%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET916+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 : n014.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 02:15:45 PM UTC 2026
% Result : Theorem 2.15s 0.73s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 108 ( 34 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 140 ( 59 ~; 51 |; 26 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 4 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(t57_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( ~ disjoint(unordered_pair(X1,X3),X2)
& ~ in(X3,X2)
& ~ in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(c_0_4,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27] :
( ( X27 = set_intersection2(X25,X26)
| in(esk2_3(X25,X26,X27),X27)
| in(esk2_3(X25,X26,X27),X26) )
& ( X27 = set_intersection2(X25,X26)
| in(esk2_3(X25,X26,X27),X27)
| in(esk2_3(X25,X26,X27),X25) )
& ( X27 = set_intersection2(X25,X26)
| ~ in(esk2_3(X25,X26,X27),X26)
| ~ in(esk2_3(X25,X26,X27),X25)
| ~ in(esk2_3(X25,X26,X27),X27) )
& ( X22 != set_intersection2(X20,X21)
| in(X24,X22)
| ~ in(X24,X21)
| ~ in(X24,X20) )
& ( X22 != set_intersection2(X20,X21)
| ~ in(X23,X22)
| in(X23,X21) )
& ( X22 != set_intersection2(X20,X21)
| ~ in(X23,X22)
| in(X23,X20) ) ),
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)],[d3_xboole_0])])])])])])]) ).
fof(c_0_5,plain,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( X18 = unordered_pair(X16,X17)
| esk1_3(X16,X17,X18) = X17
| esk1_3(X16,X17,X18) = X16
| in(esk1_3(X16,X17,X18),X18) )
& ( X18 = unordered_pair(X16,X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| esk1_3(X16,X17,X18) != X17 )
& ( X18 = unordered_pair(X16,X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| esk1_3(X16,X17,X18) != X16 )
& ( X13 != unordered_pair(X11,X12)
| in(X15,X13)
| X15 != X12 )
& ( X13 != unordered_pair(X11,X12)
| in(X15,X13)
| X15 != X11 )
& ( X13 != unordered_pair(X11,X12)
| X14 = X12
| X14 = X11
| ~ in(X14,X13) ) ),
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_tarski])])])])])])]) ).
cnf(c_0_7,plain,
( X3 != set_intersection2(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X34,X35,X37,X38,X39] :
( ( ~ disjoint(X37,X38)
| ~ in(X39,set_intersection2(X37,X38)) )
& ( in(esk5_2(X34,X35),set_intersection2(X34,X35))
| disjoint(X34,X35) ) ),
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_5])])])])])]) ).
cnf(c_0_9,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( in(esk5_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ disjoint(unordered_pair(X1,X3),X2)
& ~ in(X3,X2)
& ~ in(X1,X2) ),
inference(assume_negation,[status(cth)],[t57_zfmisc_1]) ).
cnf(c_0_14,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( in(esk5_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ disjoint(unordered_pair(X1,X3),X2)
& ~ in(X3,X2)
& ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(esk5_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
( disjoint(unordered_pair(X1,X2),X3)
| esk5_2(unordered_pair(X1,X2),X3) = X1
| esk5_2(unordered_pair(X1,X2),X3) = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,negated_conjecture,
( ~ disjoint(unordered_pair(esk6_0,esk8_0),esk7_0)
& ~ in(esk8_0,esk7_0)
& ~ in(esk6_0,esk7_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_21,plain,
( in(X1,X3)
| disjoint(unordered_pair(X1,X2),X3)
| esk5_2(unordered_pair(X1,X2),X3) = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ disjoint(unordered_pair(esk6_0,esk8_0),esk7_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( in(X2,X3)
| in(X1,X3)
| disjoint(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ in(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk8_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:43:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 2.15/0.73 % Version: 3.5.1
% 2.15/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.15/0.73 % Starting new_bool_1 with 300s (1) cores
% 2.15/0.73 % Starting sh5l with 300s (1) cores
% 2.15/0.73 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3259775 completed with status 0
% 2.15/0.73 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.15/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.73 % No SInE strategy applied
% 2.15/0.73 % Search class: FGHSS-FFMF32-SFFFFFNN
% 2.15/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.73 % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.15/0.73 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 2.15/0.73 % Starting new_bool_3 with 248s (1) cores
% 2.15/0.73 % Starting new_bool_1 with 241s (1) cores
% 2.15/0.73 % new_bool_1 with pid 3259785 completed with status 0
% 2.15/0.73 % Result found by new_bool_1
% 2.15/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.15/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.73 % No SInE strategy applied
% 2.15/0.73 % Search class: FGHSS-FFMF32-SFFFFFNN
% 2.15/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.73 % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.15/0.73 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 2.15/0.73 % Starting new_bool_3 with 248s (1) cores
% 2.15/0.73 % Starting new_bool_1 with 241s (1) cores
% 2.15/0.73 % Preprocessing time : 0.001 s
% 2.15/0.73 % Presaturation interreduction done
% 2.15/0.73
% 2.15/0.73 % Proof found!
% 2.15/0.73 % SZS status Theorem
% 2.15/0.73 % SZS output start CNFRefutation
% See solution above
% 2.15/0.73 % Parsed axioms : 11
% 2.15/0.73 % Removed by relevancy pruning/SinE : 0
% 2.15/0.73 % Initial clauses : 24
% 2.15/0.73 % Removed in clause preprocessing : 0
% 2.15/0.73 % Initial clauses in saturation : 24
% 2.15/0.73 % Processed clauses : 2447
% 2.15/0.73 % ...of these trivial : 135
% 2.15/0.73 % ...subsumed : 1825
% 2.15/0.73 % ...remaining for further processing : 487
% 2.15/0.73 % Other redundant clauses eliminated : 34
% 2.15/0.73 % Clauses deleted for lack of memory : 0
% 2.15/0.73 % Backward-subsumed : 4
% 2.15/0.73 % Backward-rewritten : 12
% 2.15/0.73 % Generated clauses : 17719
% 2.15/0.73 % ...of the previous two non-redundant : 15620
% 2.15/0.73 % ...aggressively subsumed : 0
% 2.15/0.73 % Contextual simplify-reflections : 2
% 2.15/0.73 % Paramodulations : 17627
% 2.15/0.73 % Factorizations : 60
% 2.15/0.73 % NegExts : 0
% 2.15/0.73 % Equation resolutions : 34
% 2.15/0.73 % Disequality decompositions : 0
% 2.15/0.73 % Total rewrite steps : 3810
% 2.15/0.73 % ...of those cached : 3357
% 2.15/0.73 % Propositional unsat checks : 0
% 2.15/0.73 % Propositional check models : 0
% 2.15/0.73 % Propositional check unsatisfiable : 0
% 2.15/0.73 % Propositional clauses : 0
% 2.15/0.73 % Propositional clauses after purity: 0
% 2.15/0.73 % Propositional unsat core size : 0
% 2.15/0.73 % Propositional preprocessing time : 0.000
% 2.15/0.73 % Propositional encoding time : 0.000
% 2.15/0.73 % Propositional solver time : 0.000
% 2.15/0.73 % Success case prop preproc time : 0.000
% 2.15/0.73 % Success case prop encoding time : 0.000
% 2.15/0.73 % Success case prop solver time : 0.000
% 2.15/0.73 % Current number of processed clauses : 441
% 2.15/0.73 % Positive orientable unit clauses : 64
% 2.15/0.73 % Positive unorientable unit clauses: 3
% 2.15/0.73 % Negative unit clauses : 61
% 2.15/0.73 % Non-unit-clauses : 313
% 2.15/0.73 % Current number of unprocessed clauses: 13189
% 2.15/0.73 % ...number of literals in the above : 36941
% 2.15/0.73 % Current number of archived formulas : 0
% 2.15/0.73 % Current number of archived clauses : 40
% 2.15/0.73 % Clause-clause subsumption calls (NU) : 21408
% 2.15/0.73 % Rec. Clause-clause subsumption calls : 16864
% 2.15/0.73 % Non-unit clause-clause subsumptions : 931
% 2.15/0.73 % Unit Clause-clause subsumption calls : 1144
% 2.15/0.73 % Rewrite failures with RHS unbound : 28
% 2.15/0.73 % BW rewrite match attempts : 739
% 2.15/0.73 % BW rewrite match successes : 30
% 2.15/0.73 % Condensation attempts : 0
% 2.15/0.73 % Condensation successes : 0
% 2.15/0.73 % Termbank termtop insertions : 262212
% 2.15/0.73 % Search garbage collected termcells : 416
% 2.15/0.73
% 2.15/0.73 % -------------------------------------------------
% 2.15/0.73 % User time : 0.279 s
% 2.15/0.73 % System time : 0.024 s
% 2.15/0.73 % Total time : 0.303 s
% 2.15/0.73 % Maximum resident set size: 3640 pages
% 2.15/0.73
% 2.15/0.73 % -------------------------------------------------
% 2.15/0.73 % User time : 1.278 s
% 2.15/0.73 % System time : 0.078 s
% 2.15/0.73 % Total time : 1.356 s
% 2.15/0.73 % Maximum resident set size: 4864 pages
% 2.15/0.73 % E exiting
%------------------------------------------------------------------------------