%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM691_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 01:50:10 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 40 ~; 24 |; 3 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 42 :)
% 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,
u: nat ).
tff(decl_27,type,
more: ( nat * nat ) > $o ).
tff(decl_28,type,
pl: ( nat * nat ) > nat ).
tff(satz23,conjecture,
( ~ more(pl(x,z),pl(y,u))
=> ( pl(x,z) = pl(y,u) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).
tff(satz22b,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( more(X2,X3)
=> ( ( ~ more(X4,X5)
=> ( X4 = X5 ) )
=> more(pl(X2,X4),pl(X3,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
tff(n,axiom,
( ~ more(z,u)
=> ( z = u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
tff(m,axiom,
( ~ more(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(satz22a,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( ~ more(X2,X3)
=> ( X2 = X3 ) )
=> ( more(X4,X5)
=> more(pl(X2,X4),pl(X3,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).
tff(c_0_5,negated_conjecture,
~ ( ~ more(pl(x,z),pl(y,u))
=> ( pl(x,z) = pl(y,u) ) ),
inference(assume_negation,[status(cth)],[satz23]) ).
tff(c_0_6,negated_conjecture,
~ ( ~ more(pl(x,z),pl(y,u))
=> ( pl(x,z) = pl(y,u) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
tff(c_0_7,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( more(X2,X3)
=> ( ( ~ more(X4,X5)
=> ( X4 = X5 ) )
=> more(pl(X2,X4),pl(X3,X5)) ) ),
inference(fof_simplification,[status(thm)],[satz22b]) ).
tff(c_0_8,negated_conjecture,
( ( pl(x,z) != pl(y,u) )
& ~ more(pl(x,z),pl(y,u)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
tff(c_0_9,plain,
! [X10: nat,X11: nat,X12: nat,X13: nat] :
( ( ~ more(X10,X11)
| more(pl(X10,X12),pl(X11,X13))
| ( X12 != X13 ) )
& ( ~ more(X10,X11)
| more(pl(X10,X12),pl(X11,X13))
| ~ more(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
tff(c_0_10,plain,
( ~ more(z,u)
=> ( z = u ) ),
inference(fof_simplification,[status(thm)],[n]) ).
tcf(c_0_11,negated_conjecture,
~ more(pl(x,z),pl(y,u)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ~ more(X4,X5)
| ~ more(X2,X3)
| more(pl(X4,X2),pl(X5,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_13,plain,
( ( z = u )
| more(z,u) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
tff(c_0_14,plain,
( ~ more(x,y)
=> ( x = y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
tcf(c_0_15,negated_conjecture,
( ~ more(z,u)
| ~ more(x,y) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_16,plain,
( ( z = u )
| more(z,u) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tff(c_0_17,plain,
( ( x = y )
| more(x,y) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
tcf(c_0_18,negated_conjecture,
( ~ more(x,y)
| ( z = u ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
tcf(c_0_19,plain,
( ( x = y )
| more(x,y) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_20,negated_conjecture,
( ( z = u )
| ( y = x ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_21,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ~ more(X4,X5)
| ( X2 != X3 )
| more(pl(X4,X2),pl(X5,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_22,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( ~ more(X2,X3)
=> ( X2 = X3 ) )
=> ( more(X4,X5)
=> more(pl(X2,X4),pl(X3,X5)) ) ),
inference(fof_simplification,[status(thm)],[satz22a]) ).
tcf(c_0_23,negated_conjecture,
( ~ more(pl(x,u),pl(y,u))
| ( y = x ) ),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
tcf(c_0_24,plain,
! [X2: nat,X3: nat,X4: nat] :
( ~ more(X2,X4)
| more(pl(X2,X3),pl(X4,X3)) ),
inference(er,[status(thm)],[c_0_21]) ).
tff(c_0_25,plain,
! [X6: nat,X7: nat,X8: nat,X9: nat] :
( ( more(pl(X6,X8),pl(X7,X9))
| ~ more(X8,X9)
| ( X6 != X7 ) )
& ( more(pl(X6,X8),pl(X7,X9))
| ~ more(X8,X9)
| ~ more(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
tcf(c_0_26,negated_conjecture,
y = x,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]) ).
tcf(c_0_27,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ~ more(X4,X5)
| ( X2 != X3 )
| more(pl(X2,X4),pl(X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_28,negated_conjecture,
~ more(pl(x,z),pl(x,u)),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
tcf(c_0_29,plain,
! [X2: nat,X3: nat,X4: nat] :
( ~ more(X3,X4)
| more(pl(X2,X3),pl(X2,X4)) ),
inference(er,[status(thm)],[c_0_27]) ).
tcf(c_0_30,negated_conjecture,
pl(x,z) != pl(y,u),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_31,negated_conjecture,
~ more(z,u),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
tcf(c_0_32,negated_conjecture,
pl(x,z) != pl(x,u),
inference(rw,[status(thm)],[c_0_30,c_0_26]) ).
tcf(c_0_33,plain,
z = u,
inference(sr,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM691_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:56:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % new_bool_1 with pid 3253435 completed with status 0
% 0.14/0.43 % Result found by new_bool_1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 3253439 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 13
% 0.14/0.43 % Removed by relevancy pruning/SinE : 8
% 0.14/0.43 % Initial clauses : 8
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 8
% 0.14/0.43 % Processed clauses : 23
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 2
% 0.14/0.43 % ...remaining for further processing : 21
% 0.14/0.43 % Other redundant clauses eliminated : 2
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 1
% 0.14/0.43 % Backward-rewritten : 10
% 0.14/0.43 % Generated clauses : 16
% 0.14/0.43 % ...of the previous two non-redundant : 18
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 2
% 0.14/0.43 % Paramodulations : 13
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 2
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 11
% 0.14/0.43 % ...of those cached : 9
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 7
% 0.14/0.43 % Positive orientable unit clauses : 2
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 2
% 0.14/0.43 % Non-unit-clauses : 3
% 0.14/0.43 % Current number of unprocessed clauses: 1
% 0.14/0.43 % ...number of literals in the above : 2
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 12
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 19
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 19
% 0.14/0.43 % Non-unit clause-clause subsumptions : 4
% 0.14/0.43 % Unit Clause-clause subsumption calls : 3
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 2
% 0.14/0.43 % BW rewrite match successes : 2
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 722
% 0.14/0.43 % Search garbage collected termcells : 91
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.005 s
% 0.14/0.43 % System time : 0.001 s
% 0.14/0.43 % Total time : 0.006 s
% 0.14/0.43 % Maximum resident set size: 3640 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.008 s
% 0.14/0.43 % System time : 0.004 s
% 0.14/0.43 % Total time : 0.011 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------