%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU406+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:25:00 PM UTC 2026
% Result : Theorem 9.37s 2.13s
% Output : CNFRefutation 9.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 115 ( 24 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 121 ( 49 ~; 35 |; 31 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 3 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d4_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/sandbox2/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
=> r1_xboole_0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',symmetry_r1_xboole_0) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : r1_xboole_0(k4_xboole_0(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t79_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(t83_xboole_1,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
<=> k4_xboole_0(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t83_xboole_1) ).
fof(t40_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t40_xboole_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/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t39_xboole_1) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_9,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]) ).
fof(c_0_10,plain,
! [X572,X573] :
( r1_xboole_0(X573,X572)
| ~ r1_xboole_0(X572,X573) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_11,plain,
! [X126,X127] : r1_xboole_0(k4_xboole_0(X126,X127),X127),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
fof(c_0_12,plain,
! [X54,X55,X56,X57,X58,X59,X60,X61] :
( ( X61 = k4_xboole_0(X59,X60)
| r2_hidden(esk8_3(X59,X60,X61),X61)
| ~ r2_hidden(esk8_3(X59,X60,X61),X60) )
& ( X61 = k4_xboole_0(X59,X60)
| r2_hidden(esk8_3(X59,X60,X61),X61)
| r2_hidden(esk8_3(X59,X60,X61),X59) )
& ( X61 = k4_xboole_0(X59,X60)
| r2_hidden(esk8_3(X59,X60,X61),X60)
| ~ r2_hidden(esk8_3(X59,X60,X61),X59)
| ~ r2_hidden(esk8_3(X59,X60,X61),X61) )
& ( X56 != k4_xboole_0(X54,X55)
| r2_hidden(X58,X56)
| r2_hidden(X58,X55)
| ~ r2_hidden(X58,X54) )
& ( X56 != k4_xboole_0(X54,X55)
| ~ r2_hidden(X57,X56)
| ~ r2_hidden(X57,X55) )
& ( X56 != k4_xboole_0(X54,X55)
| ~ r2_hidden(X57,X56)
| r2_hidden(X57,X54) ) ),
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_8])])])])])])]) ).
fof(c_0_13,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_9])])])]) ).
fof(c_0_14,plain,
! [X229,X230] : k2_xboole_0(X229,X230) = k2_xboole_0(X230,X229),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_15,plain,
! [X136,X137] :
( ( r1_xboole_0(X136,X137)
| k4_xboole_0(X136,X137) != X136 )
& ( k4_xboole_0(X136,X137) = X136
| ~ r1_xboole_0(X136,X137) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])])]) ).
cnf(c_0_16,plain,
( ~ r1_xboole_0(X1,X2)
| r1_xboole_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
r1_xboole_0(k4_xboole_0(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( X4 != k4_xboole_0(X2,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X85,X86] : k4_xboole_0(k2_xboole_0(X85,X86),X86) = k4_xboole_0(X85,X86),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(c_0_22,plain,
! [X83,X84] : k2_xboole_0(X83,k4_xboole_0(X84,X83)) = k2_xboole_0(X83,X84),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_23,plain,
( ~ r1_xboole_0(X1,X2)
| k4_xboole_0(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
r1_xboole_0(X1,k4_xboole_0(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
( ~ r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,negated_conjecture,
( r2_hidden(esk2_0,X1)
| r2_hidden(esk2_0,k4_xboole_0(k2_xboole_0(esk4_0,esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_34,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_13]) ).
cnf(c_0_35,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_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,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_13]) ).
cnf(c_0_38,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_13]) ).
cnf(c_0_39,negated_conjecture,
( r2_hidden(esk1_0,X1)
| r2_hidden(esk1_0,k4_xboole_0(k2_xboole_0(esk4_0,esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU406+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.45 % Computer : n006.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Mon Sep 21 06:20:45 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 9.37/2.13 % Version: 3.5.1
% 9.37/2.13 % Preprocessing class: FMLMSMLLSSSNFFN.
% 9.37/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.37/2.13 % Starting new_bool_3 with 900s (3) cores
% 9.37/2.13 % Starting new_bool_1 with 900s (3) cores
% 9.37/2.13 % Starting sh5l with 300s (1) cores
% 9.37/2.13 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2p with 300s (1) cores
% 9.37/2.13 % new_bool_3 with pid 2172580 completed with status 0
% 9.37/2.13 % Result found by new_bool_3
% 9.37/2.13 % Preprocessing class: FMLMSMLLSSSNFFN.
% 9.37/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.37/2.13 % Starting new_bool_3 with 900s (3) cores
% 9.37/2.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.37/2.13 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.37/2.13 % Search class: FGHSM-SSLM32-MFFFFFNN
% 9.37/2.13 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 9.37/2.13 % Starting SubtermCWHack with 82s (1) cores
% 9.37/2.13 % Starting new_bool_3 with 91s (1) cores
% 9.37/2.13 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 9.37/2.13 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2172587 completed with status 0
% 9.37/2.13 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 9.37/2.13 % Preprocessing class: FMLMSMLLSSSNFFN.
% 9.37/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.37/2.13 % Starting new_bool_3 with 900s (3) cores
% 9.37/2.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.37/2.13 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.37/2.13 % Search class: FGHSM-SSLM32-MFFFFFNN
% 9.37/2.13 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 9.37/2.13 % Starting SubtermCWHack with 82s (1) cores
% 9.37/2.13 % Starting new_bool_3 with 91s (1) cores
% 9.37/2.13 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 9.37/2.13 % Preprocessing time : 0.023 s
% 9.37/2.13 % Presaturation interreduction done
% 9.37/2.13
% 9.37/2.13 % Proof found!
% 9.37/2.13 % SZS status Theorem
% 9.37/2.13 % SZS output start CNFRefutation
% See solution above
% 9.37/2.13 % Parsed axioms : 4434
% 9.37/2.13 % Removed by relevancy pruning/SinE : 3811
% 9.37/2.13 % Initial clauses : 1092
% 9.37/2.13 % Removed in clause preprocessing : 32
% 9.37/2.13 % Initial clauses in saturation : 1060
% 9.37/2.13 % Processed clauses : 10586
% 9.37/2.13 % ...of these trivial : 63
% 9.37/2.13 % ...subsumed : 7103
% 9.37/2.13 % ...remaining for further processing : 3419
% 9.37/2.13 % Other redundant clauses eliminated : 598
% 9.37/2.13 % Clauses deleted for lack of memory : 0
% 9.37/2.13 % Backward-subsumed : 97
% 9.37/2.13 % Backward-rewritten : 66
% 9.37/2.13 % Generated clauses : 46528
% 9.37/2.13 % ...of the previous two non-redundant : 41781
% 9.37/2.13 % ...aggressively subsumed : 0
% 9.37/2.13 % Contextual simplify-reflections : 52
% 9.37/2.13 % Paramodulations : 45901
% 9.37/2.13 % Factorizations : 22
% 9.37/2.13 % NegExts : 0
% 9.37/2.13 % Equation resolutions : 611
% 9.37/2.13 % Disequality decompositions : 0
% 9.37/2.13 % Total rewrite steps : 14732
% 9.37/2.13 % ...of those cached : 12377
% 9.37/2.13 % Propositional unsat checks : 0
% 9.37/2.13 % Propositional check models : 0
% 9.37/2.13 % Propositional check unsatisfiable : 0
% 9.37/2.13 % Propositional clauses : 0
% 9.37/2.13 % Propositional clauses after purity: 0
% 9.37/2.13 % Propositional unsat core size : 0
% 9.37/2.13 % Propositional preprocessing time : 0.000
% 9.37/2.13 % Propositional encoding time : 0.000
% 9.37/2.13 % Propositional solver time : 0.000
% 9.37/2.13 % Success case prop preproc time : 0.000
% 9.37/2.13 % Success case prop encoding time : 0.000
% 9.37/2.13 % Success case prop solver time : 0.000
% 9.37/2.13 % Current number of processed clauses : 2186
% 9.37/2.13 % Positive orientable unit clauses : 304
% 9.37/2.13 % Positive unorientable unit clauses: 3
% 9.37/2.13 % Negative unit clauses : 401
% 9.37/2.13 % Non-unit-clauses : 1478
% 9.37/2.13 % Current number of unprocessed clauses: 33133
% 9.37/2.13 % ...number of literals in the above : 101289
% 9.37/2.13 % Current number of archived formulas : 0
% 9.37/2.13 % Current number of archived clauses : 1125
% 9.37/2.13 % Clause-clause subsumption calls (NU) : 1057623
% 9.37/2.13 % Rec. Clause-clause subsumption calls : 509348
% 9.37/2.13 % Non-unit clause-clause subsumptions : 2680
% 9.37/2.13 % Unit Clause-clause subsumption calls : 80067
% 9.37/2.13 % Rewrite failures with RHS unbound : 0
% 9.37/2.13 % BW rewrite match attempts : 284
% 9.37/2.13 % BW rewrite match successes : 171
% 9.37/2.13 % Condensation attempts : 0
% 9.37/2.13 % Condensation successes : 0
% 9.37/2.13 % Termbank termtop insertions : 664727
% 9.37/2.13 % Search garbage collected termcells : 47978
% 9.37/2.13
% 9.37/2.13 % -------------------------------------------------
% 9.37/2.13 % User time : 1.229 s
% 9.37/2.13 % System time : 0.052 s
% 9.37/2.13 % Total time : 1.281 s
% 9.37/2.13 % Maximum resident set size: 12328 pages
% 9.37/2.13
% 9.37/2.13 % -------------------------------------------------
% 9.37/2.13 % User time : 3.640 s
% 9.37/2.13 % System time : 0.155 s
% 9.37/2.13 % Total time : 3.795 s
% 9.37/2.13 % Maximum resident set size: 10240 pages
% 9.37/2.13 % E exiting
%------------------------------------------------------------------------------