TSTP Solution File: SEU156+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU156+3 : TPTP v8.1.2. Released v3.2.0.
% 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 16:22:52 EDT 2023
% Result : Theorem 0.22s 0.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 57 ( 20 unt; 11 typ; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 27 ~; 29 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 9 sgn; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_23,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
singleton: $i > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_0: $i ).
tff(decl_28,type,
esk2_0: $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(t33_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t10_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[t33_zfmisc_1]) ).
fof(c_0_8,plain,
! [X7,X8] : ordered_pair(X7,X8) = unordered_pair(unordered_pair(X7,X8),singleton(X7)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X22] : unordered_pair(X22,X22) = singleton(X22),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_10,negated_conjecture,
( ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0)
& ( esk3_0 != esk5_0
| esk4_0 != esk6_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X5,X6] : unordered_pair(X5,X6) = unordered_pair(X6,X5),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_16,plain,
! [X14,X15,X16,X17] :
( unordered_pair(X14,X15) != unordered_pair(X16,X17)
| X14 = X16
| X14 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)) = unordered_pair(unordered_pair(esk3_0,esk4_0),unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X25,X26,X27] :
( singleton(X25) != unordered_pair(X26,X27)
| X25 = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
cnf(c_0_20,plain,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
unordered_pair(unordered_pair(esk3_0,esk3_0),unordered_pair(esk3_0,esk4_0)) = unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( X1 = unordered_pair(esk3_0,esk3_0)
| X1 = unordered_pair(esk3_0,esk4_0)
| unordered_pair(X1,X2) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
| unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( X1 = unordered_pair(esk3_0,esk4_0)
| X1 = unordered_pair(esk3_0,esk3_0)
| unordered_pair(X2,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0)
| X1 = esk3_0
| unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
fof(c_0_29,plain,
! [X28,X29,X30] :
( singleton(X28) != unordered_pair(X29,X30)
| X29 = X30 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
cnf(c_0_30,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk6_0) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
esk3_0 = esk5_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X4,X1) != unordered_pair(X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( esk3_0 != esk5_0
| esk4_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,plain,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_32,c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0)
| X1 = esk4_0
| X1 = esk5_0
| unordered_pair(X2,X1) != unordered_pair(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
esk4_0 != esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk3_0,esk3_0)
| unordered_pair(X1,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_40,negated_conjecture,
esk6_0 = esk5_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]),c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
| unordered_pair(X1,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk5_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_31]),c_0_31]),c_0_31]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk5_0),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_43,negated_conjecture,
esk4_0 != esk5_0,
inference(rw,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU156+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % 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 14:03:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.22/0.57 start to proof: theBenchmark
% 0.22/0.60 % Version : CSE_E---1.5
% 0.22/0.60 % Problem : theBenchmark.p
% 0.22/0.60 % Proof found
% 0.22/0.60 % SZS status Theorem for theBenchmark.p
% 0.22/0.60 % SZS output start Proof
% See solution above
% 0.22/0.60 % Total time : 0.016000 s
% 0.22/0.60 % SZS output end Proof
% 0.22/0.60 % Total time : 0.019000 s
%------------------------------------------------------------------------------