%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET894+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 : 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 02:15:42 PM UTC 2026
% Result : Theorem 11.73s 7.00s
% Output : CNFRefutation 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 125 ( 76 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 131 ( 44 ~; 71 |; 12 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 110 ( 0 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(X6,X2)
& in(X5,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t35_zfmisc_1,conjecture,
! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X16 = singleton(X15)
| esk1_2(X15,X16) = X15
| in(esk1_2(X15,X16),X16) )
& ( X16 = singleton(X15)
| esk1_2(X15,X16) != X15
| ~ in(esk1_2(X15,X16),X16) )
& ( X12 != singleton(X11)
| in(X14,X12)
| X14 != X11 )
& ( X12 != singleton(X11)
| X13 = X11
| ~ in(X13,X12) ) ),
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_6,plain,
! [X18,X19,X20,X21,X24,X25,X26,X27,X28,X29,X31,X32] :
( ( X29 = cartesian_product2(X27,X28)
| in(esk4_3(X27,X28,X29),X29)
| esk4_3(X27,X28,X29) = ordered_pair(esk5_3(X27,X28,X29),esk6_3(X27,X28,X29)) )
& ( X29 = cartesian_product2(X27,X28)
| in(esk4_3(X27,X28,X29),X29)
| in(esk6_3(X27,X28,X29),X28) )
& ( X29 = cartesian_product2(X27,X28)
| in(esk4_3(X27,X28,X29),X29)
| in(esk5_3(X27,X28,X29),X27) )
& ( X29 = cartesian_product2(X27,X28)
| esk4_3(X27,X28,X29) != ordered_pair(X31,X32)
| ~ in(X32,X28)
| ~ in(X31,X27)
| ~ in(esk4_3(X27,X28,X29),X29) )
& ( X20 != cartesian_product2(X18,X19)
| in(X24,X20)
| X24 != ordered_pair(X25,X26)
| ~ in(X26,X19)
| ~ in(X25,X18) )
& ( X20 != cartesian_product2(X18,X19)
| ~ in(X21,X20)
| X21 = ordered_pair(esk2_4(X18,X19,X20,X21),esk3_4(X18,X19,X20,X21)) )
& ( X20 != cartesian_product2(X18,X19)
| ~ in(X21,X20)
| in(esk3_4(X18,X19,X20,X21),X19) )
& ( X20 != cartesian_product2(X18,X19)
| ~ in(X21,X20)
| in(esk2_4(X18,X19,X20,X21),X18) ) ),
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_zfmisc_1])])])])])])]) ).
fof(c_0_7,plain,
! [X35,X36] : ordered_pair(X35,X36) = unordered_pair(unordered_pair(X35,X36),singleton(X35)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X3 = cartesian_product2(X1,X2)
| in(esk4_3(X1,X2,X3),X3)
| esk4_3(X1,X2,X3) = ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X3 = cartesian_product2(X1,X2)
| in(esk4_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( in(esk4_3(X1,X2,X3),X3)
| esk4_3(X1,X2,X3) = unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),singleton(esk5_3(X1,X2,X3)))
| X3 = cartesian_product2(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(esk5_3(X1,X2,singleton(X3)),X1)
| singleton(X3) = cartesian_product2(X1,X2)
| esk4_3(X1,X2,singleton(X3)) = X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( X3 = cartesian_product2(X1,X2)
| in(esk4_3(X1,X2,X3),X3)
| in(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( in(esk4_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2)
| unordered_pair(singleton(esk5_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3))) = esk4_3(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( singleton(X3) = cartesian_product2(singleton(X1),X2)
| esk5_3(singleton(X1),X2,singleton(X3)) = X1
| esk4_3(singleton(X1),X2,singleton(X3)) = X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_20,plain,
( in(esk6_3(X1,X2,singleton(X3)),X2)
| singleton(X3) = cartesian_product2(X1,X2)
| esk4_3(X1,X2,singleton(X3)) = X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_21,plain,
( esk4_3(X1,X2,X3) != ordered_pair(X4,X5)
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk4_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( singleton(X3) = cartesian_product2(singleton(X1),X2)
| esk4_3(singleton(X1),X2,singleton(X3)) = X3
| unordered_pair(singleton(X1),unordered_pair(X1,esk6_3(singleton(X1),X2,singleton(X3)))) = esk4_3(singleton(X1),X2,singleton(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]) ).
cnf(c_0_23,plain,
( singleton(X3) = cartesian_product2(X1,singleton(X2))
| esk6_3(X1,singleton(X2),singleton(X3)) = X2
| esk4_3(X1,singleton(X2),singleton(X3)) = X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_24,plain,
( ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk4_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| X3 = cartesian_product2(X1,X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_25,plain,
( singleton(X3) = cartesian_product2(singleton(X1),singleton(X2))
| esk4_3(singleton(X1),singleton(X2),singleton(X3)) = X3
| unordered_pair(singleton(X1),unordered_pair(X1,X2)) = esk4_3(singleton(X1),singleton(X2),singleton(X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[t35_zfmisc_1]) ).
cnf(c_0_28,plain,
( ~ in(X4,X2)
| ~ in(X5,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| esk4_3(X2,X3,X1) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| X1 = cartesian_product2(X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_29,plain,
( singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2))
| esk4_3(singleton(X1),singleton(X2),singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))) = unordered_pair(singleton(X1),unordered_pair(X1,X2)) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_25])]) ).
cnf(c_0_30,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
fof(c_0_31,negated_conjecture,
cartesian_product2(singleton(esk10_0),singleton(esk11_0)) != singleton(ordered_pair(esk10_0,esk11_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_32,plain,
( ~ in(X3,singleton(X1))
| ~ in(X4,singleton(X2))
| unordered_pair(singleton(X1),unordered_pair(X1,X2)) != unordered_pair(singleton(X3),unordered_pair(X3,X4))
| singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
cartesian_product2(singleton(esk10_0),singleton(esk11_0)) != singleton(ordered_pair(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_34,plain,
singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_30]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
cartesian_product2(singleton(esk10_0),singleton(esk11_0)) != singleton(unordered_pair(unordered_pair(esk10_0,esk11_0),singleton(esk10_0))),
inference(rw,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_36,plain,
singleton(unordered_pair(unordered_pair(X1,X2),singleton(X1))) = cartesian_product2(singleton(X1),singleton(X2)),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.38 % Computer : n015.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 05:46:41 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 11.73/7.00 % Version: 3.5.1
% 11.73/7.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 11.73/7.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.73/7.00 % Starting new_bool_3 with 300s (1) cores
% 11.73/7.00 % Starting new_bool_1 with 300s (1) cores
% 11.73/7.00 % Starting sh5l with 300s (1) cores
% 11.73/7.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 685418 completed with status 0
% 11.73/7.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 11.73/7.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 11.73/7.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.73/7.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.73/7.00 % No SInE strategy applied
% 11.73/7.00 % Search class: FGHSF-FFMF32-MFFFFFNN
% 11.73/7.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.73/7.00 % Starting SubtermCWHack with 136s (1) cores
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 11.73/7.00 % Starting new_bool_3 with 136s (1) cores
% 11.73/7.00 % Starting new_bool_1 with 136s (1) cores
% 11.73/7.00 % new_bool_3 with pid 685428 completed with status 0
% 11.73/7.00 % Result found by new_bool_3
% 11.73/7.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 11.73/7.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.73/7.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.73/7.00 % No SInE strategy applied
% 11.73/7.00 % Search class: FGHSF-FFMF32-MFFFFFNN
% 11.73/7.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.73/7.00 % Starting SubtermCWHack with 136s (1) cores
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 11.73/7.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 11.73/7.00 % Starting new_bool_3 with 136s (1) cores
% 11.73/7.00 % Preprocessing time : 0.002 s
% 11.73/7.00 % Presaturation interreduction done
% 11.73/7.00
% 11.73/7.00 % Proof found!
% 11.73/7.00 % SZS status Theorem
% 11.73/7.00 % SZS output start CNFRefutation
% See solution above
% 11.73/7.00 % Parsed axioms : 11
% 11.73/7.00 % Removed by relevancy pruning/SinE : 0
% 11.73/7.00 % Initial clauses : 24
% 11.73/7.00 % Removed in clause preprocessing : 1
% 11.73/7.00 % Initial clauses in saturation : 23
% 11.73/7.00 % Processed clauses : 3435
% 11.73/7.00 % ...of these trivial : 199
% 11.73/7.00 % ...subsumed : 2330
% 11.73/7.00 % ...remaining for further processing : 906
% 11.73/7.00 % Other redundant clauses eliminated : 20
% 11.73/7.00 % Clauses deleted for lack of memory : 0
% 11.73/7.00 % Backward-subsumed : 0
% 11.73/7.00 % Backward-rewritten : 15
% 11.73/7.00 % Generated clauses : 58317
% 11.73/7.00 % ...of the previous two non-redundant : 52065
% 11.73/7.00 % ...aggressively subsumed : 0
% 11.73/7.00 % Contextual simplify-reflections : 2
% 11.73/7.00 % Paramodulations : 58286
% 11.73/7.00 % Factorizations : 12
% 11.73/7.00 % NegExts : 0
% 11.73/7.00 % Equation resolutions : 21
% 11.73/7.00 % Disequality decompositions : 0
% 11.73/7.00 % Total rewrite steps : 6539
% 11.73/7.00 % ...of those cached : 6176
% 11.73/7.00 % Propositional unsat checks : 0
% 11.73/7.00 % Propositional check models : 0
% 11.73/7.00 % Propositional check unsatisfiable : 0
% 11.73/7.00 % Propositional clauses : 0
% 11.73/7.00 % Propositional clauses after purity: 0
% 11.73/7.00 % Propositional unsat core size : 0
% 11.73/7.00 % Propositional preprocessing time : 0.000
% 11.73/7.00 % Propositional encoding time : 0.000
% 11.73/7.00 % Propositional solver time : 0.000
% 11.73/7.00 % Success case prop preproc time : 0.000
% 11.73/7.00 % Success case prop encoding time : 0.000
% 11.73/7.00 % Success case prop solver time : 0.000
% 11.73/7.00 % Current number of processed clauses : 863
% 11.73/7.00 % Positive orientable unit clauses : 81
% 11.73/7.00 % Positive unorientable unit clauses: 1
% 11.73/7.00 % Negative unit clauses : 100
% 11.73/7.00 % Non-unit-clauses : 681
% 11.73/7.00 % Current number of unprocessed clauses: 48665
% 11.73/7.00 % ...number of literals in the above : 172220
% 11.73/7.00 % Current number of archived formulas : 0
% 11.73/7.00 % Current number of archived clauses : 38
% 11.73/7.00 % Clause-clause subsumption calls (NU) : 68470
% 11.73/7.00 % Rec. Clause-clause subsumption calls : 45731
% 11.73/7.00 % Non-unit clause-clause subsumptions : 887
% 11.73/7.00 % Unit Clause-clause subsumption calls : 3326
% 11.73/7.00 % Rewrite failures with RHS unbound : 0
% 11.73/7.00 % BW rewrite match attempts : 595
% 11.73/7.00 % BW rewrite match successes : 19
% 11.73/7.00 % Condensation attempts : 0
% 11.73/7.00 % Condensation successes : 0
% 11.73/7.00 % Termbank termtop insertions : 2394708
% 11.73/7.00 % Search garbage collected termcells : 481
% 11.73/7.00
% 11.73/7.00 % -------------------------------------------------
% 11.73/7.00 % User time : 1.454 s
% 11.73/7.00 % System time : 0.065 s
% 11.73/7.00 % Total time : 1.519 s
% 11.73/7.00 % Maximum resident set size: 3336 pages
% 11.73/7.00
% 11.73/7.00 % -------------------------------------------------
% 11.73/7.00 % User time : 7.270 s
% 11.73/7.00 % System time : 0.302 s
% 11.73/7.00 % Total time : 7.571 s
% 11.73/7.00 % Maximum resident set size: 4608 pages
% 11.73/7.00 % E exiting
%------------------------------------------------------------------------------