%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU406+1 : 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 : n002.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 91 ( 14 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 43 ~; 32 |; 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,X1)
| r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
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(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,
! [X49,X50,X51,X52,X53,X54,X55,X56] :
( ( ~ r2_hidden(X52,X51)
| r2_hidden(X52,X49)
| r2_hidden(X52,X50)
| X51 != k2_xboole_0(X49,X50) )
& ( ~ r2_hidden(X53,X49)
| r2_hidden(X53,X51)
| X51 != k2_xboole_0(X49,X50) )
& ( ~ r2_hidden(X53,X50)
| r2_hidden(X53,X51)
| X51 != k2_xboole_0(X49,X50) )
& ( ~ r2_hidden(esk5_3(X54,X55,X56),X54)
| ~ r2_hidden(esk5_3(X54,X55,X56),X56)
| X56 = k2_xboole_0(X54,X55) )
& ( ~ r2_hidden(esk5_3(X54,X55,X56),X55)
| ~ r2_hidden(esk5_3(X54,X55,X56),X56)
| X56 = k2_xboole_0(X54,X55) )
& ( r2_hidden(esk5_3(X54,X55,X56),X56)
| r2_hidden(esk5_3(X54,X55,X56),X54)
| r2_hidden(esk5_3(X54,X55,X56),X55)
| X56 = k2_xboole_0(X54,X55) ) ),
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_5,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]) ).
cnf(c_0_6,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_4]) ).
fof(c_0_7,plain,
! [X72,X73] : k2_xboole_0(X72,k4_xboole_0(X73,X72)) = k2_xboole_0(X72,X73),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_8,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_5])])]) ).
fof(c_0_9,plain,
! [X47,X48] : k2_xboole_0(X47,X48) = k2_xboole_0(X48,X47),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_10,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,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(esk1_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,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,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_8]) ).
cnf(c_0_19,negated_conjecture,
( r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,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_8]) ).
cnf(c_0_21,negated_conjecture,
( r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| r2_hidden(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,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_8]) ).
cnf(c_0_24,negated_conjecture,
r2_hidden(esk2_0,esk4_0),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
r2_hidden(esk1_0,esk4_0),
inference(sr,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24])]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU406+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 03:03:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------