TSTP Solution File: SET665+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n013.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 : Tue Aug 22 10:56:50 EDT 2023
% Result : Theorem 8.88s 3.17s
% Output : CNFRefutation 9.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 98 ( 18 unt; 29 typ; 0 def)
% Number of atoms : 198 ( 8 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 215 ( 86 ~; 85 |; 8 &)
% ( 8 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 25 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 4 con; 0-3 aty)
% Number of variables : 109 (; 107 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > identity_relation_of > set_type > binary_relation_type > #skF_15 > #skF_8 > #skF_4 > #skF_12 > #skF_6 > #skF_10 > #skF_13 > #skF_11 > #skF_3 > #skF_14 > #skF_2 > #skF_7 > #skF_1 > #skF_9 > #skF_5
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(identity_relation_of,type,
identity_relation_of: $i > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(f_322,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_28) ).
tff(f_316,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
tff(f_135,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
tff(f_265,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
tff(f_273,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
tff(f_286,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
tff(f_215,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
tff(f_250,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
tff(f_167,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
tff(f_43,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(D,E),B)
=> member(ordered_pair(D,E),C) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f_130,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( member(C,B)
& ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
tff(f_306,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
tff(f_107,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,cross_product(B,C))
<=> ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ilf_type(F,set_type)
& member(E,B)
& member(F,C)
& ( D = ordered_pair(E,F) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
tff(c_124,plain,
~ subset(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),
inference(cnfTransformation,[status(thm)],[f_322]) ).
tff(c_122,plain,
! [B_207] : ilf_type(B_207,set_type),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_46,plain,
! [B_114] :
( ilf_type(identity_relation_of(B_114),binary_relation_type)
| ~ ilf_type(B_114,set_type) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_198,plain,
! [B_114] : ilf_type(identity_relation_of(B_114),binary_relation_type),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_46]) ).
tff(c_100,plain,
! [B_186,C_192] :
( member('#skF_12'(B_186,C_192),B_186)
| member(B_186,power_set(C_192))
| ~ ilf_type(C_192,set_type)
| ~ ilf_type(B_186,set_type) ),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_472,plain,
! [B_278,C_279] :
( member('#skF_12'(B_278,C_279),B_278)
| member(B_278,power_set(C_279)) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_100]) ).
tff(c_98,plain,
! [B_186,C_192] :
( ~ member('#skF_12'(B_186,C_192),C_192)
| member(B_186,power_set(C_192))
| ~ ilf_type(C_192,set_type)
| ~ ilf_type(B_186,set_type) ),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_151,plain,
! [B_186,C_192] :
( ~ member('#skF_12'(B_186,C_192),C_192)
| member(B_186,power_set(C_192)) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_98]) ).
tff(c_496,plain,
! [B_284] : member(B_284,power_set(B_284)),
inference(resolution,[status(thm)],[c_472,c_151]) ).
tff(c_106,plain,
! [B_196] :
( ~ empty(power_set(B_196))
| ~ ilf_type(B_196,set_type) ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_143,plain,
! [B_196] : ~ empty(power_set(B_196)),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_106]) ).
tff(c_108,plain,
! [B_197,C_199] :
( ilf_type(B_197,member_type(C_199))
| ~ member(B_197,C_199)
| ~ ilf_type(C_199,set_type)
| empty(C_199)
| ~ ilf_type(B_197,set_type) ),
inference(cnfTransformation,[status(thm)],[f_286]) ).
tff(c_407,plain,
! [B_268,C_269] :
( ilf_type(B_268,member_type(C_269))
| ~ member(B_268,C_269)
| empty(C_269) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_108]) ).
tff(c_76,plain,
! [C_150,B_148] :
( ilf_type(C_150,subset_type(B_148))
| ~ ilf_type(C_150,member_type(power_set(B_148)))
| ~ ilf_type(C_150,set_type)
| ~ ilf_type(B_148,set_type) ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_173,plain,
! [C_150,B_148] :
( ilf_type(C_150,subset_type(B_148))
| ~ ilf_type(C_150,member_type(power_set(B_148))) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_76]) ).
tff(c_414,plain,
! [B_268,B_148] :
( ilf_type(B_268,subset_type(B_148))
| ~ member(B_268,power_set(B_148))
| empty(power_set(B_148)) ),
inference(resolution,[status(thm)],[c_407,c_173]) ).
tff(c_418,plain,
! [B_268,B_148] :
( ilf_type(B_268,subset_type(B_148))
| ~ member(B_268,power_set(B_148)) ),
inference(negUnitSimplification,[status(thm)],[c_143,c_414]) ).
tff(c_508,plain,
! [B_285] : ilf_type(B_285,subset_type(B_285)),
inference(resolution,[status(thm)],[c_496,c_418]) ).
tff(c_94,plain,
! [D_185,B_179,C_183] :
( relation_like(D_185)
| ~ ilf_type(D_185,subset_type(cross_product(B_179,C_183)))
| ~ ilf_type(C_183,set_type)
| ~ ilf_type(B_179,set_type) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_155,plain,
! [D_185,B_179,C_183] :
( relation_like(D_185)
| ~ ilf_type(D_185,subset_type(cross_product(B_179,C_183))) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_94]) ).
tff(c_513,plain,
! [B_179,C_183] : relation_like(cross_product(B_179,C_183)),
inference(resolution,[status(thm)],[c_508,c_155]) ).
tff(c_58,plain,
! [B_128] :
( ilf_type(B_128,binary_relation_type)
| ~ relation_like(B_128)
| ~ ilf_type(B_128,set_type) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_186,plain,
! [B_128] :
( ilf_type(B_128,binary_relation_type)
| ~ relation_like(B_128) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_58]) ).
tff(c_6,plain,
! [B_1,C_15] :
( member(ordered_pair('#skF_1'(B_1,C_15),'#skF_2'(B_1,C_15)),B_1)
| subset(B_1,C_15)
| ~ ilf_type(C_15,binary_relation_type)
| ~ ilf_type(B_1,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_44,plain,
! [C_111,B_107,D_113] :
( member(C_111,B_107)
| ~ member(ordered_pair(C_111,D_113),identity_relation_of(B_107))
| ~ ilf_type(D_113,set_type)
| ~ ilf_type(C_111,set_type)
| ~ ilf_type(B_107,set_type) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_460,plain,
! [C_275,B_276,D_277] :
( member(C_275,B_276)
| ~ member(ordered_pair(C_275,D_277),identity_relation_of(B_276)) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_122,c_44]) ).
tff(c_464,plain,
! [B_276,C_15] :
( member('#skF_1'(identity_relation_of(B_276),C_15),B_276)
| subset(identity_relation_of(B_276),C_15)
| ~ ilf_type(C_15,binary_relation_type)
| ~ ilf_type(identity_relation_of(B_276),binary_relation_type) ),
inference(resolution,[status(thm)],[c_6,c_460]) ).
tff(c_4637,plain,
! [B_630,C_631] :
( member('#skF_1'(identity_relation_of(B_630),C_631),B_630)
| subset(identity_relation_of(B_630),C_631)
| ~ ilf_type(C_631,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_464]) ).
tff(c_114,plain,
! [C_205,B_202] :
( ~ member(C_205,B_202)
| ~ ilf_type(C_205,set_type)
| ~ empty(B_202)
| ~ ilf_type(B_202,set_type) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_135,plain,
! [C_205,B_202] :
( ~ member(C_205,B_202)
| ~ empty(B_202) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_114]) ).
tff(c_4722,plain,
! [B_632,C_633] :
( ~ empty(B_632)
| subset(identity_relation_of(B_632),C_633)
| ~ ilf_type(C_633,binary_relation_type) ),
inference(resolution,[status(thm)],[c_4637,c_135]) ).
tff(c_4773,plain,
( ~ empty('#skF_15')
| ~ ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type) ),
inference(resolution,[status(thm)],[c_4722,c_124]) ).
tff(c_4774,plain,
~ ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type),
inference(splitLeft,[status(thm)],[c_4773]) ).
tff(c_4777,plain,
~ relation_like(cross_product('#skF_15','#skF_15')),
inference(resolution,[status(thm)],[c_186,c_4774]) ).
tff(c_4781,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_513,c_4777]) ).
tff(c_4783,plain,
ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type),
inference(splitRight,[status(thm)],[c_4773]) ).
tff(c_310,plain,
! [B_249,C_250] :
( member(ordered_pair('#skF_1'(B_249,C_250),'#skF_2'(B_249,C_250)),B_249)
| subset(B_249,C_250)
| ~ ilf_type(C_250,binary_relation_type)
| ~ ilf_type(B_249,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_42,plain,
! [D_113,C_111,B_107] :
( ( D_113 = C_111 )
| ~ member(ordered_pair(C_111,D_113),identity_relation_of(B_107))
| ~ ilf_type(D_113,set_type)
| ~ ilf_type(C_111,set_type)
| ~ ilf_type(B_107,set_type) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_202,plain,
! [D_113,C_111,B_107] :
( ( D_113 = C_111 )
| ~ member(ordered_pair(C_111,D_113),identity_relation_of(B_107)) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_122,c_42]) ).
tff(c_314,plain,
! [B_107,C_250] :
( ( '#skF_2'(identity_relation_of(B_107),C_250) = '#skF_1'(identity_relation_of(B_107),C_250) )
| subset(identity_relation_of(B_107),C_250)
| ~ ilf_type(C_250,binary_relation_type)
| ~ ilf_type(identity_relation_of(B_107),binary_relation_type) ),
inference(resolution,[status(thm)],[c_310,c_202]) ).
tff(c_6936,plain,
! [B_737,C_738] :
( ( '#skF_2'(identity_relation_of(B_737),C_738) = '#skF_1'(identity_relation_of(B_737),C_738) )
| subset(identity_relation_of(B_737),C_738)
| ~ ilf_type(C_738,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_314]) ).
tff(c_6978,plain,
( ( '#skF_2'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')) = '#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')) )
| ~ ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type) ),
inference(resolution,[status(thm)],[c_6936,c_124]) ).
tff(c_6997,plain,
'#skF_2'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')) = '#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_4783,c_6978]) ).
tff(c_7146,plain,
( member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),identity_relation_of('#skF_15'))
| subset(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))
| ~ ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type)
| ~ ilf_type(identity_relation_of('#skF_15'),binary_relation_type) ),
inference(superposition,[status(thm),theory(equality)],[c_6997,c_6]) ).
tff(c_7159,plain,
( member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),identity_relation_of('#skF_15'))
| subset(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_4783,c_7146]) ).
tff(c_7160,plain,
member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),identity_relation_of('#skF_15')),
inference(negUnitSimplification,[status(thm)],[c_124,c_7159]) ).
tff(c_200,plain,
! [C_111,B_107,D_113] :
( member(C_111,B_107)
| ~ member(ordered_pair(C_111,D_113),identity_relation_of(B_107)) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_122,c_44]) ).
tff(c_7486,plain,
member('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_15'),
inference(resolution,[status(thm)],[c_7160,c_200]) ).
tff(c_26,plain,
! [E_101,F_103,B_51,C_79] :
( member(ordered_pair(E_101,F_103),cross_product(B_51,C_79))
| ~ member(F_103,C_79)
| ~ member(E_101,B_51)
| ~ ilf_type(F_103,set_type)
| ~ ilf_type(E_101,set_type)
| ~ ilf_type(ordered_pair(E_101,F_103),set_type)
| ~ ilf_type(C_79,set_type)
| ~ ilf_type(B_51,set_type) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_218,plain,
! [E_101,F_103,B_51,C_79] :
( member(ordered_pair(E_101,F_103),cross_product(B_51,C_79))
| ~ member(F_103,C_79)
| ~ member(E_101,B_51) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_122,c_122,c_122,c_26]) ).
tff(c_4,plain,
! [B_1,C_15] :
( ~ member(ordered_pair('#skF_1'(B_1,C_15),'#skF_2'(B_1,C_15)),C_15)
| subset(B_1,C_15)
| ~ ilf_type(C_15,binary_relation_type)
| ~ ilf_type(B_1,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_7149,plain,
( ~ member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),cross_product('#skF_15','#skF_15'))
| subset(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))
| ~ ilf_type(cross_product('#skF_15','#skF_15'),binary_relation_type)
| ~ ilf_type(identity_relation_of('#skF_15'),binary_relation_type) ),
inference(superposition,[status(thm),theory(equality)],[c_6997,c_4]) ).
tff(c_7162,plain,
( ~ member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),cross_product('#skF_15','#skF_15'))
| subset(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_4783,c_7149]) ).
tff(c_7163,plain,
~ member(ordered_pair('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15'))),cross_product('#skF_15','#skF_15')),
inference(negUnitSimplification,[status(thm)],[c_124,c_7162]) ).
tff(c_8248,plain,
~ member('#skF_1'(identity_relation_of('#skF_15'),cross_product('#skF_15','#skF_15')),'#skF_15'),
inference(resolution,[status(thm)],[c_218,c_7163]) ).
tff(c_8252,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7486,c_8248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 16:14:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 8.88/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.88/3.18
% 8.88/3.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.09/3.24
% 9.09/3.24 Inference rules
% 9.09/3.24 ----------------------
% 9.09/3.24 #Ref : 2
% 9.09/3.24 #Sup : 1710
% 9.09/3.24 #Fact : 0
% 9.09/3.24 #Define : 0
% 9.09/3.24 #Split : 3
% 9.09/3.24 #Chain : 0
% 9.09/3.24 #Close : 0
% 9.09/3.24
% 9.09/3.24 Ordering : KBO
% 9.09/3.24
% 9.09/3.24 Simplification rules
% 9.09/3.24 ----------------------
% 9.09/3.24 #Subsume : 540
% 9.09/3.24 #Demod : 302
% 9.09/3.24 #Tautology : 214
% 9.09/3.24 #SimpNegUnit : 44
% 9.09/3.24 #BackRed : 1
% 9.09/3.24
% 9.09/3.24 #Partial instantiations: 0
% 9.09/3.24 #Strategies tried : 1
% 9.09/3.24
% 9.09/3.24 Timing (in seconds)
% 9.09/3.24 ----------------------
% 9.09/3.25 Preprocessing : 0.63
% 9.09/3.25 Parsing : 0.32
% 9.09/3.25 CNF conversion : 0.06
% 9.09/3.25 Main loop : 1.50
% 9.09/3.25 Inferencing : 0.53
% 9.09/3.25 Reduction : 0.40
% 9.09/3.25 Demodulation : 0.27
% 9.09/3.25 BG Simplification : 0.05
% 9.09/3.25 Subsumption : 0.42
% 9.09/3.25 Abstraction : 0.04
% 9.09/3.25 MUC search : 0.00
% 9.09/3.25 Cooper : 0.00
% 9.09/3.25 Total : 2.21
% 9.09/3.25 Index Insertion : 0.00
% 9.09/3.25 Index Deletion : 0.00
% 9.09/3.25 Index Matching : 0.00
% 9.09/3.25 BG Taut test : 0.00
%------------------------------------------------------------------------------