite steps : 57
% 0.14/5.44 % ...of those cached : 46
% 0.14/5.44 % Propositional unsat checks : 0
% 0.14/5.44 % Propositional check models : 0
% 0.14/5.44 % Propositional check unsatisfiable : 0
% 0.14/5.44 % Propositional clauses : 0
% 0.14/5.44 % Propositional clauses after purity: 0
% 0.14/5.44 % Propositional unsat core size : 0
% 0.14/5.44 % Propositional preprocessing time : 0.000
% 0.14/5.44 % Propositional encoding time : 0.000
% 0.14/5.44 % Propositional solver time : 0.000
% 0.14/5.44 % Success case prop preproc time : 0.000
% 0.14/5.44 % Success case prop encoding time : 0.000
% 0.14/5.44 % Success case prop solver time : 0.000
% 0.14/5.44 % Current number of processed clauses : 12
% 0.14/5.44 % Positive orientable unit clauses : 2
% 0.14/5.44 % Positive unorientable unit clauses: 1
% 0.14/5.44 % Negative unit clauses : 9
% 0.14/5.44 % Non-unit-clauses : 0
% 0.14/5.44 % Current number of unprocessed clauses: 34
% 0.14/5.44 % ...number of literals in the above : 42
% 0.14/5.44 % Current number of archived formulas : 0
% 0.14/5.44 % Current number of archived clauses : 13
% 0.14/5.44 % Clause-clause subsumption calls (NU) : 96
% 0.14/5.44 % Rec. Clause-clause subsumption calls : 96
% 0.14/5.44 % Non-unit clause-clause subsumptions : 5
% 0.14/5.44 % Unit Clause-clause subsumption calls : 12
% 0.14/5.44 % Rewrite failures with RHS unbound : 0
% 0.14/5.44 % BW rewrite match attempts : 3
% 0.14/5.44 % BW rewrite match successes : 3
% 0.14/5.44 % Condensation attempts : 0
% 0.14/5.44 % Condensation successes : 0
% 0.14/5.44 % Termbank termtop insertions : 1087
% 0.14/5.44 % Search garbage collected termcells : 101
% 0.14/5.44
% 0.14/5.44 % -------------------------------------------------
% 0.14/5.44 % User time : 0.001 s
% 0.14/5.44 % System time : 0.004 s
% 0.14/5.44 % Total time : 0.005 s
% 0.14/5.44 % Maximum resident set size: 3636 pages
% 0.14/5.44
% 0.14/5.44 % -------------------------------------------------
% 0.14/5.44 % User time : 0.003 s
% 0.14/5.44 % System time : 0.008 s
% 0.14/5.44 % Total time : 0.010 s
% 0.14/5.44 % Maximum resident set size: 4608 pages
% 0.14/5.44 % E exiting
%------------------------------------------------------------------------------