TSTP Solution File: SEU187+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU187+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 : n003.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 16:23:10 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 61 ( 10 unt; 22 typ; 0 def)
% Number of atoms : 116 ( 38 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 128 ( 51 ~; 60 |; 9 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 17 >; 13 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 70 ( 5 sgn; 36 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
relation: $i > $o ).
tff(decl_25,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
relation_dom: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_rng: $i > $i ).
tff(decl_29,type,
singleton: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk7_1: $i > $i ).
tff(decl_39,type,
esk8_0: $i ).
tff(decl_40,type,
esk9_0: $i ).
tff(decl_41,type,
esk10_0: $i ).
tff(decl_42,type,
esk11_0: $i ).
tff(decl_43,type,
esk12_2: ( $i * $i ) > $i ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_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(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(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(t60_relat_1,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_9,plain,
! [X10,X11,X12,X14,X15,X16,X18] :
( ( ~ in(X12,X11)
| in(ordered_pair(X12,esk1_3(X10,X11,X12)),X10)
| X11 != relation_dom(X10)
| ~ relation(X10) )
& ( ~ in(ordered_pair(X14,X15),X10)
| in(X14,X11)
| X11 != relation_dom(X10)
| ~ relation(X10) )
& ( ~ in(esk2_2(X10,X16),X16)
| ~ in(ordered_pair(esk2_2(X10,X16),X18),X10)
| X16 = relation_dom(X10)
| ~ relation(X10) )
& ( in(esk2_2(X10,X16),X16)
| in(ordered_pair(esk2_2(X10,X16),esk3_2(X10,X16)),X10)
| X16 = relation_dom(X10)
| ~ relation(X10) ) ),
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)],[d4_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X30,X31] : ordered_pair(X30,X31) = unordered_pair(unordered_pair(X30,X31),singleton(X30)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_11,plain,
( in(esk2_2(X1,X2),X2)
| in(ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_14,plain,
! [X20,X21,X22,X24,X25,X26,X28] :
( ( ~ in(X22,X21)
| in(ordered_pair(esk4_3(X20,X21,X22),X22),X20)
| X21 != relation_rng(X20)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X25,X24),X20)
| in(X24,X21)
| X21 != relation_rng(X20)
| ~ relation(X20) )
& ( ~ in(esk5_2(X20,X26),X26)
| ~ in(ordered_pair(X28,esk5_2(X20,X26)),X20)
| X26 = relation_rng(X20)
| ~ relation(X20) )
& ( in(esk5_2(X20,X26),X26)
| in(ordered_pair(esk6_2(X20,X26),esk5_2(X20,X26)),X20)
| X26 = relation_rng(X20)
| ~ relation(X20) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(c_0_15,plain,
! [X53,X54] :
( ~ in(X53,X54)
| ~ empty(X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_16,plain,
( X2 = relation_dom(X1)
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),singleton(esk2_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X7] :
( ~ empty(X7)
| relation(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
cnf(c_0_19,plain,
( in(esk5_2(X1,X2),X2)
| in(ordered_pair(esk6_2(X1,X2),esk5_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[t60_relat_1]) ).
cnf(c_0_21,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk2_2(X2,X1)),unordered_pair(esk2_2(X2,X1),esk3_2(X2,X1))),X2)
| in(esk2_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( X2 = relation_rng(X1)
| in(esk5_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk6_2(X1,X2),esk5_2(X1,X2)),singleton(esk6_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_12]) ).
fof(c_0_25,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( X1 = relation_dom(X2)
| in(esk2_2(X2,X1),X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
fof(c_0_27,plain,
! [X52] :
( ~ empty(X52)
| X52 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_28,plain,
( X1 = relation_rng(X2)
| in(unordered_pair(singleton(esk6_2(X2,X1)),unordered_pair(esk5_2(X2,X1),esk6_2(X2,X1))),X2)
| in(esk5_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17]) ).
cnf(c_0_29,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( X1 = relation_dom(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_31,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_32,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( X1 = relation_rng(X2)
| in(esk5_2(X2,X1),X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( relation_rng(empty_set) != empty_set
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_35,plain,
( X1 = relation_rng(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( ~ empty(X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31])]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
~ empty(X1),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_38,plain,
$false,
inference(sr,[status(thm)],[c_0_31,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU187+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 18:57:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.012000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.015000 s
%------------------------------------------------------------------------------