%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET595+4 : 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 : n015.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 02:14:28 PM UTC 2026
% Result : Theorem 33.27s 5.33s
% Output : CNFRefutation 33.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 45 ~; 50 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 3 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI27,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(union(difference(X4,X1),X1),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI27) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(union(difference(X4,X1),X1),X4) ),
inference(assume_negation,[status(cth)],[thI27]) ).
fof(c_0_7,negated_conjecture,
( ~ equal_set(union(difference(esk5_0,esk4_0),esk4_0),esk5_0)
& subset(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_6])])])]) ).
fof(c_0_8,plain,
! [X12,X13] :
( ( equal_set(X12,X13)
| ~ subset(X13,X12)
| ~ subset(X12,X13) )
& ( ~ equal_set(X12,X13)
| subset(X13,X12) )
& ( ~ equal_set(X12,X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_set(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk1_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk1_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
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])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ subset(union(difference(esk5_0,esk4_0),esk4_0),esk5_0)
| ~ subset(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_15,plain,
! [X19,X20,X21] :
( ( member(X19,union(X20,X21))
| ~ member(X19,X21) )
& ( member(X19,union(X20,X21))
| ~ member(X19,X20) )
& ( member(X19,X21)
| member(X19,X20)
| ~ member(X19,union(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(esk5_0,union(difference(esk5_0,esk4_0),esk4_0))
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),union(difference(esk5_0,esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X23,X24,X25] :
( ( member(X23,difference(X25,X24))
| member(X23,X24)
| ~ member(X23,X25) )
& ( ~ member(X23,difference(X25,X24))
| ~ member(X23,X24) )
& ( ~ member(X23,difference(X25,X24))
| member(X23,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_19,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),union(difference(esk5_0,esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( ~ subset(esk5_0,union(difference(esk5_0,esk4_0),esk4_0))
| ~ member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk4_0)
| member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),difference(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk5_0)
| member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
fof(c_0_25,plain,
! [X14,X15] :
( ( member(X14,power_set(X15))
| ~ subset(X14,X15) )
& ( subset(X14,X15)
| ~ member(X14,power_set(X15)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])])]) ).
cnf(c_0_26,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
( member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( ~ subset(X1,X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(esk4_0,X1)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),X1)
| member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,plain,
( ~ member(esk1_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_32,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,negated_conjecture,
member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]) ).
cnf(c_0_35,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X2)
| member(X1,power_set(union(X2,X3))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),X1)
| member(esk1_2(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),difference(esk5_0,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X3)
| member(X1,power_set(union(X2,X3))) ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_39,plain,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,negated_conjecture,
member(esk5_0,power_set(union(difference(esk5_0,esk4_0),esk4_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
subset(esk5_0,union(difference(esk5_0,esk4_0),esk4_0)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),union(difference(esk5_0,esk4_0),esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
( member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk4_0)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),difference(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
~ member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_41])]) ).
cnf(c_0_45,negated_conjecture,
member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( ~ subset(esk4_0,X1)
| member(esk1_2(union(difference(esk5_0,esk4_0),esk4_0),esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:31:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 33.27/5.33 % Version: 3.5.1
% 33.27/5.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.27/5.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.27/5.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.27/5.33 % Starting new_bool_3 with 300s (1) cores
% 33.27/5.33 % Starting new_bool_1 with 300s (1) cores
% 33.27/5.33 % Starting sh5l with 300s (1) cores
% 33.27/5.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 651854 completed with status 0
% 33.27/5.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 33.27/5.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.27/5.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.27/5.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.27/5.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.27/5.33 % No SInE strategy applied
% 33.27/5.33 % Search class: FGHSF-FFMF21-SFFFFFNN
% 33.27/5.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.27/5.33 % Starting SubtermCWHack with 136s (1) cores
% 33.27/5.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 33.27/5.33 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 33.27/5.33 % Starting new_bool_3 with 136s (1) cores
% 33.27/5.33 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 33.27/5.33 % G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 651864 completed with status 0
% 33.27/5.33 % Result found by G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 33.27/5.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 33.27/5.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.27/5.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 33.27/5.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.27/5.33 % No SInE strategy applied
% 33.27/5.33 % Search class: FGHSF-FFMF21-SFFFFFNN
% 33.27/5.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.27/5.33 % Starting SubtermCWHack with 136s (1) cores
% 33.27/5.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 33.27/5.33 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 33.27/5.33 % Preprocessing time : 0.002 s
% 33.27/5.33 % Presaturation interreduction done
% 33.27/5.33
% 33.27/5.33 % Proof found!
% 33.27/5.33 % SZS status Theorem
% 33.27/5.33 % SZS output start CNFRefutation
% See solution above
% 33.27/5.33 % Parsed axioms : 12
% 33.27/5.33 % Removed by relevancy pruning/SinE : 0
% 33.27/5.33 % Initial clauses : 31
% 33.27/5.33 % Removed in clause preprocessing : 0
% 33.27/5.33 % Initial clauses in saturation : 31
% 33.27/5.33 % Processed clauses : 6649
% 33.27/5.33 % ...of these trivial : 3442
% 33.27/5.33 % ...subsumed : 436
% 33.27/5.33 % ...remaining for further processing : 2771
% 33.27/5.33 % Other redundant clauses eliminated : 3
% 33.27/5.33 % Clauses deleted for lack of memory : 0
% 33.27/5.33 % Backward-subsumed : 215
% 33.27/5.33 % Backward-rewritten : 145
% 33.27/5.33 % Generated clauses : 471738
% 33.27/5.33 % ...of the previous two non-redundant : 359255
% 33.27/5.33 % ...aggressively subsumed : 0
% 33.27/5.33 % Contextual simplify-reflections : 3
% 33.27/5.33 % Paramodulations : 471725
% 33.27/5.33 % Factorizations : 10
% 33.27/5.33 % NegExts : 0
% 33.27/5.33 % Equation resolutions : 3
% 33.27/5.33 % Disequality decompositions : 0
% 33.27/5.33 % Total rewrite steps : 116253
% 33.27/5.33 % ...of those cached : 110689
% 33.27/5.33 % Propositional unsat checks : 0
% 33.27/5.33 % Propositional check models : 0
% 33.27/5.33 % Propositional check unsatisfiable : 0
% 33.27/5.33 % Propositional clauses : 0
% 33.27/5.33 % Propositional clauses after purity: 0
% 33.27/5.33 % Propositional unsat core size : 0
% 33.27/5.33 % Propositional preprocessing time : 0.000
% 33.27/5.33 % Propositional encoding time : 0.000
% 33.27/5.33 % Propositional solver time : 0.000
% 33.27/5.33 % Success case prop preproc time : 0.000
% 33.27/5.33 % Success case prop encoding time : 0.000
% 33.27/5.33 % Success case prop solver time : 0.000
% 33.27/5.33 % Current number of processed clauses : 2377
% 33.27/5.33 % Positive orientable unit clauses : 492
% 33.27/5.33 % Positive unorientable unit clauses: 0
% 33.27/5.33 % Negative unit clauses : 4
% 33.27/5.33 % Non-unit-clauses : 1881
% 33.27/5.33 % Current number of unprocessed clauses: 350396
% 33.27/5.33 % ...number of literals in the above : 531614
% 33.27/5.33 % Current number of archived formulas : 0
% 33.27/5.33 % Current number of archived clauses : 391
% 33.27/5.33 % Clause-clause subsumption calls (NU) : 1056801
% 33.27/5.33 % Rec. Clause-clause subsumption calls : 720658
% 33.27/5.33 % Non-unit clause-clause subsumptions : 636
% 33.27/5.33 % Unit Clause-clause subsumption calls : 28384
% 33.27/5.33 % Rewrite failures with RHS unbound : 0
% 33.27/5.33 % BW rewrite match attempts : 9851
% 33.27/5.33 % BW rewrite match successes : 125
% 33.27/5.33 % Condensation attempts : 0
% 33.27/5.33 % Condensation successes : 0
% 33.27/5.33 % Termbank termtop insertions : 5611297
% 33.27/5.33 % Search garbage collected termcells : 459
% 33.27/5.33
% 33.27/5.33 % -------------------------------------------------
% 33.27/5.33 % User time : 4.455 s
% 33.27/5.33 % System time : 0.227 s
% 33.27/5.33 % Total time : 4.682 s
% 33.27/5.33 % Maximum resident set size: 3648 pages
% 33.27/5.33
% 33.27/5.33 % -------------------------------------------------
% 33.27/5.33 % User time : 22.495 s
% 33.27/5.33 % System time : 1.261 s
% 33.27/5.33 % Total time : 23.756 s
% 33.27/5.33 % Maximum resident set size: 4608 pages
% 33.27/5.33 % E exiting
%------------------------------------------------------------------------------