TSTP Solution File: SEU126+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 16:22:34 EDT 2023
% Result : Theorem 0.20s 0.75s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 33 ( 8 unt; 11 typ; 0 def)
% Number of atoms : 68 ( 21 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 69 ( 23 ~; 32 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
tff(decl_32,type,
esk6_0: $i ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_xboole_1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(c_0_4,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( ~ in(X14,X13)
| in(X14,X11)
| in(X14,X12)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X11)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X12)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(esk1_3(X16,X17,X18),X16)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( ~ in(esk1_3(X16,X17,X18),X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X18)
| in(esk1_3(X16,X17,X18),X16)
| in(esk1_3(X16,X17,X18),X17)
| X18 = set_union2(X16,X17) ) ),
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])])])])])]) ).
cnf(c_0_5,plain,
( in(esk1_3(X1,X2,X3),X3)
| in(esk1_3(X1,X2,X3),X1)
| in(esk1_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X20,X21,X22,X23,X24] :
( ( ~ subset(X20,X21)
| ~ in(X22,X20)
| in(X22,X21) )
& ( in(esk2_2(X23,X24),X23)
| subset(X23,X24) )
& ( ~ in(esk2_2(X23,X24),X24)
| subset(X23,X24) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_7,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk1_3(X1,X2,X3),X2)
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X1)
| in(esk1_3(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[t12_xboole_1]) ).
cnf(c_0_10,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
fof(c_0_12,negated_conjecture,
( subset(esk5_0,esk6_0)
& set_union2(esk5_0,esk6_0) != esk6_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_14,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X3)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
set_union2(esk5_0,esk6_0) != esk6_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( set_union2(esk5_0,X1) = X1
| in(esk1_3(esk5_0,X1,X1),esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
set_union2(esk6_0,esk5_0) != esk6_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk1_3(esk5_0,esk6_0,esk6_0),esk6_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_17]),c_0_19]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_17]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n015.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 19:29:05 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.75 % Version : CSE_E---1.5
% 0.20/0.75 % Problem : theBenchmark.p
% 0.20/0.75 % Proof found
% 0.20/0.75 % SZS status Theorem for theBenchmark.p
% 0.20/0.75 % SZS output start Proof
% See solution above
% 0.20/0.76 % Total time : 0.181000 s
% 0.20/0.76 % SZS output end Proof
% 0.20/0.76 % Total time : 0.184000 s
%------------------------------------------------------------------------------