%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:19:02 PM UTC 2026
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 123 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 50 ~; 61 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 73 ( 15 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t134_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( ( X2 = X4
& X1 = X3 )
| X2 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X2,X4)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( ( X2 = X4
& X1 = X3 )
| X2 = empty_set
| X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_6,plain,
! [X15,X16,X17,X18] :
( ( in(ordered_pair(X15,X16),cartesian_product2(X17,X18))
| ~ in(X16,X18)
| ~ in(X15,X17) )
& ( ~ in(ordered_pair(X15,X16),cartesian_product2(X17,X18))
| in(X16,X18) )
& ( ~ in(ordered_pair(X15,X16),cartesian_product2(X17,X18))
| in(X15,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])])]) ).
fof(c_0_7,negated_conjecture,
( ( esk2_0 != esk4_0
| esk1_0 != esk3_0 )
& esk2_0 != empty_set
& esk1_0 != empty_set
& cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0) ),
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_8,plain,
! [X9,X10,X11] :
( ( X11 = empty_set
| in(esk5_1(X11),X11) )
& ( ~ in(X10,X9)
| X9 != empty_set ) ),
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,
( ~ in(X3,X4)
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X21,X22] :
( ( X21 = X22
| in(esk6_2(X21,X22),X22)
| in(esk6_2(X21,X22),X21) )
& ( X21 = X22
| ~ in(esk6_2(X21,X22),X22)
| ~ in(esk6_2(X21,X22),X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).
cnf(c_0_13,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(X1,esk3_0)
| ~ in(X2,esk4_0)
| in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X2
| in(esk6_2(X1,X2),X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk3_0)
| ~ in(X2,esk4_0)
| in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( in(esk6_2(empty_set,X1),X1)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,esk3_0)
| in(X1,esk1_0)
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( in(esk6_2(esk3_0,X1),X1)
| in(esk6_2(esk3_0,X1),esk1_0)
| esk3_0 = X1
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(ordered_pair(X2,X1),cartesian_product2(esk1_0,esk2_0))
| in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_24,plain,
( ~ in(esk6_2(X1,X2),X2)
| ~ in(esk6_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( in(esk6_2(esk3_0,esk1_0),esk1_0)
| esk4_0 = empty_set
| esk3_0 = esk1_0 ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,esk1_0)
| ~ in(X2,esk2_0)
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_27,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(X2,esk1_0)
| ~ in(X1,esk2_0)
| in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_29,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk6_2(esk3_0,esk1_0),esk3_0)
| esk3_0 = esk1_0
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(X1,esk1_0)
| in(X1,esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(X1,esk2_0)
| in(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( ~ in(X2,esk3_0)
| ~ in(X1,esk4_0)
| in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( ~ in(X1,esk2_0)
| esk3_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(X2,esk3_0)
| in(esk6_2(X1,esk4_0),X1)
| in(esk6_2(X1,esk4_0),esk2_0)
| X1 = esk4_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_37,negated_conjecture,
esk3_0 = esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_27]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(X2,esk1_0)
| in(esk6_2(X1,esk4_0),X1)
| in(esk6_2(X1,esk4_0),esk2_0)
| X1 = esk4_0 ),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( esk2_0 != esk4_0
| esk1_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( in(esk6_2(X1,esk4_0),X1)
| in(esk6_2(X1,esk4_0),esk2_0)
| X1 = esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_18]),c_0_29]) ).
cnf(c_0_41,negated_conjecture,
esk4_0 != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(esk6_2(X1,esk4_0),X1)
| ~ in(esk6_2(X1,esk4_0),esk2_0)
| X1 = esk4_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_43,negated_conjecture,
in(esk6_2(esk2_0,esk4_0),esk2_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_43])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 05:46:48 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 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
% 0.19/0.53 % Version: 3.5.1
% 0.19/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 % Starting sh5l with 300s (1) cores
% 0.19/0.53 % sh5l with pid 2133207 completed with status 0
% 0.19/0.53 % Result found by sh5l
% 0.19/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 % Starting sh5l with 300s (1) cores
% 0.19/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.19/0.53 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.53 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.19/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.53 % SubtermCWHack with pid 2133209 completed with status 0
% 0.19/0.53 % Result found by SubtermCWHack
% 0.19/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 % Starting sh5l with 300s (1) cores
% 0.19/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.19/0.53 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.53 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.19/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.53 % Preprocessing time : 0.002 s
% 0.19/0.53
% 0.19/0.53 % Proof found!
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 % SZS output start CNFRefutation
% See solution above
% 0.39/0.53 % Parsed axioms : 12
% 0.39/0.53 % Removed by relevancy pruning/SinE : 0
% 0.39/0.53 % Initial clauses : 21
% 0.39/0.53 % Removed in clause preprocessing : 0
% 0.39/0.53 % Initial clauses in saturation : 21
% 0.39/0.53 % Processed clauses : 182
% 0.39/0.53 % ...of these trivial : 24
% 0.39/0.53 % ...subsumed : 43
% 0.39/0.53 % ...remaining for further processing : 115
% 0.39/0.53 % Other redundant clauses eliminated : 3
% 0.39/0.53 % Clauses deleted for lack of memory : 0
% 0.39/0.53 % Backward-subsumed : 21
% 0.39/0.53 % Backward-rewritten : 28
% 0.39/0.53 % Generated clauses : 358
% 0.39/0.53 % ...of the previous two non-redundant : 339
% 0.39/0.53 % ...aggressively subsumed : 0
% 0.39/0.53 % Contextual simplify-reflections : 1
% 0.39/0.53 % Paramodulations : 349
% 0.39/0.53 % Factorizations : 6
% 0.39/0.53 % NegExts : 0
% 0.39/0.53 % Equation resolutions : 3
% 0.39/0.53 % Disequality decompositions : 0
% 0.39/0.53 % Total rewrite steps : 103
% 0.39/0.53 % ...of those cached : 73
% 0.39/0.53 % Propositional unsat checks : 0
% 0.39/0.53 % Propositional check models : 0
% 0.39/0.53 % Propositional check unsatisfiable : 0
% 0.39/0.53 % Propositional clauses : 0
% 0.39/0.53 % Propositional clauses after purity: 0
% 0.39/0.53 % Propositional unsat core size : 0
% 0.39/0.53 % Propositional preprocessing time : 0.000
% 0.39/0.53 % Propositional encoding time : 0.000
% 0.39/0.53 % Propositional solver time : 0.000
% 0.39/0.53 % Success case prop preproc time : 0.000
% 0.39/0.53 % Success case prop encoding time : 0.000
% 0.39/0.53 % Success case prop solver time : 0.000
% 0.39/0.53 % Current number of processed clauses : 63
% 0.39/0.53 % Positive orientable unit clauses : 20
% 0.39/0.53 % Positive unorientable unit clauses: 1
% 0.39/0.53 % Negative unit clauses : 11
% 0.39/0.53 % Non-unit-clauses : 31
% 0.39/0.53 % Current number of unprocessed clauses: 90
% 0.39/0.53 % ...number of literals in the above : 161
% 0.39/0.53 % Current number of archived formulas : 0
% 0.39/0.53 % Current number of archived clauses : 49
% 0.39/0.53 % Clause-clause subsumption calls (NU) : 952
% 0.39/0.53 % Rec. Clause-clause subsumption calls : 731
% 0.39/0.53 % Non-unit clause-clause subsumptions : 50
% 0.39/0.53 % Unit Clause-clause subsumption calls : 73
% 0.39/0.53 % Rewrite failures with RHS unbound : 0
% 0.39/0.53 % BW rewrite match attempts : 4
% 0.39/0.53 % BW rewrite match successes : 1
% 0.39/0.53 % Condensation attempts : 0
% 0.39/0.53 % Condensation successes : 0
% 0.39/0.53 % Termbank termtop insertions : 5791
% 0.39/0.53 % Search garbage collected termcells : 249
% 0.39/0.53
% 0.39/0.53 % -------------------------------------------------
% 0.39/0.53 % User time : 0.024 s
% 0.39/0.53 % System time : 0.003 s
% 0.39/0.53 % Total time : 0.027 s
% 0.39/0.53 % Maximum resident set size: 3588 pages
% 0.39/0.53
% 0.39/0.53 % -------------------------------------------------
% 0.39/0.53 % User time : 0.027 s
% 0.39/0.53 % System time : 0.009 s
% 0.39/0.53 % Total time : 0.036 s
% 0.39/0.53 % Maximum resident set size: 4608 pages
% 0.39/0.53 % E exiting
%------------------------------------------------------------------------------