%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET919+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 : n008.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 218.77s 32.19s
% Output : CNFRefutation 218.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 140 ( 72 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 159 ( 59 ~; 72 |; 19 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 6 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t60_zfmisc_1,conjecture,
! [X1,X2,X3] :
( in(X1,X2)
=> ( set_intersection2(unordered_pair(X1,X3),X2) = singleton(X1)
| ( X1 != X3
& in(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
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/sandbox2/benchmark/theBenchmark.p',d3_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(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,X2)
=> ( set_intersection2(unordered_pair(X1,X3),X2) = singleton(X1)
| ( X1 != X3
& in(X3,X2) ) ) ),
inference(assume_negation,[status(cth)],[t60_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,X2)
=> ( set_intersection2(unordered_pair(X1,X3),X2) = singleton(X1)
| ( X1 != X3
& in(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
( set_intersection2(unordered_pair(esk1_0,esk3_0),esk2_0) != singleton(esk1_0)
& ( esk1_0 = esk3_0
| ~ in(esk3_0,esk2_0) )
& in(esk1_0,esk2_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_8,plain,
! [X15,X16] : set_intersection2(X15,X16) = set_intersection2(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_9,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( X24 = set_intersection2(X22,X23)
| in(esk5_3(X22,X23,X24),X24)
| in(esk5_3(X22,X23,X24),X23) )
& ( X24 = set_intersection2(X22,X23)
| in(esk5_3(X22,X23,X24),X24)
| in(esk5_3(X22,X23,X24),X22) )
& ( X24 = set_intersection2(X22,X23)
| ~ in(esk5_3(X22,X23,X24),X23)
| ~ in(esk5_3(X22,X23,X24),X22)
| ~ in(esk5_3(X22,X23,X24),X24) )
& ( X19 != set_intersection2(X17,X18)
| in(X21,X19)
| ~ in(X21,X18)
| ~ in(X21,X17) )
& ( X19 != set_intersection2(X17,X18)
| ~ in(X20,X19)
| in(X20,X18) )
& ( X19 != set_intersection2(X17,X18)
| ~ in(X20,X19)
| in(X20,X17) ) ),
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])])])])])])]) ).
cnf(c_0_10,negated_conjecture,
set_intersection2(unordered_pair(esk1_0,esk3_0),esk2_0) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( X13 = singleton(X12)
| esk4_2(X12,X13) = X12
| in(esk4_2(X12,X13),X13) )
& ( X13 = singleton(X12)
| esk4_2(X12,X13) != X12
| ~ in(esk4_2(X12,X13),X13) )
& ( X9 != singleton(X8)
| in(X11,X9)
| X11 != X8 )
& ( X9 != singleton(X8)
| X10 = X8
| ~ in(X10,X9) ) ),
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])])])])])])]) ).
fof(c_0_13,plain,
! [X29,X30,X31,X32,X33,X34,X35,X36] :
( ( X36 = unordered_pair(X34,X35)
| esk6_3(X34,X35,X36) = X35
| esk6_3(X34,X35,X36) = X34
| in(esk6_3(X34,X35,X36),X36) )
& ( X36 = unordered_pair(X34,X35)
| ~ in(esk6_3(X34,X35,X36),X36)
| esk6_3(X34,X35,X36) != X35 )
& ( X36 = unordered_pair(X34,X35)
| ~ in(esk6_3(X34,X35,X36),X36)
| esk6_3(X34,X35,X36) != X34 )
& ( X31 != unordered_pair(X29,X30)
| in(X33,X31)
| X33 != X30 )
& ( X31 != unordered_pair(X29,X30)
| in(X33,X31)
| X33 != X29 )
& ( X31 != unordered_pair(X29,X30)
| X32 = X30
| X32 = X29
| ~ in(X32,X31) ) ),
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_14,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
singleton(esk1_0) != set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X2 = singleton(X1)
| esk4_2(X1,X2) = X1
| in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( in(esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))),set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0)))
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_20,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( in(esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))),unordered_pair(esk1_0,esk3_0))
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk3_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( X3 != set_intersection2(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( esk4_2(X1,X2) != X1
| ~ in(esk4_2(X1,X2),X2)
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( esk3_0 != esk1_0
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0 ),
inference(ef,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0)))
| esk3_0 != esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]) ).
cnf(c_0_30,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
in(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
( in(esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))),esk2_0)
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,negated_conjecture,
esk3_0 != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
( in(esk3_0,esk2_0)
| esk4_2(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0))) = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(esk1_0,set_intersection2(esk2_0,unordered_pair(esk1_0,esk3_0)))
| in(esk3_0,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_15]) ).
cnf(c_0_37,negated_conjecture,
( ~ in(esk3_0,esk2_0)
| esk1_0 = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_38,negated_conjecture,
in(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:44:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 218.77/32.19 % Version: 3.5.1
% 218.77/32.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 218.77/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.77/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.77/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.77/32.19 % Starting new_bool_1 with 300s (1) cores
% 218.77/32.19 % Starting sh5l with 300s (1) cores
% 218.77/32.19 % new_bool_3 with pid 267646 completed with status 0
% 218.77/32.19 % Result found by new_bool_3
% 218.77/32.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 218.77/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.77/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.77/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.77/32.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.77/32.19 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.77/32.19 % Search class: FGHSS-FFMF32-SFFFFFNN
% 218.77/32.19 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 218.77/32.19 % Starting SubtermCWHack with 31s (1) cores
% 218.77/32.19 % SubtermCWHack with pid 267655 completed with status 8
% 218.77/32.19 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 114s (1) cores
% 218.77/32.19 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 268588 completed with status 0
% 218.77/32.19 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 218.77/32.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 218.77/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.77/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.77/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.77/32.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.77/32.19 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.77/32.19 % Search class: FGHSS-FFMF32-SFFFFFNN
% 218.77/32.19 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 218.77/32.19 % Starting SubtermCWHack with 31s (1) cores
% 218.77/32.19 % SubtermCWHack with pid 267655 completed with status 8
% 218.77/32.19 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 114s (1) cores
% 218.77/32.19 % Preprocessing time : 0.001 s
% 218.77/32.19 % Presaturation interreduction done
% 218.77/32.19
% 218.77/32.19 % Proof found!
% 218.77/32.19 % SZS status Theorem
% 218.77/32.19 % SZS output start CNFRefutation
% See solution above
% 218.77/32.19 % Parsed axioms : 10
% 218.77/32.19 % Removed by relevancy pruning/SinE : 2
% 218.77/32.19 % Initial clauses : 23
% 218.77/32.19 % Removed in clause preprocessing : 0
% 218.77/32.19 % Initial clauses in saturation : 23
% 218.77/32.19 % Processed clauses : 91
% 218.77/32.19 % ...of these trivial : 0
% 218.77/32.19 % ...subsumed : 19
% 218.77/32.19 % ...remaining for further processing : 72
% 218.77/32.19 % Other redundant clauses eliminated : 12
% 218.77/32.19 % Clauses deleted for lack of memory : 0
% 218.77/32.19 % Backward-subsumed : 2
% 218.77/32.19 % Backward-rewritten : 4
% 218.77/32.19 % Generated clauses : 108
% 218.77/32.19 % ...of the previous two non-redundant : 93
% 218.77/32.19 % ...aggressively subsumed : 0
% 218.77/32.19 % Contextual simplify-reflections : 0
% 218.77/32.19 % Paramodulations : 98
% 218.77/32.19 % Factorizations : 1
% 218.77/32.19 % NegExts : 0
% 218.77/32.19 % Equation resolutions : 12
% 218.77/32.19 % Disequality decompositions : 0
% 218.77/32.19 % Total rewrite steps : 18
% 218.77/32.19 % ...of those cached : 9
% 218.77/32.19 % Propositional unsat checks : 0
% 218.77/32.19 % Propositional check models : 0
% 218.77/32.19 % Propositional check unsatisfiable : 0
% 218.77/32.19 % Propositional clauses : 0
% 218.77/32.19 % Propositional clauses after purity: 0
% 218.77/32.19 % Propositional unsat core size : 0
% 218.77/32.19 % Propositional preprocessing time : 0.000
% 218.77/32.19 % Propositional encoding time : 0.000
% 218.77/32.19 % Propositional solver time : 0.000
% 218.77/32.19 % Success case prop preproc time : 0.000
% 218.77/32.19 % Success case prop encoding time : 0.000
% 218.77/32.19 % Success case prop solver time : 0.000
% 218.77/32.19 % Current number of processed clauses : 35
% 218.77/32.19 % Positive orientable unit clauses : 6
% 218.77/32.19 % Positive unorientable unit clauses: 2
% 218.77/32.19 % Negative unit clauses : 6
% 218.77/32.19 % Non-unit-clauses : 21
% 218.77/32.19 % Current number of unprocessed clauses: 48
% 218.77/32.19 % ...number of literals in the above : 153
% 218.77/32.19 % Current number of archived formulas : 0
% 218.77/32.19 % Current number of archived clauses : 29
% 218.77/32.19 % Clause-clause subsumption calls (NU) : 266
% 218.77/32.19 % Rec. Clause-clause subsumption calls : 248
% 218.77/32.19 % Non-unit clause-clause subsumptions : 12
% 218.77/32.19 % Unit Clause-clause subsumption calls : 18
% 218.77/32.19 % Rewrite failures with RHS unbound : 0
% 218.77/32.19 % BW rewrite match attempts : 27
% 218.77/32.19 % BW rewrite match successes : 23
% 218.77/32.19 % Condensation attempts : 0
% 218.77/32.19 % Condensation successes : 0
% 218.77/32.19 % Termbank termtop insertions : 2678
% 218.77/32.19 % Search garbage collected termcells : 506
% 218.77/32.19
% 218.77/32.19 % -------------------------------------------------
% 218.77/32.19 % User time : 30.013 s
% 218.77/32.19 % System time : 1.118 s
% 218.77/32.19 % Total time : 31.130 s
% 218.77/32.19 % Maximum resident set size: 3636 pages
% 218.77/32.19
% 218.77/32.19 % -------------------------------------------------
% 218.77/32.19 % User time : 30.014 s
% 218.77/32.19 % System time : 1.124 s
% 218.77/32.19 % Total time : 31.138 s
% 218.77/32.19 % Maximum resident set size: 4608 pages
% 218.77/32.19 % E exiting
%------------------------------------------------------------------------------