%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:14:06 PM UTC 2026
% Result : Theorem 0.23s 10.58s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 75 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 32 ~; 31 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X3,X5)
& member(X5,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(thI39,conjecture,
! [X1] : equal_set(sum(singleton(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI39) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_5,plain,
! [X15,X16] :
( ( member(X15,singleton(X16))
| X15 != X16 )
& ( X15 = X16
| ~ member(X15,singleton(X16)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])]) ).
fof(c_0_6,plain,
! [X9,X10,X12,X13,X14] :
( ( member(X12,sum(X13))
| ~ member(X12,X14)
| ~ member(X14,X13) )
& ( ~ member(X9,sum(X10))
| member(X9,esk2_2(X9,X10)) )
& ( ~ member(X9,sum(X10))
| member(esk2_2(X9,X10),X10) ) ),
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)],[sum])])])])])])]) ).
cnf(c_0_7,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ member(X1,sum(X2))
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] : equal_set(sum(singleton(X1)),X1),
inference(assume_negation,[status(cth)],[thI39]) ).
cnf(c_0_10,plain,
( ~ member(X1,sum(X2))
| member(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ member(X1,sum(singleton(X2)))
| esk2_2(X1,singleton(X2)) = X2 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_12,plain,
! [X17,X18,X19,X20,X21] :
( ( subset(X20,X21)
| ~ member(esk3_2(X20,X21),X21) )
& ( subset(X20,X21)
| member(esk3_2(X20,X21),X20) )
& ( member(X19,X18)
| ~ member(X19,X17)
| ~ subset(X17,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)],[subset])])])])])])]) ).
fof(c_0_13,negated_conjecture,
~ equal_set(sum(singleton(esk1_0)),esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X7,X8] :
( ( equal_set(X7,X8)
| ~ subset(X8,X7)
| ~ subset(X7,X8) )
& ( ~ equal_set(X7,X8)
| subset(X8,X7) )
& ( ~ equal_set(X7,X8)
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_15,plain,
( ~ member(X1,sum(singleton(X2)))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
~ equal_set(sum(singleton(esk1_0)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( subset(sum(singleton(X1)),X2)
| member(esk3_2(sum(singleton(X1)),X2),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ member(X3,X1)
| ~ member(X1,X2)
| member(X3,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( ~ subset(sum(singleton(esk1_0)),esk1_0)
| ~ subset(esk1_0,sum(singleton(esk1_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
subset(sum(singleton(X1)),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ member(X1,X3)
| subset(X1,X2)
| member(esk3_2(X1,X2),sum(X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,plain,
( X1 != X2
| member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,negated_conjecture,
~ subset(esk1_0,sum(singleton(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_27,plain,
( ~ member(X1,X2)
| subset(X1,sum(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_28,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/10.48 % Computer : n002.cluster.edu
% 0.19/10.48 % Model : x86_64 x86_64
% 0.19/10.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.48 % Memory : 8046.5625MB
% 0.19/10.48 % OS : Linux 6.8.0-71-generic
% 0.19/10.48 % CPULimit : 300
% 0.19/10.48 % WCLimit : 300
% 0.19/10.48 % DateTime : Mon Sep 21 05:13:27 UTC 2026
% 0.19/10.49 % CPUTime :
% 0.19/10.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/10.53 Running first-order theorem proving
% 0.23/10.53 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
% 0.23/10.58 % Version: 3.5.1
% 0.23/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/10.58 % Starting new_bool_3 with 300s (1) cores
% 0.23/10.58 % Starting new_bool_1 with 300s (1) cores
% 0.23/10.58 % Starting sh5l with 300s (1) cores
% 0.23/10.58 % new_bool_3 with pid 2500342 completed with status 0
% 0.23/10.58 % Result found by new_bool_3
% 0.23/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/10.58 % Starting new_bool_3 with 300s (1) cores
% 0.23/10.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/10.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/10.58 % Search class: FGUSF-FFSF21-SFFFFFNN
% 0.23/10.58 % partial match(1): FGHSF-FFSF21-SFFFFFNN
% 0.23/10.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/10.58 % Starting SubtermCWHack with 31s (1) cores
% 0.23/10.58 % SubtermCWHack with pid 2500345 completed with status 0
% 0.23/10.58 % Result found by SubtermCWHack
% 0.23/10.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/10.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/10.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/10.58 % Starting new_bool_3 with 300s (1) cores
% 0.23/10.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/10.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/10.58 % Search class: FGUSF-FFSF21-SFFFFFNN
% 0.23/10.58 % partial match(1): FGHSF-FFSF21-SFFFFFNN
% 0.23/10.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/10.58 % Starting SubtermCWHack with 31s (1) cores
% 0.23/10.58 % Preprocessing time : 0.001 s
% 0.23/10.58
% 0.23/10.58 % Proof found!
% 0.23/10.58 % SZS status Theorem
% 0.23/10.58 % SZS output start CNFRefutation
% See solution above
% 0.23/10.58 % Parsed axioms : 12
% 0.23/10.58 % Removed by relevancy pruning/SinE : 7
% 0.23/10.58 % Initial clauses : 12
% 0.23/10.58 % Removed in clause preprocessing : 0
% 0.23/10.58 % Initial clauses in saturation : 12
% 0.23/10.58 % Processed clauses : 43
% 0.23/10.58 % ...of these trivial : 0
% 0.23/10.58 % ...subsumed : 1
% 0.23/10.58 % ...remaining for further processing : 42
% 0.23/10.58 % Other redundant clauses eliminated : 1
% 0.23/10.58 % Clauses deleted for lack of memory : 0
% 0.23/10.58 % Backward-subsumed : 0
% 0.23/10.58 % Backward-rewritten : 1
% 0.23/10.58 % Generated clauses : 109
% 0.23/10.58 % ...of the previous two non-redundant : 95
% 0.23/10.58 % ...aggressively subsumed : 0
% 0.23/10.58 % Contextual simplify-reflections : 0
% 0.23/10.58 % Paramodulations : 108
% 0.23/10.58 % Factorizations : 0
% 0.23/10.58 % NegExts : 0
% 0.23/10.58 % Equation resolutions : 1
% 0.23/10.58 % Disequality decompositions : 0
% 0.23/10.58 % Total rewrite steps : 12
% 0.23/10.58 % ...of those cached : 3
% 0.23/10.58 % Propositional unsat checks : 0
% 0.23/10.58 % Propositional check models : 0
% 0.23/10.58 % Propositional check unsatisfiable : 0
% 0.23/10.58 % Propositional clauses : 0
% 0.23/10.58 % Propositional clauses after purity: 0
% 0.23/10.58 % Propositional unsat core size : 0
% 0.23/10.58 % Propositional preprocessing time : 0.000
% 0.23/10.58 % Propositional encoding time : 0.000
% 0.23/10.58 % Propositional solver time : 0.000
% 0.23/10.58 % Success case prop preproc time : 0.000
% 0.23/10.58 % Success case prop encoding time : 0.000
% 0.23/10.58 % Success case prop solver time : 0.000
% 0.23/10.58 % Current number of processed clauses : 40
% 0.23/10.58 % Positive orientable unit clauses : 13
% 0.23/10.58 % Positive unorientable unit clauses: 0
% 0.23/10.58 % Negative unit clauses : 2
% 0.23/10.58 % Non-unit-clauses : 25
% 0.23/10.58 % Current number of unprocessed clauses: 64
% 0.23/10.58 % ...number of literals in the above : 108
% 0.23/10.58 % Current number of archived formulas : 0
% 0.23/10.58 % Current number of archived clauses : 1
% 0.23/10.58 % Clause-clause subsumption calls (NU) : 53
% 0.23/10.58 % Rec. Clause-clause subsumption calls : 52
% 0.23/10.58 % Non-unit clause-clause subsumptions : 1
% 0.23/10.58 % Unit Clause-clause subsumption calls : 5
% 0.23/10.58 % Rewrite failures with RHS unbound : 0
% 0.23/10.58 % BW rewrite match attempts : 29
% 0.23/10.58 % BW rewrite match successes : 1
% 0.23/10.58 % Condensation attempts : 0
% 0.23/10.58 % Condensation successes : 0
% 0.23/10.58 % Termbank termtop insertions : 2523
% 0.23/10.58 % Search garbage collected termcells : 268
% 0.23/10.58
% 0.23/10.58 % -------------------------------------------------
% 0.23/10.58 % User time : 0.008 s
% 0.23/10.58 % System time : 0.003 s
% 0.23/10.58 % Total time : 0.011 s
% 0.23/10.58 % Maximum resident set size: 3648 pages
% 0.23/10.58
% 0.23/10.58 % -------------------------------------------------
% 0.23/10.58 % User time : 0.012 s
% 0.23/10.58 % System time : 0.007 s
% 0.23/10.58 % Total time : 0.019 s
% 0.23/10.58 % Maximum resident set size: 4864 pages
% 0.23/10.58 % E exiting
%------------------------------------------------------------------------------