%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:19:01 PM UTC 2026
% Result : Theorem 0.23s 0.59s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 66 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 31 ~; 21 |; 13 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 80 ( 11 sgn 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t104_zfmisc_1,axiom,
! [X1,X2,X3,X4,X5] :
~ ( ! [X6,X7] :
~ ( in(X7,set_intersection2(X3,X5))
& in(X6,set_intersection2(X2,X4))
& X1 = ordered_pair(X6,X7) )
& in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(t127_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( disjoint(X3,X4)
| disjoint(X1,X2) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(c_0_5,plain,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_6,plain,
! [X34,X35,X37,X38,X39] :
( ( ~ disjoint(X37,X38)
| ~ in(X39,set_intersection2(X37,X38)) )
& ( in(esk9_2(X34,X35),set_intersection2(X34,X35))
| disjoint(X34,X35) ) ),
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_5])])])])])]) ).
fof(c_0_7,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27)))
| in(esk4_5(X23,X24,X25,X26,X27),set_intersection2(X25,X27)) )
& ( ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27)))
| in(esk3_5(X23,X24,X25,X26,X27),set_intersection2(X24,X26)) )
& ( ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27)))
| X23 = ordered_pair(esk3_5(X23,X24,X25,X26,X27),esk4_5(X23,X24,X25,X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t104_zfmisc_1])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( disjoint(X3,X4)
| disjoint(X1,X2) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(assume_negation,[status(cth)],[t127_zfmisc_1]) ).
cnf(c_0_9,plain,
( ~ disjoint(X2,X3)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
| in(esk3_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X12,X13] : set_intersection2(X12,X13) = set_intersection2(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_12,plain,
! [X21,X22] :
( disjoint(X22,X21)
| ~ disjoint(X21,X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_13,negated_conjecture,
( ~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0))
& ( disjoint(esk7_0,esk8_0)
| disjoint(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_8])])])]) ).
cnf(c_0_14,plain,
( ~ in(X3,set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X5)))
| ~ disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( in(esk9_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
| in(esk4_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( disjoint(esk7_0,esk8_0)
| disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ disjoint(X1,X3)
| disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( ~ in(X3,set_intersection2(cartesian_product2(X4,X1),cartesian_product2(X5,X2)))
| ~ disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_23,plain,
( in(esk9_2(X1,X2),set_intersection2(X2,X1))
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( disjoint(esk8_0,esk7_0)
| disjoint(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ disjoint(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ disjoint(X4,X2)
| disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
disjoint(esk8_0,esk7_0),
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 05:46:02 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.55 Running first-order theorem proving
% 0.23/0.55 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
% 0.23/0.59 % Version: 3.5.1
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.59 % Starting sh5l with 300s (1) cores
% 0.23/0.59 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2131604 completed with status 0
% 0.23/0.59 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.59 % No SInE strategy applied
% 0.23/0.59 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.23/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.23/0.59 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.59 % SubtermCWHack with pid 2131608 completed with status 0
% 0.23/0.59 % Result found by SubtermCWHack
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.59 % No SInE strategy applied
% 0.23/0.59 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.23/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.59 % Preprocessing time : 0.001 s
% 0.23/0.59
% 0.23/0.59 % Proof found!
% 0.23/0.59 % SZS status Theorem
% 0.23/0.59 % SZS output start CNFRefutation
% See solution above
% 0.23/0.59 % Parsed axioms : 12
% 0.23/0.59 % Removed by relevancy pruning/SinE : 0
% 0.23/0.59 % Initial clauses : 16
% 0.23/0.59 % Removed in clause preprocessing : 1
% 0.23/0.59 % Initial clauses in saturation : 15
% 0.23/0.59 % Processed clauses : 98
% 0.23/0.59 % ...of these trivial : 1
% 0.23/0.59 % ...subsumed : 53
% 0.23/0.59 % ...remaining for further processing : 44
% 0.23/0.59 % Other redundant clauses eliminated : 0
% 0.23/0.59 % Clauses deleted for lack of memory : 0
% 0.23/0.59 % Backward-subsumed : 0
% 0.23/0.59 % Backward-rewritten : 0
% 0.23/0.59 % Generated clauses : 141
% 0.23/0.59 % ...of the previous two non-redundant : 131
% 0.23/0.59 % ...aggressively subsumed : 0
% 0.23/0.59 % Contextual simplify-reflections : 0
% 0.23/0.59 % Paramodulations : 139
% 0.23/0.59 % Factorizations : 0
% 0.23/0.59 % NegExts : 0
% 0.23/0.59 % Equation resolutions : 0
% 0.23/0.59 % Disequality decompositions : 0
% 0.23/0.59 % Total rewrite steps : 6
% 0.23/0.59 % ...of those cached : 2
% 0.23/0.59 % Propositional unsat checks : 0
% 0.23/0.59 % Propositional check models : 0
% 0.23/0.59 % Propositional check unsatisfiable : 0
% 0.23/0.59 % Propositional clauses : 0
% 0.23/0.59 % Propositional clauses after purity: 0
% 0.23/0.59 % Propositional unsat core size : 0
% 0.23/0.59 % Propositional preprocessing time : 0.000
% 0.23/0.59 % Propositional encoding time : 0.000
% 0.23/0.59 % Propositional solver time : 0.000
% 0.23/0.59 % Success case prop preproc time : 0.000
% 0.23/0.59 % Success case prop encoding time : 0.000
% 0.23/0.59 % Success case prop solver time : 0.000
% 0.23/0.59 % Current number of processed clauses : 42
% 0.23/0.59 % Positive orientable unit clauses : 4
% 0.23/0.59 % Positive unorientable unit clauses: 2
% 0.23/0.59 % Negative unit clauses : 8
% 0.23/0.59 % Non-unit-clauses : 28
% 0.23/0.59 % Current number of unprocessed clauses: 46
% 0.23/0.59 % ...number of literals in the above : 92
% 0.23/0.59 % Current number of archived formulas : 0
% 0.23/0.59 % Current number of archived clauses : 3
% 0.23/0.59 % Clause-clause subsumption calls (NU) : 180
% 0.23/0.59 % Rec. Clause-clause subsumption calls : 177
% 0.23/0.59 % Non-unit clause-clause subsumptions : 40
% 0.23/0.59 % Unit Clause-clause subsumption calls : 41
% 0.23/0.59 % Rewrite failures with RHS unbound : 0
% 0.23/0.59 % BW rewrite match attempts : 2
% 0.23/0.59 % BW rewrite match successes : 2
% 0.23/0.59 % Condensation attempts : 0
% 0.23/0.59 % Condensation successes : 0
% 0.23/0.59 % Termbank termtop insertions : 2183
% 0.23/0.59 % Search garbage collected termcells : 173
% 0.23/0.59
% 0.23/0.59 % -------------------------------------------------
% 0.23/0.59 % User time : 0.006 s
% 0.23/0.59 % System time : 0.006 s
% 0.23/0.59 % Total time : 0.012 s
% 0.23/0.59 % Maximum resident set size: 3592 pages
% 0.23/0.59
% 0.23/0.59 % -------------------------------------------------
% 0.23/0.59 % User time : 0.020 s
% 0.23/0.59 % System time : 0.017 s
% 0.23/0.59 % Total time : 0.036 s
% 0.23/0.59 % Maximum resident set size: 4864 pages
% 0.23/0.59 % E exiting
%------------------------------------------------------------------------------