%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:23:55 PM UTC 2026
% Result : Theorem 203.98s 29.96s
% Output : CNFRefutation 203.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 99 ( 32 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 112 ( 44 ~; 50 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 4 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t40_xboole_1,conjecture,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(assume_negation,[status(cth)],[t40_xboole_1]) ).
fof(c_0_6,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( X24 = set_union2(X22,X23)
| in(esk2_3(X22,X23,X24),X23)
| in(esk2_3(X22,X23,X24),X22)
| in(esk2_3(X22,X23,X24),X24) )
& ( X24 = set_union2(X22,X23)
| ~ in(esk2_3(X22,X23,X24),X24)
| ~ in(esk2_3(X22,X23,X24),X23) )
& ( X24 = set_union2(X22,X23)
| ~ in(esk2_3(X22,X23,X24),X24)
| ~ in(esk2_3(X22,X23,X24),X22) )
& ( X19 != set_union2(X17,X18)
| in(X21,X19)
| ~ in(X21,X18) )
& ( X19 != set_union2(X17,X18)
| in(X21,X19)
| ~ in(X21,X17) )
& ( X19 != set_union2(X17,X18)
| in(X20,X18)
| in(X20,X17)
| ~ in(X20,X19) ) ),
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])])])])])])]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_8,negated_conjecture,
set_difference(set_union2(esk10_0,esk11_0),esk11_0) != set_difference(esk10_0,esk11_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_10,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,lemma,
! [X93,X94] : set_union2(X93,set_difference(X94,X93)) = set_union2(X93,X94),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_12,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( X48 = set_difference(X46,X47)
| in(esk5_3(X46,X47,X48),X48)
| ~ in(esk5_3(X46,X47,X48),X47) )
& ( X48 = set_difference(X46,X47)
| in(esk5_3(X46,X47,X48),X48)
| in(esk5_3(X46,X47,X48),X46) )
& ( X48 = set_difference(X46,X47)
| in(esk5_3(X46,X47,X48),X47)
| ~ in(esk5_3(X46,X47,X48),X46)
| ~ in(esk5_3(X46,X47,X48),X48) )
& ( X43 != set_difference(X41,X42)
| in(X45,X43)
| in(X45,X42)
| ~ in(X45,X41) )
& ( X43 != set_difference(X41,X42)
| ~ in(X44,X43)
| ~ in(X44,X42) )
& ( X43 != set_difference(X41,X42)
| ~ in(X44,X43)
| in(X44,X41) ) ),
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)],[c_0_7])])])])])])]) ).
cnf(c_0_13,negated_conjecture,
set_difference(set_union2(esk10_0,esk11_0),esk11_0) != set_difference(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( X3 != set_difference(X4,X2)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
set_difference(set_union2(esk11_0,esk10_0),esk11_0) != set_difference(esk10_0,esk11_0),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( X3 = set_difference(X1,X2)
| in(esk5_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,lemma,
( ~ in(X1,set_difference(X3,X2))
| in(X1,set_union2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ in(esk5_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( ~ in(X1,X3)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X2 != set_union2(X3,X4)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,plain,
( ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| in(esk5_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
in(esk5_3(set_union2(esk11_0,esk10_0),esk11_0,set_difference(esk10_0,esk11_0)),set_union2(esk11_0,esk10_0)),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk5_3(set_union2(esk11_0,esk10_0),esk11_0,set_difference(esk10_0,esk11_0)),esk11_0),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21])]),c_0_22]) ).
cnf(c_0_27,plain,
( ~ in(X1,set_union2(X3,X2))
| in(X1,X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk5_3(set_union2(esk11_0,esk10_0),esk11_0,set_difference(esk10_0,esk11_0)),set_difference(esk10_0,esk11_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24])]),c_0_25])]),c_0_26]) ).
cnf(c_0_29,lemma,
( ~ in(X1,set_union2(X3,X2))
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_30,lemma,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 05:54:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 203.98/29.96 % Version: 3.5.1
% 203.98/29.96 % Preprocessing class: FSMSSMSSSSSNFFN.
% 203.98/29.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.98/29.96 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 203.98/29.96 % Starting new_bool_3 with 300s (1) cores
% 203.98/29.96 % Starting new_bool_1 with 300s (1) cores
% 203.98/29.96 % Starting sh5l with 300s (1) cores
% 203.98/29.96 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2571645 completed with status 0
% 203.98/29.96 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 203.98/29.96 % Preprocessing class: FSMSSMSSSSSNFFN.
% 203.98/29.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.98/29.96 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 203.98/29.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 203.98/29.96 % No SInE strategy applied
% 203.98/29.96 % Search class: FGHSM-FFMF32-SFFFFFNN
% 203.98/29.96 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 203.98/29.96 % Starting SubtermCWHack with 136s (1) cores
% 203.98/29.96 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 203.98/29.96 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 164s (1) cores
% 203.98/29.96 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 203.98/29.96 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A with 136s (1) cores
% 203.98/29.96 % G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A with pid 2571656 completed with status 0
% 203.98/29.96 % Result found by G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A
% 203.98/29.96 % Preprocessing class: FSMSSMSSSSSNFFN.
% 203.98/29.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.98/29.96 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 203.98/29.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 203.98/29.96 % No SInE strategy applied
% 203.98/29.96 % Search class: FGHSM-FFMF32-SFFFFFNN
% 203.98/29.96 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 203.98/29.96 % Starting SubtermCWHack with 136s (1) cores
% 203.98/29.96 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 203.98/29.96 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 164s (1) cores
% 203.98/29.96 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 203.98/29.96 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A with 136s (1) cores
% 203.98/29.96 % Preprocessing time : 0.003 s
% 203.98/29.96 % Presaturation interreduction done
% 203.98/29.96
% 203.98/29.96 % Proof found!
% 203.98/29.96 % SZS status Theorem
% 203.98/29.96 % SZS output start CNFRefutation
% See solution above
% 203.98/29.96 % Parsed axioms : 49
% 203.98/29.96 % Removed by relevancy pruning/SinE : 0
% 203.98/29.96 % Initial clauses : 76
% 203.98/29.96 % Removed in clause preprocessing : 4
% 203.98/29.96 % Initial clauses in saturation : 72
% 203.98/29.96 % Processed clauses : 25009
% 203.98/29.96 % ...of these trivial : 1067
% 203.98/29.96 % ...subsumed : 21669
% 203.98/29.96 % ...remaining for further processing : 2273
% 203.98/29.96 % Other redundant clauses eliminated : 11757
% 203.98/29.96 % Clauses deleted for lack of memory : 0
% 203.98/29.96 % Backward-subsumed : 101
% 203.98/29.96 % Backward-rewritten : 13
% 203.98/29.96 % Generated clauses : 1360356
% 203.98/29.96 % ...of the previous two non-redundant : 1279136
% 203.98/29.96 % ...aggressively subsumed : 0
% 203.98/29.96 % Contextual simplify-reflections : 47
% 203.98/29.96 % Paramodulations : 1348251
% 203.98/29.96 % Factorizations : 338
% 203.98/29.96 % NegExts : 0
% 203.98/29.96 % Equation resolutions : 11767
% 203.98/29.96 % Disequality decompositions : 0
% 203.98/29.96 % Total rewrite steps : 225230
% 203.98/29.96 % ...of those cached : 224627
% 203.98/29.96 % Propositional unsat checks : 0
% 203.98/29.96 % Propositional check models : 0
% 203.98/29.96 % Propositional check unsatisfiable : 0
% 203.98/29.96 % Propositional clauses : 0
% 203.98/29.96 % Propositional clauses after purity: 0
% 203.98/29.96 % Propositional unsat core size : 0
% 203.98/29.96 % Propositional preprocessing time : 0.000
% 203.98/29.96 % Propositional encoding time : 0.000
% 203.98/29.96 % Propositional solver time : 0.000
% 203.98/29.96 % Success case prop preproc time : 0.000
% 203.98/29.96 % Success case prop encoding time : 0.000
% 203.98/29.96 % Success case prop solver time : 0.000
% 203.98/29.96 % Current number of processed clauses : 2079
% 203.98/29.96 % Positive orientable unit clauses : 130
% 203.98/29.96 % Positive unorientable unit clauses: 2
% 203.98/29.96 % Negative unit clauses : 334
% 203.98/29.96 % Non-unit-clauses : 1613
% 203.98/29.96 % Current number of unprocessed clauses: 1250785
% 203.98/29.96 % ...number of literals in the above : 6654952
% 203.98/29.96 % Current number of archived formulas : 0
% 203.98/29.96 % Current number of archived clauses : 182
% 203.98/29.96 % Clause-clause subsumption calls (NU) : 570682
% 203.98/29.96 % Rec. Clause-clause subsumption calls : 306903
% 203.98/29.96 % Non-unit clause-clause subsumptions : 6519
% 203.98/29.96 % Unit Clause-clause subsumption calls : 21161
% 203.98/29.96 % Rewrite failures with RHS unbound : 0
% 203.98/29.96 % BW rewrite match attempts : 72
% 203.98/29.96 % BW rewrite match successes : 37
% 203.98/29.96 % Condensation attempts : 0
% 203.98/29.96 % Condensation successes : 0
% 203.98/29.96 % Termbank termtop insertions : 23509553
% 203.98/29.96 % Search garbage collected termcells : 1052
% 203.98/29.96
% 203.98/29.96 % -------------------------------------------------
% 203.98/29.96 % User time : 28.103 s
% 203.98/29.96 % System time : 0.960 s
% 203.98/29.96 % Total time : 29.063 s
% 203.98/29.96 % Maximum resident set size: 3412 pages
% 203.98/29.96
% 203.98/29.96 % -------------------------------------------------
% 203.98/29.96 % User time : 139.133 s
% 203.98/29.96 % System time : 5.233 s
% 203.98/29.96 % Total time : 144.366 s
% 203.98/29.96 % Maximum resident set size: 4608 pages
% 203.98/29.96 % E exiting
%------------------------------------------------------------------------------