%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET610+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 : n016.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 02:14:43 PM UTC 2026
% Result : Theorem 33.32s 15.32s
% Output : CNFRefutation 33.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 23 unt; 0 def)
% Number of atoms : 130 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 109 ( 39 ~; 53 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 155 ( 16 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_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(prove_th83,conjecture,
! [X1,X2] : difference(union(X1,X2),X2) = difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th83) ).
fof(c_0_6,plain,
! [X7,X8,X9] :
( ( member(X9,union(X7,X8))
| ~ member(X9,X8) )
& ( member(X9,union(X7,X8))
| ~ member(X9,X7) )
& ( member(X9,X8)
| member(X9,X7)
| ~ member(X9,union(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_7,plain,
! [X24,X25,X26,X27,X28] :
( ( subset(X27,X28)
| ~ member(esk3_2(X27,X28),X28) )
& ( subset(X27,X28)
| member(esk3_2(X27,X28),X27) )
& ( member(X26,X25)
| ~ member(X26,X24)
| ~ subset(X24,X25) ) ),
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_8,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(c_0_9,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X10,X11,X12] :
( ( member(X12,difference(X10,X11))
| member(X12,X11)
| ~ member(X12,X10) )
& ( ~ member(X12,difference(X10,X11))
| ~ member(X12,X11) )
& ( ~ member(X12,difference(X10,X11))
| member(X12,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,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk3_2(union(X1,X2),X3),X1)
| member(esk3_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( member(esk3_2(union(X1,X2),X1),X2)
| subset(union(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
fof(c_0_19,plain,
! [X15,X16] : union(X15,X16) = union(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_20,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_21,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_23,plain,
! [X13,X14] :
( ( X13 = X14
| ~ subset(X14,X13)
| ~ subset(X13,X14) )
& ( X13 != X14
| subset(X14,X13) )
& ( X13 != X14
| subset(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_24,plain,
( member(esk3_2(union(X1,difference(X2,X3)),X1),X2)
| subset(union(X1,difference(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_25,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_26,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,plain,
( member(esk3_2(difference(union(X1,X2),X3),X4),X1)
| member(esk3_2(difference(union(X1,X2),X3),X4),X2)
| subset(difference(union(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_29,plain,
( ~ member(esk3_2(X1,union(difference(X2,X3),X4)),X2)
| member(esk3_2(X1,union(difference(X2,X3),X4)),X3)
| subset(X1,union(difference(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( member(esk3_2(union(X1,X2),union(X3,X1)),X2)
| subset(union(X1,X2),union(X3,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_31,plain,
( ~ member(esk3_2(X1,union(X2,union(X3,X4))),X4)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_32,plain,
( member(esk3_2(union(X1,X2),union(X1,X3)),X2)
| subset(union(X1,X2),union(X1,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_33,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_35,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_37,plain,
subset(difference(X1,X2),union(X3,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_38,plain,
( ~ member(esk3_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_39,plain,
( member(esk3_2(difference(union(X1,X2),X3),X1),X2)
| subset(difference(union(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_40,plain,
( member(esk3_2(union(X1,X2),union(difference(X2,X3),X1)),X3)
| subset(union(X1,X2),union(difference(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_43,plain,
( ~ member(X1,difference(X3,X4))
| member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_44,negated_conjecture,
~ ! [X1,X2] : difference(union(X1,X2),X2) = difference(X1,X2),
inference(assume_negation,[status(cth)],[prove_th83]) ).
cnf(c_0_45,plain,
subset(difference(union(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_40]),c_0_26]) ).
cnf(c_0_47,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( ~ member(esk3_2(X1,difference(X2,X3)),X2)
| member(esk3_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_49,plain,
( member(esk3_2(difference(X1,X2),X3),union(X4,X1))
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_10]) ).
fof(c_0_50,negated_conjecture,
difference(union(esk4_0,esk5_0),esk5_0) != difference(esk4_0,esk5_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_51,plain,
subset(difference(union(X1,X2),X1),X2),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_52,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_47])]) ).
cnf(c_0_53,plain,
( member(esk3_2(difference(X1,X2),difference(union(X3,X1),X4)),X4)
| subset(difference(X1,X2),difference(union(X3,X1),X4)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
difference(union(esk4_0,esk5_0),esk5_0) != difference(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
subset(difference(union(X1,X2),X1),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
difference(union(esk5_0,esk4_0),esk5_0) != difference(esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_54,c_0_26]) ).
cnf(c_0_58,plain,
difference(union(X1,X2),X1) = difference(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_55]),c_0_56])]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET610+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/10.37 % Computer : n016.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Mon Sep 21 05:33:48 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 33.32/15.32 % Version: 3.5.1
% 33.32/15.32 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.32/15.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.32/15.32 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.32/15.32 % Starting new_bool_3 with 300s (1) cores
% 33.32/15.32 % Starting new_bool_1 with 300s (1) cores
% 33.32/15.32 % Starting sh5l with 300s (1) cores
% 33.32/15.32 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1653804 completed with status 0
% 33.32/15.32 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 33.32/15.32 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.32/15.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.32/15.32 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.32/15.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.32/15.32 % No SInE strategy applied
% 33.32/15.32 % Search class: FGHSS-FFSF22-SFFFFFNN
% 33.32/15.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.32/15.32 % Starting SubtermCWHack with 136s (1) cores
% 33.32/15.32 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 33.32/15.32 % Starting G----_0010_evo with 136s (1) cores
% 33.32/15.32 % Starting new_bool_3 with 136s (1) cores
% 33.32/15.32 % Starting new_bool_1 with 136s (1) cores
% 33.32/15.32 % SubtermCWHack with pid 1653810 completed with status 0
% 33.32/15.32 % Result found by SubtermCWHack
% 33.32/15.32 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.32/15.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.32/15.32 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.32/15.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.32/15.32 % No SInE strategy applied
% 33.32/15.32 % Search class: FGHSS-FFSF22-SFFFFFNN
% 33.32/15.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.32/15.32 % Starting SubtermCWHack with 136s (1) cores
% 33.32/15.32 % Preprocessing time : 0.001 s
% 33.32/15.32
% 33.32/15.32 % Proof found!
% 33.32/15.32 % SZS status Theorem
% 33.32/15.32 % SZS output start CNFRefutation
% See solution above
% 33.32/15.32 % Parsed axioms : 9
% 33.32/15.32 % Removed by relevancy pruning/SinE : 0
% 33.32/15.32 % Initial clauses : 21
% 33.32/15.32 % Removed in clause preprocessing : 2
% 33.32/15.32 % Initial clauses in saturation : 19
% 33.32/15.32 % Processed clauses : 27853
% 33.32/15.32 % ...of these trivial : 1768
% 33.32/15.32 % ...subsumed : 24419
% 33.32/15.32 % ...remaining for further processing : 1666
% 33.32/15.32 % Other redundant clauses eliminated : 2
% 33.32/15.32 % Clauses deleted for lack of memory : 0
% 33.32/15.32 % Backward-subsumed : 17
% 33.32/15.32 % Backward-rewritten : 105
% 33.32/15.32 % Generated clauses : 463862
% 33.32/15.32 % ...of the previous two non-redundant : 351682
% 33.32/15.32 % ...aggressively subsumed : 0
% 33.32/15.32 % Contextual simplify-reflections : 7
% 33.32/15.32 % Paramodulations : 462584
% 33.32/15.32 % Factorizations : 1276
% 33.32/15.32 % NegExts : 0
% 33.32/15.32 % Equation resolutions : 2
% 33.32/15.32 % Disequality decompositions : 0
% 33.32/15.32 % Total rewrite steps : 382668
% 33.32/15.32 % ...of those cached : 360719
% 33.32/15.32 % Propositional unsat checks : 0
% 33.32/15.32 % Propositional check models : 0
% 33.32/15.32 % Propositional check unsatisfiable : 0
% 33.32/15.32 % Propositional clauses : 0
% 33.32/15.32 % Propositional clauses after purity: 0
% 33.32/15.32 % Propositional unsat core size : 0
% 33.32/15.32 % Propositional preprocessing time : 0.000
% 33.32/15.32 % Propositional encoding time : 0.000
% 33.32/15.32 % Propositional solver time : 0.000
% 33.32/15.32 % Success case prop preproc time : 0.000
% 33.32/15.32 % Success case prop encoding time : 0.000
% 33.32/15.32 % Success case prop solver time : 0.000
% 33.32/15.32 % Current number of processed clauses : 1542
% 33.32/15.32 % Positive orientable unit clauses : 516
% 33.32/15.32 % Positive unorientable unit clauses: 25
% 33.32/15.32 % Negative unit clauses : 34
% 33.32/15.32 % Non-unit-clauses : 967
% 33.32/15.32 % Current number of unprocessed clauses: 322787
% 33.32/15.32 % ...number of literals in the above : 930964
% 33.32/15.32 % Current number of archived formulas : 0
% 33.32/15.32 % Current number of archived clauses : 122
% 33.32/15.32 % Clause-clause subsumption calls (NU) : 396521
% 33.32/15.32 % Rec. Clause-clause subsumption calls : 158387
% 33.32/15.32 % Non-unit clause-clause subsumptions : 11704
% 33.32/15.32 % Unit Clause-clause subsumption calls : 78826
% 33.32/15.32 % Rewrite failures with RHS unbound : 1993
% 33.32/15.32 % BW rewrite match attempts : 11617
% 33.32/15.32 % BW rewrite match successes : 224
% 33.32/15.32 % Condensation attempts : 0
% 33.32/15.32 % Condensation successes : 0
% 33.32/15.32 % Termbank termtop insertions : 7855777
% 33.32/15.32 % Search garbage collected termcells : 346
% 33.32/15.32
% 33.32/15.32 % -------------------------------------------------
% 33.32/15.32 % User time : 4.319 s
% 33.32/15.32 % System time : 0.192 s
% 33.32/15.32 % Total time : 4.510 s
% 33.32/15.32 % Maximum resident set size: 3636 pages
% 33.32/15.32
% 33.32/15.32 % -------------------------------------------------
% 33.32/15.32 % User time : 22.462 s
% 33.32/15.32 % System time : 1.023 s
% 33.32/15.32 % Total time : 23.485 s
% 33.32/15.32 % Maximum resident set size: 4864 pages
% 33.32/15.32 % E exiting
%------------------------------------------------------------------------------