%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:15:53 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 12 unt; 0 def)
% Number of atoms : 131 ( 48 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 54 ~; 63 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 17 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,plain,
! [X17,X18,X19,X20] :
( ( in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| ~ in(X18,X20)
| ~ in(X17,X19) )
& ( ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| in(X18,X20) )
& ( ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| in(X17,X19) ) ),
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_6,plain,
! [X13,X14] : ordered_pair(X13,X14) = unordered_pair(unordered_pair(X13,X14),singleton(X13)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,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_8,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
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_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ( esk5_0 != esk7_0
| esk4_0 != esk6_0 )
& esk5_0 != empty_set
& esk4_0 != empty_set
& cartesian_product2(esk4_0,esk5_0) = cartesian_product2(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_7])])])]) ).
fof(c_0_12,plain,
! [X9,X10,X11] :
( ( X11 = empty_set
| in(esk1_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_8])])])])])]) ).
cnf(c_0_13,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( ~ in(X1,X2)
| ~ in(X3,X4)
| in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X29,X30] :
( ( X29 = X30
| in(esk8_2(X29,X30),X30)
| in(esk8_2(X29,X30),X29) )
& ( X29 = X30
| ~ in(esk8_2(X29,X30),X30)
| ~ in(esk8_2(X29,X30),X29) ) ),
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_18,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X2,esk7_0)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( X1 = X2
| in(esk8_2(X1,X2),X2)
| in(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0))
| in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X2,esk7_0)
| in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( in(esk8_2(empty_set,X1),X1)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(X1,esk4_0)
| ~ in(X2,esk5_0)
| in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_28,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(X1,esk6_0)
| in(X1,esk4_0)
| esk7_0 = empty_set ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk5_0))
| in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_31,plain,
( ~ in(esk8_2(X1,X2),X2)
| ~ in(esk8_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(X1,esk4_0)
| in(X1,esk6_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( in(esk8_2(X1,esk6_0),X1)
| in(esk8_2(X1,esk6_0),esk4_0)
| X1 = esk6_0
| esk7_0 = empty_set ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
( ~ in(X2,esk4_0)
| ~ in(X1,esk5_0)
| in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(esk8_2(X1,esk6_0),X1)
| ~ in(esk8_2(X1,esk6_0),esk4_0)
| X1 = esk6_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( in(esk8_2(esk4_0,esk6_0),esk4_0)
| esk7_0 = empty_set
| esk6_0 = esk4_0 ),
inference(ef,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(X1,esk5_0)
| in(X1,esk7_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( esk6_0 = esk4_0
| esk7_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(X2,esk6_0)
| ~ in(X1,esk7_0)
| in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_41,negated_conjecture,
( ~ in(X1,esk5_0)
| esk6_0 = esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(X2,esk6_0)
| in(esk8_2(esk7_0,X1),X1)
| in(esk8_2(esk7_0,X1),esk5_0)
| esk7_0 = X1 ),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_43,negated_conjecture,
esk6_0 = esk4_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_25]),c_0_28]) ).
cnf(c_0_44,negated_conjecture,
( ~ in(X2,esk4_0)
| in(esk8_2(esk7_0,X1),X1)
| in(esk8_2(esk7_0,X1),esk5_0)
| esk7_0 = X1 ),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( esk5_0 != esk7_0
| esk4_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_46,negated_conjecture,
( in(esk8_2(esk7_0,X1),X1)
| in(esk8_2(esk7_0,X1),esk5_0)
| esk7_0 = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_25]),c_0_35]) ).
cnf(c_0_47,negated_conjecture,
esk7_0 != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_43])]) ).
cnf(c_0_48,negated_conjecture,
in(esk8_2(esk7_0,esk5_0),esk5_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_46]),c_0_47]) ).
cnf(c_0_49,negated_conjecture,
~ in(esk8_2(esk7_0,esk5_0),esk7_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_48]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:47:30 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3537611 completed with status 0
% 0.13/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.43 % SubtermCWHack with pid 3537615 completed with status 0
% 0.13/0.43 % Result found by SubtermCWHack
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 12
% 0.13/0.43 % Removed by relevancy pruning/SinE : 0
% 0.13/0.43 % Initial clauses : 21
% 0.13/0.43 % Removed in clause preprocessing : 1
% 0.13/0.43 % Initial clauses in saturation : 20
% 0.13/0.43 % Processed clauses : 321
% 0.13/0.43 % ...of these trivial : 1
% 0.13/0.43 % ...subsumed : 188
% 0.13/0.43 % ...remaining for further processing : 132
% 0.13/0.43 % Other redundant clauses eliminated : 3
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 23
% 0.13/0.43 % Backward-rewritten : 34
% 0.13/0.43 % Generated clauses : 479
% 0.13/0.43 % ...of the previous two non-redundant : 464
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 1
% 0.13/0.43 % Paramodulations : 468
% 0.13/0.43 % Factorizations : 8
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 3
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 49
% 0.13/0.43 % ...of those cached : 46
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 72
% 0.13/0.43 % Positive orientable unit clauses : 10
% 0.13/0.43 % Positive unorientable unit clauses: 1
% 0.13/0.43 % Negative unit clauses : 16
% 0.13/0.43 % Non-unit-clauses : 45
% 0.13/0.43 % Current number of unprocessed clauses: 41
% 0.13/0.43 % ...number of literals in the above : 133
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 58
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 2005
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 1718
% 0.13/0.43 % Non-unit clause-clause subsumptions : 160
% 0.13/0.43 % Unit Clause-clause subsumption calls : 187
% 0.13/0.43 % Rewrite failures with RHS unbound : 0
% 0.13/0.43 % BW rewrite match attempts : 1
% 0.13/0.43 % BW rewrite match successes : 1
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 6802
% 0.13/0.43 % Search garbage collected termcells : 244
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.010 s
% 0.13/0.43 % System time : 0.005 s
% 0.13/0.43 % Total time : 0.015 s
% 0.13/0.43 % Maximum resident set size: 3588 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.041 s
% 0.13/0.43 % System time : 0.019 s
% 0.13/0.43 % Total time : 0.060 s
% 0.13/0.43 % Maximum resident set size: 4864 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------