%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 0.12s 0.49s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 85 ( 33 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 36 |; 9 &)
% ( 4 <=>; 4 =>; 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 : 53 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_ordinal1,conjecture,
! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t12_ordinal1]) ).
fof(c_0_7,plain,
! [X49] : in(X49,succ(X49)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_8,plain,
! [X12] : succ(X12) = set_union2(X12,singleton(X12)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_9,negated_conjecture,
( esk14_0 != esk15_0
& succ(esk14_0) = succ(esk15_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,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_11,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
succ(esk14_0) = succ(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,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_15,plain,
( X2 != set_union2(X3,X4)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
set_union2(esk15_0,singleton(esk15_0)) = set_union2(esk14_0,singleton(esk14_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]) ).
fof(c_0_18,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_19,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(X1,set_union2(X3,X2))
| in(X1,X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
in(esk14_0,set_union2(esk15_0,singleton(esk15_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X5,X6] :
( ~ in(X6,X5)
| ~ in(X5,X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_23,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( in(esk14_0,esk15_0)
| in(esk14_0,singleton(esk15_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk14_0 != esk15_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
in(esk14_0,esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(X1,set_union2(esk15_0,singleton(esk15_0)))
| in(X1,esk14_0)
| in(X1,singleton(esk14_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk15_0,esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
in(esk15_0,singleton(esk14_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:26:49 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.49 % Version: 3.5.1
% 0.12/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.49 % Starting sh5l with 300s (1) cores
% 0.12/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1488299 completed with status 0
% 0.12/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.49 % No SInE strategy applied
% 0.12/0.49 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.12/0.49 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.12/0.49 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.12/0.49 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1488305 completed with status 0
% 0.12/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.49 % No SInE strategy applied
% 0.12/0.49 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.12/0.49 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.49 % Preprocessing time : 0.002 s
% 0.12/0.49 % Presaturation interreduction done
% 0.12/0.49
% 0.12/0.49 % Proof found!
% 0.12/0.49 % SZS status Theorem
% 0.12/0.49 % SZS output start CNFRefutation
% See solution above
% 0.12/0.49 % Parsed axioms : 35
% 0.12/0.49 % Removed by relevancy pruning/SinE : 0
% 0.12/0.49 % Initial clauses : 61
% 0.12/0.49 % Removed in clause preprocessing : 3
% 0.12/0.49 % Initial clauses in saturation : 58
% 0.12/0.49 % Processed clauses : 293
% 0.12/0.49 % ...of these trivial : 4
% 0.12/0.49 % ...subsumed : 112
% 0.12/0.49 % ...remaining for further processing : 177
% 0.12/0.49 % Other redundant clauses eliminated : 6
% 0.12/0.49 % Clauses deleted for lack of memory : 0
% 0.12/0.49 % Backward-subsumed : 9
% 0.12/0.49 % Backward-rewritten : 7
% 0.12/0.49 % Generated clauses : 421
% 0.12/0.49 % ...of the previous two non-redundant : 380
% 0.12/0.49 % ...aggressively subsumed : 0
% 0.12/0.49 % Contextual simplify-reflections : 2
% 0.12/0.49 % Paramodulations : 410
% 0.12/0.49 % Factorizations : 6
% 0.12/0.49 % NegExts : 0
% 0.12/0.49 % Equation resolutions : 6
% 0.12/0.49 % Disequality decompositions : 0
% 0.12/0.49 % Total rewrite steps : 68
% 0.12/0.49 % ...of those cached : 48
% 0.12/0.49 % Propositional unsat checks : 0
% 0.12/0.49 % Propositional check models : 0
% 0.12/0.49 % Propositional check unsatisfiable : 0
% 0.12/0.49 % Propositional clauses : 0
% 0.12/0.49 % Propositional clauses after purity: 0
% 0.12/0.49 % Propositional unsat core size : 0
% 0.12/0.49 % Propositional preprocessing time : 0.000
% 0.12/0.49 % Propositional encoding time : 0.000
% 0.12/0.49 % Propositional solver time : 0.000
% 0.12/0.49 % Success case prop preproc time : 0.000
% 0.12/0.49 % Success case prop encoding time : 0.000
% 0.12/0.49 % Success case prop solver time : 0.000
% 0.12/0.49 % Current number of processed clauses : 101
% 0.12/0.49 % Positive orientable unit clauses : 33
% 0.12/0.49 % Positive unorientable unit clauses: 1
% 0.12/0.49 % Negative unit clauses : 28
% 0.12/0.49 % Non-unit-clauses : 39
% 0.12/0.49 % Current number of unprocessed clauses: 160
% 0.12/0.49 % ...number of literals in the above : 414
% 0.12/0.49 % Current number of archived formulas : 0
% 0.12/0.49 % Current number of archived clauses : 72
% 0.12/0.49 % Clause-clause subsumption calls (NU) : 398
% 0.12/0.49 % Rec. Clause-clause subsumption calls : 316
% 0.12/0.49 % Non-unit clause-clause subsumptions : 35
% 0.12/0.49 % Unit Clause-clause subsumption calls : 661
% 0.12/0.49 % Rewrite failures with RHS unbound : 0
% 0.12/0.49 % BW rewrite match attempts : 37
% 0.12/0.49 % BW rewrite match successes : 28
% 0.12/0.49 % Condensation attempts : 0
% 0.12/0.49 % Condensation successes : 0
% 0.12/0.49 % Termbank termtop insertions : 6420
% 0.12/0.49 % Search garbage collected termcells : 531
% 0.12/0.49
% 0.12/0.49 % -------------------------------------------------
% 0.12/0.49 % User time : 0.015 s
% 0.12/0.49 % System time : 0.006 s
% 0.12/0.49 % Total time : 0.021 s
% 0.12/0.49 % Maximum resident set size: 3600 pages
% 0.12/0.49
% 0.12/0.49 % -------------------------------------------------
% 0.12/0.49 % User time : 0.072 s
% 0.12/0.49 % System time : 0.015 s
% 0.12/0.49 % Total time : 0.087 s
% 0.12/0.49 % Maximum resident set size: 4608 pages
% 0.12/0.49 % E exiting
%------------------------------------------------------------------------------