%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET577+3 : 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 : n008.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 02:17:21 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 120 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 50 |; 10 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 9 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th18,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X3)
| member(X4,X2) ) )
=> X1 = union(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X3)
| member(X4,X2) ) )
=> X1 = union(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th18]) ).
fof(c_0_6,plain,
! [X14,X15,X16,X17,X18] :
( ( subset(X17,X18)
| ~ member(esk4_2(X17,X18),X18) )
& ( subset(X17,X18)
| member(esk4_2(X17,X18),X17) )
& ( member(X16,X15)
| ~ member(X16,X14)
| ~ subset(X14,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)],[subset_defn])])])])])])]) ).
fof(c_0_7,plain,
! [X9,X10,X11] :
( ( member(X11,union(X9,X10))
| ~ member(X11,X10) )
& ( member(X11,union(X9,X10))
| ~ member(X11,X9) )
& ( member(X11,X10)
| member(X11,X9)
| ~ member(X11,union(X9,X10)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_8,negated_conjecture,
! [X8] :
( esk1_0 != union(esk2_0,esk3_0)
& ( member(X8,esk1_0)
| ~ member(X8,esk3_0) )
& ( member(X8,esk1_0)
| ~ member(X8,esk2_0) )
& ( member(X8,esk3_0)
| member(X8,esk2_0)
| ~ member(X8,esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
cnf(c_0_9,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( member(esk4_2(esk2_0,X1),esk1_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X12,X13] : union(X12,X13) = union(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_16,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
subset(esk2_0,union(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( member(esk4_2(union(X1,X2),X3),X1)
| member(esk4_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( member(esk4_2(esk3_0,X1),esk1_0)
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_22,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
subset(esk2_0,union(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X27,X28] :
( ( X27 = X28
| ~ subset(X28,X27)
| ~ subset(X27,X28) )
& ( X27 != X28
| subset(X28,X27) )
& ( X27 != X28
| subset(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_25,plain,
( member(esk4_2(union(X1,X1),X2),X1)
| subset(union(X1,X1),X2) ),
inference(ef,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_27,negated_conjecture,
subset(esk3_0,union(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_28,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,union(esk1_0,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_32,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,union(X2,esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_34,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(esk4_2(X1,union(esk1_0,X2)),esk2_0)
| subset(X1,union(esk1_0,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_29]) ).
cnf(c_0_36,plain,
union(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(esk4_2(X1,union(X2,esk1_0)),esk3_0)
| subset(X1,union(X2,esk1_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_33]) ).
cnf(c_0_38,plain,
( member(esk4_2(union(X1,X2),union(X1,X3)),X2)
| subset(union(X1,X2),union(X1,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(esk4_2(X1,esk1_0),esk2_0)
| subset(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( member(esk4_2(union(X1,X2),X1),X2)
| subset(union(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_41,negated_conjecture,
subset(union(X1,esk3_0),union(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
subset(union(esk1_0,esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk3_0)
| member(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_44,negated_conjecture,
subset(union(X1,esk3_0),union(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
union(esk1_0,esk2_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_32])]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(esk4_2(X1,union(X2,esk3_0)),esk1_0)
| member(esk4_2(X1,union(X2,esk3_0)),esk2_0)
| subset(X1,union(X2,esk3_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
subset(union(esk2_0,esk3_0),esk1_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
esk1_0 != union(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(esk4_2(X1,union(esk2_0,esk3_0)),esk1_0)
| subset(X1,union(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
~ subset(esk1_0,union(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_48]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_19]),c_0_45]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.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 05:27:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % new_bool_1 with pid 226594 completed with status 0
% 0.09/0.45 % Result found by new_bool_1
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % SubtermCWHack with pid 226600 completed with status 0
% 0.09/0.45 % Result found by SubtermCWHack
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % Preprocessing time : 0.001 s
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 7
% 0.09/0.45 % Removed by relevancy pruning/SinE : 0
% 0.09/0.45 % Initial clauses : 19
% 0.09/0.45 % Removed in clause preprocessing : 2
% 0.09/0.45 % Initial clauses in saturation : 17
% 0.09/0.45 % Processed clauses : 748
% 0.09/0.45 % ...of these trivial : 130
% 0.09/0.45 % ...subsumed : 413
% 0.09/0.45 % ...remaining for further processing : 205
% 0.09/0.45 % Other redundant clauses eliminated : 2
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 0
% 0.09/0.45 % Backward-rewritten : 10
% 0.09/0.45 % Generated clauses : 3740
% 0.09/0.45 % ...of the previous two non-redundant : 2478
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 0
% 0.09/0.45 % Paramodulations : 3694
% 0.09/0.45 % Factorizations : 44
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 2
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 2381
% 0.09/0.45 % ...of those cached : 2080
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 193
% 0.09/0.45 % Positive orientable unit clauses : 74
% 0.09/0.45 % Positive unorientable unit clauses: 1
% 0.09/0.45 % Negative unit clauses : 2
% 0.09/0.45 % Non-unit-clauses : 116
% 0.09/0.45 % Current number of unprocessed clauses: 1706
% 0.09/0.45 % ...number of literals in the above : 4447
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 10
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 3210
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 2968
% 0.09/0.45 % Non-unit clause-clause subsumptions : 412
% 0.09/0.45 % Unit Clause-clause subsumption calls : 285
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 172
% 0.09/0.45 % BW rewrite match successes : 11
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 45897
% 0.09/0.45 % Search garbage collected termcells : 355
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.025 s
% 0.09/0.45 % System time : 0.004 s
% 0.09/0.45 % Total time : 0.029 s
% 0.09/0.45 % Maximum resident set size: 3632 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.027 s
% 0.09/0.45 % System time : 0.007 s
% 0.09/0.45 % Total time : 0.035 s
% 0.09/0.45 % Maximum resident set size: 4864 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------