%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:48:57 PM UTC 2026
% Result : Theorem 0.14s 0.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 101 ( 38 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 115 ( 45 ~; 54 |; 10 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 4 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_ordinal1,conjecture,
! [X1,X2] :
( in(X1,succ(X2))
<=> ( X1 = X2
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( in(X1,succ(X2))
<=> ( X1 = X2
| in(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t13_ordinal1]) ).
fof(c_0_5,negated_conjecture,
( ( esk14_0 = esk15_0
| in(esk14_0,esk15_0)
| in(esk14_0,succ(esk15_0)) )
& ( ~ in(esk14_0,succ(esk15_0))
| esk14_0 != esk15_0 )
& ( ~ in(esk14_0,succ(esk15_0))
| ~ in(esk14_0,esk15_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
fof(c_0_6,plain,
! [X12] : succ(X12) = set_union2(X12,singleton(X12)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_7,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27] :
( ( X27 = set_union2(X25,X26)
| in(esk2_3(X25,X26,X27),X26)
| in(esk2_3(X25,X26,X27),X25)
| in(esk2_3(X25,X26,X27),X27) )
& ( X27 = set_union2(X25,X26)
| ~ in(esk2_3(X25,X26,X27),X27)
| ~ in(esk2_3(X25,X26,X27),X26) )
& ( X27 = set_union2(X25,X26)
| ~ in(esk2_3(X25,X26,X27),X27)
| ~ in(esk2_3(X25,X26,X27),X25) )
& ( X22 != set_union2(X20,X21)
| in(X24,X22)
| ~ in(X24,X21) )
& ( X22 != set_union2(X20,X21)
| in(X24,X22)
| ~ in(X24,X20) )
& ( X22 != set_union2(X20,X21)
| in(X23,X21)
| in(X23,X20)
| ~ in(X23,X22) ) ),
inference(distribute,[status(thm)],[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)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( ~ in(esk14_0,succ(esk15_0))
| ~ in(esk14_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X3 != set_union2(X2,X4)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X13,X14,X15,X16,X17,X18] :
( ( X18 = singleton(X17)
| esk1_2(X17,X18) = X17
| in(esk1_2(X17,X18),X18) )
& ( X18 = singleton(X17)
| esk1_2(X17,X18) != X17
| ~ in(esk1_2(X17,X18),X18) )
& ( X14 != singleton(X13)
| in(X16,X14)
| X16 != X13 )
& ( X14 != singleton(X13)
| X15 = X13
| ~ in(X15,X14) ) ),
inference(distribute,[status(thm)],[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)],[d1_tarski])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( esk14_0 = esk15_0
| in(esk14_0,esk15_0)
| in(esk14_0,succ(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0)))
| ~ in(esk14_0,esk15_0) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ~ in(esk14_0,succ(esk15_0))
| esk14_0 != esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( X2 != set_union2(X3,X4)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( in(esk14_0,set_union2(esk15_0,singleton(esk15_0)))
| in(esk14_0,esk15_0)
| esk15_0 = esk14_0 ),
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk14_0,esk15_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0)))
| esk15_0 != esk14_0 ),
inference(rw,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_22,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ in(X1,set_union2(X3,X2))
| in(X1,X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( in(esk14_0,set_union2(esk15_0,singleton(esk15_0)))
| esk14_0 = esk15_0 ),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk14_0,singleton(esk15_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
esk14_0 = esk15_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_26]) ).
cnf(c_0_29,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 % Computer : n015.cluster.edu
% 0.10/0.44 % Model : x86_64 x86_64
% 0.10/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.44 % Memory : 8046.5625MB
% 0.10/0.44 % OS : Linux 6.8.0-71-generic
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Mon Sep 21 02:29:50 UTC 2026
% 0.10/0.44 % CPUTime :
% 0.10/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.48 Running first-order theorem proving
% 0.14/0.48 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
% 0.14/0.51 % Version: 3.5.1
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.51 % Starting sh5l with 300s (1) cores
% 0.14/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 357659 completed with status 0
% 0.14/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.51 % No SInE strategy applied
% 0.14/0.51 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.14/0.51 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.14/0.51 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.51 % G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 357667 completed with status 0
% 0.14/0.51 % Result found by G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.51 % No SInE strategy applied
% 0.14/0.51 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.14/0.51 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.14/0.51 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.51 % Preprocessing time : 0.001 s
% 0.14/0.51 % Presaturation interreduction done
% 0.14/0.51
% 0.14/0.51 % Proof found!
% 0.14/0.51 % SZS status Theorem
% 0.14/0.51 % SZS output start CNFRefutation
% See solution above
% 0.14/0.51 % Parsed axioms : 34
% 0.14/0.51 % Removed by relevancy pruning/SinE : 0
% 0.14/0.51 % Initial clauses : 61
% 0.14/0.51 % Removed in clause preprocessing : 3
% 0.14/0.51 % Initial clauses in saturation : 58
% 0.14/0.51 % Processed clauses : 150
% 0.14/0.51 % ...of these trivial : 4
% 0.14/0.51 % ...subsumed : 13
% 0.14/0.51 % ...remaining for further processing : 133
% 0.14/0.51 % Other redundant clauses eliminated : 6
% 0.14/0.51 % Clauses deleted for lack of memory : 0
% 0.14/0.51 % Backward-subsumed : 3
% 0.14/0.51 % Backward-rewritten : 12
% 0.14/0.51 % Generated clauses : 104
% 0.14/0.51 % ...of the previous two non-redundant : 81
% 0.14/0.51 % ...aggressively subsumed : 0
% 0.14/0.51 % Contextual simplify-reflections : 3
% 0.14/0.51 % Paramodulations : 97
% 0.14/0.51 % Factorizations : 0
% 0.14/0.51 % NegExts : 0
% 0.14/0.51 % Equation resolutions : 6
% 0.14/0.51 % Disequality decompositions : 0
% 0.14/0.51 % Total rewrite steps : 32
% 0.14/0.51 % ...of those cached : 22
% 0.14/0.51 % Propositional unsat checks : 0
% 0.14/0.51 % Propositional check models : 0
% 0.14/0.51 % Propositional check unsatisfiable : 0
% 0.14/0.51 % Propositional clauses : 0
% 0.14/0.51 % Propositional clauses after purity: 0
% 0.14/0.51 % Propositional unsat core size : 0
% 0.14/0.51 % Propositional preprocessing time : 0.000
% 0.14/0.51 % Propositional encoding time : 0.000
% 0.14/0.51 % Propositional solver time : 0.000
% 0.14/0.51 % Success case prop preproc time : 0.000
% 0.14/0.51 % Success case prop encoding time : 0.000
% 0.14/0.51 % Success case prop solver time : 0.000
% 0.14/0.51 % Current number of processed clauses : 56
% 0.14/0.51 % Positive orientable unit clauses : 27
% 0.14/0.51 % Positive unorientable unit clauses: 1
% 0.14/0.51 % Negative unit clauses : 8
% 0.14/0.51 % Non-unit-clauses : 20
% 0.14/0.51 % Current number of unprocessed clauses: 43
% 0.14/0.51 % ...number of literals in the above : 87
% 0.14/0.51 % Current number of archived formulas : 0
% 0.14/0.51 % Current number of archived clauses : 73
% 0.14/0.51 % Clause-clause subsumption calls (NU) : 169
% 0.14/0.51 % Rec. Clause-clause subsumption calls : 133
% 0.14/0.51 % Non-unit clause-clause subsumptions : 9
% 0.14/0.51 % Unit Clause-clause subsumption calls : 116
% 0.14/0.51 % Rewrite failures with RHS unbound : 0
% 0.14/0.51 % BW rewrite match attempts : 34
% 0.14/0.51 % BW rewrite match successes : 28
% 0.14/0.51 % Condensation attempts : 0
% 0.14/0.51 % Condensation successes : 0
% 0.14/0.51 % Termbank termtop insertions : 3503
% 0.14/0.51 % Search garbage collected termcells : 561
% 0.14/0.51
% 0.14/0.51 % -------------------------------------------------
% 0.14/0.51 % User time : 0.007 s
% 0.14/0.51 % System time : 0.002 s
% 0.14/0.51 % Total time : 0.009 s
% 0.14/0.51 % Maximum resident set size: 3652 pages
% 0.14/0.51
% 0.14/0.51 % -------------------------------------------------
% 0.14/0.51 % User time : 0.027 s
% 0.14/0.51 % System time : 0.014 s
% 0.14/0.51 % Total time : 0.041 s
% 0.14/0.51 % Maximum resident set size: 4608 pages
% 0.14/0.51 % E exiting
%------------------------------------------------------------------------------