%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:15:48 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 117 ( 32 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 115 ( 41 ~; 52 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 75 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t82_zfmisc_1,conjecture,
! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_zfmisc_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d9_xboole_0,axiom,
! [X1,X2] :
( inclusion_comparable(X1,X2)
<=> ( subset(X2,X1)
| subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(c_0_8,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X16 = powerset(X15)
| subset(esk1_2(X15,X16),X15)
| in(esk1_2(X15,X16),X16) )
& ( X16 = powerset(X15)
| ~ subset(esk1_2(X15,X16),X15)
| ~ in(esk1_2(X15,X16),X16) )
& ( X12 != powerset(X11)
| in(X14,X12)
| ~ subset(X14,X11) )
& ( X12 != powerset(X11)
| subset(X13,X11)
| ~ in(X13,X12) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
cnf(c_0_9,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
inference(assume_negation,[status(cth)],[t82_zfmisc_1]) ).
fof(c_0_12,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( ( X25 = set_union2(X23,X24)
| in(esk2_3(X23,X24,X25),X24)
| in(esk2_3(X23,X24,X25),X23)
| in(esk2_3(X23,X24,X25),X25) )
& ( X25 = set_union2(X23,X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| ~ in(esk2_3(X23,X24,X25),X24) )
& ( X25 = set_union2(X23,X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| ~ in(esk2_3(X23,X24,X25),X23) )
& ( X20 != set_union2(X18,X19)
| in(X22,X20)
| ~ in(X22,X19) )
& ( X20 != set_union2(X18,X19)
| in(X22,X20)
| ~ in(X22,X18) )
& ( X20 != set_union2(X18,X19)
| in(X21,X19)
| in(X21,X18)
| ~ in(X21,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)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_13,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
( ~ inclusion_comparable(esk5_0,esk6_0)
& set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
( X2 != set_union2(X3,X4)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( ~ in(X1,set_union2(X3,X2))
| in(X1,X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
in(set_union2(esk5_0,esk6_0),set_union2(powerset(esk5_0),powerset(esk6_0))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X40,X41] : subset(X40,set_union2(X40,X41)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_23,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_24,plain,
! [X9,X10] :
( ( X9 = X10
| ~ subset(X10,X9)
| ~ subset(X9,X10) )
& ( X9 != X10
| subset(X10,X9) )
& ( X9 != X10
| subset(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
cnf(c_0_25,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( in(set_union2(esk5_0,esk6_0),powerset(esk5_0))
| in(set_union2(esk5_0,esk6_0),powerset(esk6_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( in(set_union2(esk5_0,esk6_0),powerset(esk5_0))
| subset(set_union2(esk5_0,esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( in(set_union2(esk5_0,esk6_0),powerset(esk5_0))
| set_union2(esk5_0,esk6_0) = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_33,plain,
! [X27,X28] :
( ( inclusion_comparable(X27,X28)
| ~ subset(X28,X27) )
& ( inclusion_comparable(X27,X28)
| ~ subset(X27,X28) )
& ( subset(X28,X27)
| subset(X27,X28)
| ~ inclusion_comparable(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_xboole_0])])])]) ).
cnf(c_0_34,negated_conjecture,
( subset(set_union2(esk5_0,esk6_0),esk5_0)
| set_union2(esk5_0,esk6_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ inclusion_comparable(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,plain,
( ~ subset(X1,X2)
| inclusion_comparable(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( set_union2(esk5_0,esk6_0) = esk5_0
| set_union2(esk5_0,esk6_0) = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_27])]) ).
cnf(c_0_38,negated_conjecture,
~ subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( ~ subset(X1,X2)
| inclusion_comparable(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
set_union2(esk5_0,esk6_0) = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ subset(esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:44:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2128365 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 164s (1) cores
% 0.10/0.44 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A with 136s (1) cores
% 0.10/0.44 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2128376 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 164s (1) cores
% 0.10/0.44 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44 % Presaturation interreduction done
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 16
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 29
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 29
% 0.10/0.44 % Processed clauses : 122
% 0.10/0.44 % ...of these trivial : 1
% 0.10/0.44 % ...subsumed : 32
% 0.10/0.44 % ...remaining for further processing : 89
% 0.10/0.44 % Other redundant clauses eliminated : 7
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 1
% 0.10/0.44 % Backward-rewritten : 15
% 0.10/0.44 % Generated clauses : 186
% 0.10/0.44 % ...of the previous two non-redundant : 152
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 178
% 0.10/0.44 % Factorizations : 1
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 7
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 55
% 0.10/0.44 % ...of those cached : 41
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 39
% 0.10/0.44 % Positive orientable unit clauses : 8
% 0.10/0.44 % Positive unorientable unit clauses: 1
% 0.10/0.44 % Negative unit clauses : 12
% 0.10/0.44 % Non-unit-clauses : 18
% 0.10/0.44 % Current number of unprocessed clauses: 69
% 0.10/0.44 % ...number of literals in the above : 148
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 43
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 295
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 273
% 0.10/0.44 % Non-unit clause-clause subsumptions : 11
% 0.10/0.44 % Unit Clause-clause subsumption calls : 49
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 30
% 0.10/0.44 % BW rewrite match successes : 21
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 3258
% 0.10/0.44 % Search garbage collected termcells : 420
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.009 s
% 0.10/0.44 % System time : 0.002 s
% 0.10/0.44 % Total time : 0.011 s
% 0.10/0.44 % Maximum resident set size: 3588 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.031 s
% 0.10/0.44 % System time : 0.011 s
% 0.10/0.44 % Total time : 0.042 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------