TSTP Solution File: SEU204+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU204+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 : n011.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 16:23:18 EDT 2023
% Result : Theorem 62.35s 62.43s
% Output : CNFRefutation 62.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 202
% Syntax : Number of formulae : 226 ( 9 unt; 196 typ; 0 def)
% Number of atoms : 113 ( 22 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 138 ( 55 ~; 61 |; 12 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 21 >; 18 *; 0 +; 0 <<)
% Number of predicates : 175 ( 173 usr; 169 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-4 aty)
% Number of variables : 86 ( 3 sgn; 43 !; 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_image: ( $i * $i ) > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
subset: ( $i * $i ) > $o ).
tff(decl_29,type,
relation_rng: $i > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk8_1: $i > $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_1: $i > $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_1: $i > $i ).
tff(decl_47,type,
esk14_0: $i ).
tff(decl_48,type,
esk15_0: $i ).
tff(decl_49,type,
esk16_0: $i ).
tff(decl_50,type,
epred1_0: $o ).
tff(decl_51,type,
epred2_0: $o ).
tff(decl_52,type,
epred3_0: $o ).
tff(decl_53,type,
epred4_0: $o ).
tff(decl_54,type,
epred5_0: $o ).
tff(decl_55,type,
epred6_0: $o ).
tff(decl_56,type,
epred7_0: $o ).
tff(decl_57,type,
epred8_0: $o ).
tff(decl_58,type,
epred9_0: $o ).
tff(decl_59,type,
epred10_0: $o ).
tff(decl_60,type,
epred11_0: $o ).
tff(decl_61,type,
epred12_0: $o ).
tff(decl_62,type,
epred13_0: $o ).
tff(decl_63,type,
epred14_0: $o ).
tff(decl_64,type,
epred15_0: $o ).
tff(decl_65,type,
epred16_0: $o ).
tff(decl_66,type,
epred17_0: $o ).
tff(decl_67,type,
epred18_0: $o ).
tff(decl_68,type,
epred19_0: $o ).
tff(decl_69,type,
epred20_0: $o ).
tff(decl_70,type,
epred21_0: $o ).
tff(decl_71,type,
epred22_0: $o ).
tff(decl_72,type,
epred23_0: $o ).
tff(decl_73,type,
epred24_0: $o ).
tff(decl_74,type,
epred25_0: $o ).
tff(decl_75,type,
epred26_0: $o ).
tff(decl_76,type,
epred27_0: $o ).
tff(decl_77,type,
epred28_0: $o ).
tff(decl_78,type,
epred29_0: $o ).
tff(decl_79,type,
epred30_0: $o ).
tff(decl_80,type,
epred31_0: $o ).
tff(decl_81,type,
epred32_0: $o ).
tff(decl_82,type,
epred33_0: $o ).
tff(decl_83,type,
epred34_0: $o ).
tff(decl_84,type,
epred35_0: $o ).
tff(decl_85,type,
epred36_0: $o ).
tff(decl_86,type,
epred37_0: $o ).
tff(decl_87,type,
epred38_0: $o ).
tff(decl_88,type,
epred39_0: $o ).
tff(decl_89,type,
epred40_0: $o ).
tff(decl_90,type,
epred41_0: $o ).
tff(decl_91,type,
epred42_0: $o ).
tff(decl_92,type,
epred43_0: $o ).
tff(decl_93,type,
epred44_0: $o ).
tff(decl_94,type,
epred45_0: $o ).
tff(decl_95,type,
epred46_0: $o ).
tff(decl_96,type,
epred47_0: $o ).
tff(decl_97,type,
epred48_0: $o ).
tff(decl_98,type,
epred49_0: $o ).
tff(decl_99,type,
epred50_0: $o ).
tff(decl_100,type,
epred51_0: $o ).
tff(decl_101,type,
epred52_0: $o ).
tff(decl_102,type,
epred53_0: $o ).
tff(decl_103,type,
epred54_0: $o ).
tff(decl_104,type,
epred55_0: $o ).
tff(decl_105,type,
epred56_0: $o ).
tff(decl_106,type,
epred57_0: $o ).
tff(decl_107,type,
epred58_0: $o ).
tff(decl_108,type,
epred59_0: $o ).
tff(decl_109,type,
epred60_0: $o ).
tff(decl_110,type,
epred61_0: $o ).
tff(decl_111,type,
epred62_0: $o ).
tff(decl_112,type,
epred63_0: $o ).
tff(decl_113,type,
epred64_0: $o ).
tff(decl_114,type,
epred65_0: $o ).
tff(decl_115,type,
epred66_0: $o ).
tff(decl_116,type,
epred67_0: $o ).
tff(decl_117,type,
epred68_0: $o ).
tff(decl_118,type,
epred69_0: $o ).
tff(decl_119,type,
epred70_0: $o ).
tff(decl_120,type,
epred71_0: $o ).
tff(decl_121,type,
epred72_0: $o ).
tff(decl_122,type,
epred73_0: $o ).
tff(decl_123,type,
epred74_0: $o ).
tff(decl_124,type,
epred75_0: $o ).
tff(decl_125,type,
epred76_0: $o ).
tff(decl_126,type,
epred77_0: $o ).
tff(decl_127,type,
epred78_0: $o ).
tff(decl_128,type,
epred79_0: $o ).
tff(decl_129,type,
epred80_0: $o ).
tff(decl_130,type,
epred81_0: $o ).
tff(decl_131,type,
epred82_0: $o ).
tff(decl_132,type,
epred83_0: $o ).
tff(decl_133,type,
epred84_0: $o ).
tff(decl_134,type,
epred85_0: $o ).
tff(decl_135,type,
epred86_0: $o ).
tff(decl_136,type,
epred87_0: $o ).
tff(decl_137,type,
epred88_0: $o ).
tff(decl_138,type,
epred89_0: $o ).
tff(decl_139,type,
epred90_0: $o ).
tff(decl_140,type,
epred91_0: $o ).
tff(decl_141,type,
epred92_0: $o ).
tff(decl_142,type,
epred93_0: $o ).
tff(decl_143,type,
epred94_0: $o ).
tff(decl_144,type,
epred95_0: $o ).
tff(decl_145,type,
epred96_0: $o ).
tff(decl_146,type,
epred97_0: $o ).
tff(decl_147,type,
epred98_0: $o ).
tff(decl_148,type,
epred99_0: $o ).
tff(decl_149,type,
epred100_0: $o ).
tff(decl_150,type,
epred101_0: $o ).
tff(decl_151,type,
epred102_0: $o ).
tff(decl_152,type,
epred103_0: $o ).
tff(decl_153,type,
epred104_0: $o ).
tff(decl_154,type,
epred105_0: $o ).
tff(decl_155,type,
epred106_0: $o ).
tff(decl_156,type,
epred107_0: $o ).
tff(decl_157,type,
epred108_0: $o ).
tff(decl_158,type,
epred109_0: $o ).
tff(decl_159,type,
epred110_0: $o ).
tff(decl_160,type,
epred111_0: $o ).
tff(decl_161,type,
epred112_0: $o ).
tff(decl_162,type,
epred113_0: $o ).
tff(decl_163,type,
epred114_0: $o ).
tff(decl_164,type,
epred115_0: $o ).
tff(decl_165,type,
epred116_0: $o ).
tff(decl_166,type,
epred117_0: $o ).
tff(decl_167,type,
epred118_0: $o ).
tff(decl_168,type,
epred119_0: $o ).
tff(decl_169,type,
epred120_0: $o ).
tff(decl_170,type,
epred121_0: $o ).
tff(decl_171,type,
epred122_0: $o ).
tff(decl_172,type,
epred123_0: $o ).
tff(decl_173,type,
epred124_0: $o ).
tff(decl_174,type,
epred125_0: $o ).
tff(decl_175,type,
epred126_0: $o ).
tff(decl_176,type,
epred127_0: $o ).
tff(decl_177,type,
epred128_0: $o ).
tff(decl_178,type,
epred129_0: $o ).
tff(decl_179,type,
epred130_0: $o ).
tff(decl_180,type,
epred131_0: $o ).
tff(decl_181,type,
epred132_0: $o ).
tff(decl_182,type,
epred133_0: $o ).
tff(decl_183,type,
epred134_0: $o ).
tff(decl_184,type,
epred135_0: $o ).
tff(decl_185,type,
epred136_0: $o ).
tff(decl_186,type,
epred137_0: $o ).
tff(decl_187,type,
epred138_0: $o ).
tff(decl_188,type,
epred139_0: $o ).
tff(decl_189,type,
epred140_0: $o ).
tff(decl_190,type,
epred141_0: $o ).
tff(decl_191,type,
epred142_0: $o ).
tff(decl_192,type,
epred143_0: $o ).
tff(decl_193,type,
epred144_0: $o ).
tff(decl_194,type,
epred145_0: $o ).
tff(decl_195,type,
epred146_0: $o ).
tff(decl_196,type,
epred147_0: $o ).
tff(decl_197,type,
epred148_0: $o ).
tff(decl_198,type,
epred149_0: $o ).
tff(decl_199,type,
epred150_0: $o ).
tff(decl_200,type,
epred151_0: $o ).
tff(decl_201,type,
epred152_0: $o ).
tff(decl_202,type,
epred153_0: $o ).
tff(decl_203,type,
epred154_0: $o ).
tff(decl_204,type,
epred155_0: $o ).
tff(decl_205,type,
epred156_0: $o ).
tff(decl_206,type,
epred157_0: $o ).
tff(decl_207,type,
epred158_0: $o ).
tff(decl_208,type,
epred159_0: $o ).
tff(decl_209,type,
epred160_0: $o ).
tff(decl_210,type,
epred161_0: $o ).
tff(decl_211,type,
epred162_0: $o ).
tff(decl_212,type,
epred163_0: $o ).
tff(decl_213,type,
epred164_0: $o ).
tff(decl_214,type,
epred165_0: $o ).
tff(decl_215,type,
epred166_0: $o ).
tff(decl_216,type,
epred167_0: $o ).
tff(decl_217,type,
epred168_0: $o ).
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(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(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
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(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(t144_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(c_0_6,plain,
! [X29,X30,X31,X33,X34,X35,X37] :
( ( ~ in(X31,X30)
| in(ordered_pair(esk5_3(X29,X30,X31),X31),X29)
| X30 != relation_rng(X29)
| ~ relation(X29) )
& ( ~ in(ordered_pair(X34,X33),X29)
| in(X33,X30)
| X30 != relation_rng(X29)
| ~ relation(X29) )
& ( ~ in(esk6_2(X29,X35),X35)
| ~ in(ordered_pair(X37,esk6_2(X29,X35)),X29)
| X35 = relation_rng(X29)
| ~ relation(X29) )
& ( in(esk6_2(X29,X35),X35)
| in(ordered_pair(esk7_2(X29,X35),esk6_2(X29,X35)),X29)
| X35 = relation_rng(X29)
| ~ relation(X29) ) ),
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_7,plain,
! [X39,X40] : ordered_pair(X39,X40) = unordered_pair(unordered_pair(X39,X40),singleton(X39)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( in(ordered_pair(esk1_4(X11,X12,X13,X14),X14),X11)
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11) )
& ( in(esk1_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11) )
& ( ~ in(ordered_pair(X17,X16),X11)
| ~ in(X17,X12)
| in(X16,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11) )
& ( ~ in(esk2_3(X11,X18,X19),X19)
| ~ in(ordered_pair(X21,esk2_3(X11,X18,X19)),X11)
| ~ in(X21,X18)
| X19 = relation_image(X11,X18)
| ~ relation(X11) )
& ( in(ordered_pair(esk3_3(X11,X18,X19),esk2_3(X11,X18,X19)),X11)
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11) )
& ( in(esk3_3(X11,X18,X19),X18)
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11) ) ),
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)],[d13_relat_1])])])])])]) ).
cnf(c_0_11,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_12,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( in(ordered_pair(esk1_4(X1,X2,X3,X4),X4),X1)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( in(unordered_pair(unordered_pair(esk1_4(X1,X2,X3,X4),X4),singleton(esk1_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_17,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,relation_image(X2,X3),X1)),singleton(esk1_4(X2,X3,relation_image(X2,X3),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_image(X2,X3)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15])]) ).
fof(c_0_19,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ subset(X23,X24)
| ~ in(X25,X23)
| in(X25,X24) )
& ( in(esk4_2(X26,X27),X26)
| subset(X26,X27) )
& ( ~ in(esk4_2(X26,X27),X27)
| subset(X26,X27) ) ),
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])])])])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
inference(assume_negation,[status(cth)],[t144_relat_1]) ).
cnf(c_0_21,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(X1,relation_image(X2,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,negated_conjecture,
( relation(esk16_0)
& ~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( subset(relation_image(X1,X2),X3)
| in(esk4_2(relation_image(X1,X2),X3),relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:52:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 62.35/62.43 % Version : CSE_E---1.5
% 62.35/62.43 % Problem : theBenchmark.p
% 62.35/62.43 % Proof found
% 62.35/62.43 % SZS status Theorem for theBenchmark.p
% 62.35/62.43 % SZS output start Proof
% See solution above
% 62.35/62.44 % Total time : 61.849000 s
% 62.35/62.44 % SZS output end Proof
% 62.35/62.44 % Total time : 61.855000 s
%------------------------------------------------------------------------------