%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 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 02:24:59 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 89 ( 14 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 44 ~; 31 |; 28 &)
% ( 2 <=>; 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t1_latsum_1,conjecture,
! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(c_0_4,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = k2_xboole_0(X18,X19)
| r2_hidden(esk5_3(X18,X19,X20),X19)
| r2_hidden(esk5_3(X18,X19,X20),X18)
| r2_hidden(esk5_3(X18,X19,X20),X20) )
& ( X20 = k2_xboole_0(X18,X19)
| ~ r2_hidden(esk5_3(X18,X19,X20),X20)
| ~ r2_hidden(esk5_3(X18,X19,X20),X19) )
& ( X20 = k2_xboole_0(X18,X19)
| ~ r2_hidden(esk5_3(X18,X19,X20),X20)
| ~ r2_hidden(esk5_3(X18,X19,X20),X18) )
& ( X15 != k2_xboole_0(X13,X14)
| r2_hidden(X17,X15)
| ~ r2_hidden(X17,X14) )
& ( X15 != k2_xboole_0(X13,X14)
| r2_hidden(X17,X15)
| ~ r2_hidden(X17,X13) )
& ( X15 != k2_xboole_0(X13,X14)
| r2_hidden(X16,X14)
| r2_hidden(X16,X13)
| ~ r2_hidden(X16,X15) ) ),
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_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
cnf(c_0_6,plain,
( X2 != k2_xboole_0(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X36,X37] : k2_xboole_0(X36,k4_xboole_0(X37,X36)) = k2_xboole_0(X36,X37),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_8,negated_conjecture,
( ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_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,
! [X11,X12] : k2_xboole_0(X11,X12) = k2_xboole_0(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_10,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
~ r2_hidden(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_18,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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 06:22:03 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2190954 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2190960 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Preprocessing time : 0.002 s
% 0.14/0.45 % Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 24
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 34
% 0.14/0.45 % Removed in clause preprocessing : 4
% 0.14/0.45 % Initial clauses in saturation : 30
% 0.14/0.45 % Processed clauses : 204
% 0.14/0.45 % ...of these trivial : 1
% 0.14/0.45 % ...subsumed : 83
% 0.14/0.45 % ...remaining for further processing : 119
% 0.14/0.45 % Other redundant clauses eliminated : 3
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 12
% 0.14/0.45 % Backward-rewritten : 5
% 0.14/0.45 % Generated clauses : 268
% 0.14/0.45 % ...of the previous two non-redundant : 229
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 1
% 0.14/0.45 % Paramodulations : 256
% 0.14/0.45 % Factorizations : 6
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 3
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 56
% 0.14/0.45 % ...of those cached : 39
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 66
% 0.14/0.45 % Positive orientable unit clauses : 14
% 0.14/0.45 % Positive unorientable unit clauses: 1
% 0.14/0.45 % Negative unit clauses : 12
% 0.14/0.45 % Non-unit-clauses : 39
% 0.14/0.45 % Current number of unprocessed clauses: 85
% 0.14/0.45 % ...number of literals in the above : 260
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 50
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 693
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 618
% 0.14/0.45 % Non-unit clause-clause subsumptions : 74
% 0.14/0.45 % Unit Clause-clause subsumption calls : 78
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 30
% 0.14/0.45 % BW rewrite match successes : 24
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 4105
% 0.14/0.45 % Search garbage collected termcells : 346
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.012 s
% 0.14/0.45 % System time : 0.006 s
% 0.14/0.45 % Total time : 0.017 s
% 0.14/0.45 % Maximum resident set size: 3648 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.060 s
% 0.14/0.45 % System time : 0.018 s
% 0.14/0.45 % Total time : 0.078 s
% 0.14/0.45 % Maximum resident set size: 4608 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------