%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET887+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 : n007.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 02:18:50 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 136 ( 100 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 153 ( 60 ~; 62 |; 24 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 79 ( 9 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
fof(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(fof_simplification,[status(thm)],[l46_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( X1 != X4
& X1 != X3
& subset(unordered_pair(X1,X2),unordered_pair(X3,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X22,X23,X24] :
( ( subset(X22,unordered_pair(X23,X24))
| X22 != unordered_pair(X23,X24) )
& ( subset(X22,unordered_pair(X23,X24))
| X22 != singleton(X24) )
& ( subset(X22,unordered_pair(X23,X24))
| X22 != singleton(X23) )
& ( subset(X22,unordered_pair(X23,X24))
| X22 != empty_set )
& ( X22 = unordered_pair(X23,X24)
| X22 = singleton(X24)
| X22 = singleton(X23)
| X22 = empty_set
| ~ subset(X22,unordered_pair(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,negated_conjecture,
( esk5_0 != esk8_0
& esk5_0 != esk7_0
& subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_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_10,plain,
! [X36,X37,X38] :
( X36 = X37
| singleton(X36) != unordered_pair(X37,X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])])]) ).
cnf(c_0_11,plain,
( ~ subset(X1,unordered_pair(X2,X3))
| X1 = unordered_pair(X2,X3)
| X1 = singleton(X3)
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( singleton(X1) != unordered_pair(X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| singleton(esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2)
| esk8_0 = X1
| unordered_pair(esk5_0,esk6_0) = empty_set
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
esk5_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = unordered_pair(X18,X19)
| esk2_3(X18,X19,X20) = X19
| esk2_3(X18,X19,X20) = X18
| in(esk2_3(X18,X19,X20),X20) )
& ( X20 = unordered_pair(X18,X19)
| ~ in(esk2_3(X18,X19,X20),X20)
| esk2_3(X18,X19,X20) != X19 )
& ( X20 = unordered_pair(X18,X19)
| ~ in(esk2_3(X18,X19,X20),X20)
| esk2_3(X18,X19,X20) != X18 )
& ( X15 != unordered_pair(X13,X14)
| in(X17,X15)
| X17 != X14 )
& ( X15 != unordered_pair(X13,X14)
| in(X17,X15)
| X17 != X13 )
& ( X15 != unordered_pair(X13,X14)
| X16 = X14
| X16 = X13
| ~ in(X16,X15) ) ),
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_18,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2)
| esk7_0 = X1
| unordered_pair(esk5_0,esk6_0) = empty_set
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
esk5_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_23,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]) ).
fof(c_0_26,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_22])])])])])]) ).
cnf(c_0_27,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( in(esk7_0,unordered_pair(esk5_0,esk6_0))
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( esk6_0 = esk7_0
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).
cnf(c_0_31,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,negated_conjecture,
esk6_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk7_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_33]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( in(esk8_0,unordered_pair(esk5_0,esk7_0))
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( esk8_0 = esk7_0
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_36]),c_0_16]) ).
cnf(c_0_38,negated_conjecture,
esk8_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| unordered_pair(esk7_0,esk7_0) = unordered_pair(esk5_0,esk7_0) ),
inference(rw,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(X1,unordered_pair(esk5_0,esk7_0))
| X1 = esk7_0
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
unordered_pair(esk5_0,esk7_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_21]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_41]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n007.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 05:40:50 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 293281 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSS-FFMS31-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 293287 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSS-FFMS31-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44 % Presaturation interreduction done
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 12
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 24
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 24
% 0.14/0.44 % Processed clauses : 117
% 0.14/0.44 % ...of these trivial : 3
% 0.14/0.44 % ...subsumed : 30
% 0.14/0.44 % ...remaining for further processing : 84
% 0.14/0.44 % Other redundant clauses eliminated : 16
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 6
% 0.14/0.44 % Backward-rewritten : 14
% 0.14/0.44 % Generated clauses : 177
% 0.14/0.44 % ...of the previous two non-redundant : 133
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 156
% 0.14/0.44 % Factorizations : 4
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 19
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 62
% 0.14/0.44 % ...of those cached : 42
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 33
% 0.14/0.44 % Positive orientable unit clauses : 12
% 0.14/0.44 % Positive unorientable unit clauses: 1
% 0.14/0.44 % Negative unit clauses : 5
% 0.14/0.44 % Non-unit-clauses : 15
% 0.14/0.44 % Current number of unprocessed clauses: 42
% 0.14/0.44 % ...number of literals in the above : 169
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 43
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 98
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 81
% 0.14/0.44 % Non-unit clause-clause subsumptions : 20
% 0.14/0.44 % Unit Clause-clause subsumption calls : 11
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 25
% 0.14/0.44 % BW rewrite match successes : 19
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 2946
% 0.14/0.44 % Search garbage collected termcells : 370
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.009 s
% 0.14/0.44 % System time : 0.001 s
% 0.14/0.44 % Total time : 0.010 s
% 0.14/0.44 % Maximum resident set size: 3640 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.022 s
% 0.14/0.44 % System time : 0.015 s
% 0.14/0.44 % Total time : 0.037 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------