TSTP Solution File: SEU406+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : Thu Aug 31 16:25:30 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 43 ( 15 unt; 14 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
k2_xboole_0: ( $i * $i ) > $i ).
tff(decl_23,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_24,type,
k4_xboole_0: ( $i * $i ) > $i ).
tff(decl_25,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_26,type,
k1_xboole_0: $i ).
tff(decl_27,type,
v1_xboole_0: $i > $o ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk6_1: $i > $i ).
tff(decl_34,type,
esk7_0: $i ).
tff(decl_35,type,
esk8_0: $i ).
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,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( ~ r2_hidden(X16,X15)
| r2_hidden(X16,X13)
| r2_hidden(X16,X14)
| X15 != k2_xboole_0(X13,X14) )
& ( ~ r2_hidden(X17,X13)
| r2_hidden(X17,X15)
| X15 != k2_xboole_0(X13,X14) )
& ( ~ r2_hidden(X17,X14)
| r2_hidden(X17,X15)
| X15 != k2_xboole_0(X13,X14) )
& ( ~ 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),X19)
| ~ 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),X18)
| r2_hidden(esk5_3(X18,X19,X20),X19)
| X20 = k2_xboole_0(X18,X19) ) ),
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,
! [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(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,
! [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,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
% 0.00/0.13 % Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 17:32:11 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.015000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.018000 s
%------------------------------------------------------------------------------