%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:14:45 PM UTC 2026
% Result : Theorem 0.25s 0.57s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 67 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 24 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_th90,conjecture,
! [X1,X2] :
( difference(X1,X2) = difference(X2,X1)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th90) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( difference(X1,X2) = difference(X2,X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[prove_th90]) ).
fof(c_0_6,plain,
! [X6,X7,X8] :
( ( member(X8,difference(X6,X7))
| member(X8,X7)
| ~ member(X8,X6) )
& ( ~ member(X8,difference(X6,X7))
| ~ member(X8,X7) )
& ( ~ member(X8,difference(X6,X7))
| member(X8,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,negated_conjecture,
( esk1_0 != esk2_0
& difference(esk1_0,esk2_0) = difference(esk2_0,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_8,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
difference(esk1_0,esk2_0) = difference(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ member(esk5_2(X22,X23),X23) )
& ( subset(X22,X23)
| member(esk5_2(X22,X23),X22) )
& ( member(X21,X20)
| ~ member(X21,X19)
| ~ subset(X19,X20) ) ),
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_defn])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
~ member(X1,difference(esk2_0,esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_13,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( ~ member(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X25,X26] :
( ( X25 = X26
| ~ subset(X26,X25)
| ~ subset(X25,X26) )
& ( X25 != X26
| subset(X26,X25) )
& ( X25 != X26
| subset(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(esk5_2(X1,esk1_0),esk2_0)
| subset(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_9]),c_0_12]) ).
cnf(c_0_20,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
subset(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( member(esk5_2(esk1_0,X1),esk2_0)
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:30:45 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.25/0.57 % Version: 3.5.1
% 0.25/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.57 % Starting sh5l with 300s (1) cores
% 0.25/0.57 % new_bool_3 with pid 3499992 completed with status 0
% 0.25/0.57 % Result found by new_bool_3
% 0.25/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.57 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.25/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.57 % SubtermCWHack with pid 3500001 completed with status 0
% 0.25/0.57 % Result found by SubtermCWHack
% 0.25/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.57 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.25/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.57 % Preprocessing time : 0.002 s
% 0.25/0.57
% 0.25/0.57 % Proof found!
% 0.25/0.57 % SZS status Theorem
% 0.25/0.57 % SZS output start CNFRefutation
% See solution above
% 0.25/0.57 % Parsed axioms : 7
% 0.25/0.57 % Removed by relevancy pruning/SinE : 0
% 0.25/0.57 % Initial clauses : 18
% 0.25/0.57 % Removed in clause preprocessing : 2
% 0.25/0.57 % Initial clauses in saturation : 16
% 0.25/0.57 % Processed clauses : 25
% 0.25/0.57 % ...of these trivial : 0
% 0.25/0.57 % ...subsumed : 3
% 0.25/0.57 % ...remaining for further processing : 22
% 0.25/0.57 % Other redundant clauses eliminated : 2
% 0.25/0.57 % Clauses deleted for lack of memory : 0
% 0.25/0.57 % Backward-subsumed : 0
% 0.25/0.57 % Backward-rewritten : 0
% 0.25/0.57 % Generated clauses : 34
% 0.25/0.57 % ...of the previous two non-redundant : 23
% 0.25/0.57 % ...aggressively subsumed : 0
% 0.25/0.57 % Contextual simplify-reflections : 1
% 0.25/0.57 % Paramodulations : 30
% 0.25/0.57 % Factorizations : 2
% 0.25/0.57 % NegExts : 0
% 0.25/0.57 % Equation resolutions : 2
% 0.25/0.57 % Disequality decompositions : 0
% 0.25/0.57 % Total rewrite steps : 3
% 0.25/0.57 % ...of those cached : 2
% 0.25/0.57 % Propositional unsat checks : 0
% 0.25/0.57 % Propositional check models : 0
% 0.25/0.57 % Propositional check unsatisfiable : 0
% 0.25/0.57 % Propositional clauses : 0
% 0.25/0.57 % Propositional clauses after purity: 0
% 0.25/0.57 % Propositional unsat core size : 0
% 0.25/0.57 % Propositional preprocessing time : 0.000
% 0.25/0.57 % Propositional encoding time : 0.000
% 0.25/0.57 % Propositional solver time : 0.000
% 0.25/0.57 % Success case prop preproc time : 0.000
% 0.25/0.57 % Success case prop encoding time : 0.000
% 0.25/0.57 % Success case prop solver time : 0.000
% 0.25/0.57 % Current number of processed clauses : 20
% 0.25/0.57 % Positive orientable unit clauses : 4
% 0.25/0.57 % Positive unorientable unit clauses: 0
% 0.25/0.57 % Negative unit clauses : 3
% 0.25/0.57 % Non-unit-clauses : 13
% 0.25/0.57 % Current number of unprocessed clauses: 14
% 0.25/0.57 % ...number of literals in the above : 38
% 0.25/0.57 % Current number of archived formulas : 0
% 0.25/0.57 % Current number of archived clauses : 0
% 0.25/0.57 % Clause-clause subsumption calls (NU) : 13
% 0.25/0.57 % Rec. Clause-clause subsumption calls : 13
% 0.25/0.57 % Non-unit clause-clause subsumptions : 2
% 0.25/0.57 % Unit Clause-clause subsumption calls : 5
% 0.25/0.57 % Rewrite failures with RHS unbound : 0
% 0.25/0.57 % BW rewrite match attempts : 0
% 0.25/0.57 % BW rewrite match successes : 0
% 0.25/0.57 % Condensation attempts : 0
% 0.25/0.57 % Condensation successes : 0
% 0.25/0.57 % Termbank termtop insertions : 1402
% 0.25/0.57 % Search garbage collected termcells : 327
% 0.25/0.57
% 0.25/0.57 % -------------------------------------------------
% 0.25/0.57 % User time : 0.009 s
% 0.25/0.57 % System time : 0.004 s
% 0.25/0.57 % Total time : 0.013 s
% 0.25/0.57 % Maximum resident set size: 3632 pages
% 0.25/0.57
% 0.25/0.57 % -------------------------------------------------
% 0.25/0.57 % User time : 0.010 s
% 0.25/0.57 % System time : 0.011 s
% 0.25/0.57 % Total time : 0.022 s
% 0.25/0.57 % Maximum resident set size: 4864 pages
% 0.25/0.57 % E exiting
%------------------------------------------------------------------------------