%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:18:56 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 88 ( 49 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 106 ( 48 ~; 29 |; 24 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t74_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(t72_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X2,X3)
& ~ in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ( X1 = X2
| in(X2,X3) )
& ~ in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
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(t73_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X2,X3)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
inference(assume_negation,[status(cth)],[t74_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X2,X3)
& ~ in(X1,X3) ) ),
inference(fof_simplification,[status(thm)],[t72_zfmisc_1]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ( X1 = X2
| in(X2,X3) )
& ~ in(X1,X3) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_9,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set ),
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_10,plain,
! [X13,X14,X15] :
( ( set_difference(unordered_pair(X13,X14),X15) = unordered_pair(X13,X14)
| in(X14,X15)
| in(X13,X15) )
& ( set_difference(unordered_pair(X13,X14),X15) != unordered_pair(X13,X14)
| ~ in(X14,X15) )
& ( set_difference(unordered_pair(X13,X14),X15) != unordered_pair(X13,X14)
| ~ in(X13,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X8,X9,X10] :
( ( set_difference(unordered_pair(X8,X9),X10) = singleton(X8)
| in(X8,X10)
| X8 != X9 )
& ( set_difference(unordered_pair(X8,X9),X10) = singleton(X8)
| in(X8,X10)
| ~ in(X9,X10) )
& ( set_difference(unordered_pair(X8,X9),X10) != singleton(X8)
| X8 = X9
| in(X9,X10) )
& ( set_difference(unordered_pair(X8,X9),X10) != singleton(X8)
| ~ in(X8,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_12,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( set_difference(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3)
| in(X3,X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ in(X1,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( in(esk4_0,esk5_0)
| in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,esk5_0)
| in(esk3_0,esk5_0)
| set_difference(unordered_pair(X1,esk4_0),esk5_0) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_19,plain,
! [X6,X7] : unordered_pair(X6,X7) = unordered_pair(X7,X6),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_20,plain,
! [X16,X17,X18] :
( ( set_difference(unordered_pair(X16,X17),X18) = empty_set
| ~ in(X17,X18)
| ~ in(X16,X18) )
& ( set_difference(unordered_pair(X16,X17),X18) != empty_set
| in(X17,X18) )
& ( set_difference(unordered_pair(X16,X17),X18) != empty_set
| in(X16,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t73_zfmisc_1])])])]) ).
cnf(c_0_21,negated_conjecture,
( in(X1,esk5_0)
| set_difference(unordered_pair(X1,esk3_0),esk5_0) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( ~ in(X3,X2)
| ~ in(X1,X2)
| set_difference(unordered_pair(X1,X3),X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( in(X1,esk5_0)
| set_difference(unordered_pair(esk3_0,X1),esk5_0) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,esk5_0)
| set_difference(unordered_pair(X1,esk3_0),esk5_0) = empty_set ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
in(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:43:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2677006 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.42 % new_bool_1 with pid 2677014 completed with status 0
% 0.13/0.42 % Result found by new_bool_1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42 % Presaturation interreduction done
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 9
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 19
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 19
% 0.13/0.42 % Processed clauses : 100
% 0.13/0.42 % ...of these trivial : 1
% 0.13/0.42 % ...subsumed : 35
% 0.13/0.42 % ...remaining for further processing : 63
% 0.13/0.42 % Other redundant clauses eliminated : 1
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 0
% 0.13/0.42 % Backward-rewritten : 7
% 0.13/0.42 % Generated clauses : 123
% 0.13/0.42 % ...of the previous two non-redundant : 94
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 2
% 0.13/0.42 % Paramodulations : 121
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 2
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 32
% 0.13/0.42 % ...of those cached : 28
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 36
% 0.13/0.42 % Positive orientable unit clauses : 5
% 0.13/0.42 % Positive unorientable unit clauses: 1
% 0.13/0.42 % Negative unit clauses : 9
% 0.13/0.42 % Non-unit-clauses : 21
% 0.13/0.42 % Current number of unprocessed clauses: 27
% 0.13/0.42 % ...number of literals in the above : 80
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 26
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 131
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 115
% 0.13/0.42 % Non-unit clause-clause subsumptions : 33
% 0.13/0.42 % Unit Clause-clause subsumption calls : 23
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 5
% 0.13/0.42 % BW rewrite match successes : 5
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 2211
% 0.13/0.42 % Search garbage collected termcells : 176
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.005 s
% 0.13/0.42 % System time : 0.001 s
% 0.13/0.42 % Total time : 0.006 s
% 0.13/0.42 % Maximum resident set size: 3636 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.023 s
% 0.13/0.42 % System time : 0.006 s
% 0.13/0.42 % Total time : 0.029 s
% 0.13/0.42 % Maximum resident set size: 4608 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------