%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU406+2 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:12:11 PM UTC 2026
% Result : Theorem 4.94s 4.40s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 121 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 148 ( 58 ~; 49 |; 35 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1_latsum_1,conjecture,
! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
& ~ r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d4_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(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)) ) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
& ~ r2_hidden(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_6,plain,
! [X1496,X1497,X1498,X1499,X1500,X1501,X1502,X1503] :
( ( ~ r2_hidden(X1499,X1498)
| r2_hidden(X1499,X1496)
| r2_hidden(X1499,X1497)
| X1498 != k2_xboole_0(X1496,X1497) )
& ( ~ r2_hidden(X1500,X1496)
| r2_hidden(X1500,X1498)
| X1498 != k2_xboole_0(X1496,X1497) )
& ( ~ r2_hidden(X1500,X1497)
| r2_hidden(X1500,X1498)
| X1498 != k2_xboole_0(X1496,X1497) )
& ( ~ r2_hidden(esk8_3(X1501,X1502,X1503),X1501)
| ~ r2_hidden(esk8_3(X1501,X1502,X1503),X1503)
| X1503 = k2_xboole_0(X1501,X1502) )
& ( ~ r2_hidden(esk8_3(X1501,X1502,X1503),X1502)
| ~ r2_hidden(esk8_3(X1501,X1502,X1503),X1503)
| X1503 = k2_xboole_0(X1501,X1502) )
& ( r2_hidden(esk8_3(X1501,X1502,X1503),X1503)
| r2_hidden(esk8_3(X1501,X1502,X1503),X1501)
| r2_hidden(esk8_3(X1501,X1502,X1503),X1502)
| X1503 = k2_xboole_0(X1501,X1502) ) ),
inference(distribute,[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,negated_conjecture,
( r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& ( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ 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)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X1505,X1506] : k2_xboole_0(X1505,X1506) = k2_xboole_0(X1506,X1505),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_9,plain,
! [X1366,X1367,X1368,X1369,X1370,X1371,X1372,X1373] :
( ( r2_hidden(X1369,X1366)
| ~ r2_hidden(X1369,X1368)
| X1368 != k4_xboole_0(X1366,X1367) )
& ( ~ r2_hidden(X1369,X1367)
| ~ r2_hidden(X1369,X1368)
| X1368 != k4_xboole_0(X1366,X1367) )
& ( ~ r2_hidden(X1370,X1366)
| r2_hidden(X1370,X1367)
| r2_hidden(X1370,X1368)
| X1368 != k4_xboole_0(X1366,X1367) )
& ( ~ r2_hidden(esk7_3(X1371,X1372,X1373),X1373)
| ~ r2_hidden(esk7_3(X1371,X1372,X1373),X1371)
| r2_hidden(esk7_3(X1371,X1372,X1373),X1372)
| X1373 = k4_xboole_0(X1371,X1372) )
& ( r2_hidden(esk7_3(X1371,X1372,X1373),X1371)
| r2_hidden(esk7_3(X1371,X1372,X1373),X1373)
| X1373 = k4_xboole_0(X1371,X1372) )
& ( ~ r2_hidden(esk7_3(X1371,X1372,X1373),X1372)
| r2_hidden(esk7_3(X1371,X1372,X1373),X1373)
| X1373 = k4_xboole_0(X1371,X1372) ) ),
inference(distribute,[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])])])])])]) ).
cnf(c_0_10,plain,
( r2_hidden(X1,X3)
| r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| X2 != k2_xboole_0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( r2_hidden(X1,X3)
| r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| X4 != k4_xboole_0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( r2_hidden(esk2_0,esk3_0)
| r2_hidden(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( r2_hidden(esk1_0,esk3_0)
| r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
r2_hidden(esk1_0,esk3_0),
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ r2_hidden(esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_25])]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
r2_hidden(esk2_0,esk3_0),
inference(sr,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_28])]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_25])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU406+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 03:03:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.94/4.40 % Version : CSE_E---1.7
% 4.94/4.40 % Problem : theBenchmark.p
% 4.94/4.40 % SZS status Theorem for theBenchmark.p
% 4.94/4.40 % SZS output start CNFRefutation
% See solution above
% 4.94/4.41 % Total time : 3.714s
%------------------------------------------------------------------------------