TSTP Solution File: SET682+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET682+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 : n025.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 10:56:52 EDT 2023
% Result : Theorem 6.22s 2.49s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 45
% Syntax : Number of formulae : 130 ( 34 unt; 30 typ; 0 def)
% Number of atoms : 247 ( 13 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 255 ( 108 ~; 92 |; 10 &)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 23 >; 14 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 137 (; 133 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_4 > #skF_11 > #skF_14 > #skF_5 > #skF_10 > #skF_13 > #skF_8 > #skF_3 > #skF_2 > #skF_7 > #skF_1 > #skF_9 > #skF_6 > #skF_12
%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_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(domain_of,type,
domain_of: $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_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_284,negated_conjecture,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
=> ? [F] :
( ilf_type(F,member_type(C))
& member(F,range(B,C,D)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_49) ).
tff(f_258,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
tff(f_56,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f_203,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',p18) ).
tff(f_125,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',p10) ).
tff(f_244,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( range(B,C,D) = range_of(D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
tff(f_167,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',p15) ).
tff(f_138,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',p12) ).
tff(f_78,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',p4) ).
tff(f_185,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( relation_like(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
=> ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ( C = ordered_pair(D,E) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
tff(f_159,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',p14) ).
tff(f_255,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
tff(f_98,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',p6) ).
tff(f_222,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( domain(B,C,D) = domain_of(D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
tff(f_40,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
=> ? [D] :
( ilf_type(D,set_type)
& member(D,range_of(C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(c_90,plain,
ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_82,plain,
! [B_120] : ilf_type(B_120,set_type),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_6,plain,
! [E_17,B_7,C_13] :
( ilf_type(E_17,subset_type(cross_product(B_7,C_13)))
| ~ ilf_type(E_17,relation_type(B_7,C_13))
| ~ ilf_type(C_13,set_type)
| ~ ilf_type(B_7,set_type) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1725,plain,
! [E_357,B_358,C_359] :
( ilf_type(E_357,subset_type(cross_product(B_358,C_359)))
| ~ ilf_type(E_357,relation_type(B_358,C_359)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_6]) ).
tff(c_70,plain,
! [D_88,B_82,C_86] :
( relation_like(D_88)
| ~ ilf_type(D_88,subset_type(cross_product(B_82,C_86)))
| ~ ilf_type(C_86,set_type)
| ~ ilf_type(B_82,set_type) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_112,plain,
! [D_88,B_82,C_86] :
( relation_like(D_88)
| ~ ilf_type(D_88,subset_type(cross_product(B_82,C_86))) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_70]) ).
tff(c_1736,plain,
! [E_362,B_363,C_364] :
( relation_like(E_362)
| ~ ilf_type(E_362,relation_type(B_363,C_364)) ),
inference(resolution,[status(thm)],[c_1725,c_112]) ).
tff(c_1744,plain,
relation_like('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_1736]) ).
tff(c_30,plain,
! [B_38] :
( ilf_type(B_38,binary_relation_type)
| ~ relation_like(B_38)
| ~ ilf_type(B_38,set_type) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_148,plain,
! [B_38] :
( ilf_type(B_38,binary_relation_type)
| ~ relation_like(B_38) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_30]) ).
tff(c_78,plain,
! [B_106,C_110,D_112] :
( ( range(B_106,C_110,D_112) = range_of(D_112) )
| ~ ilf_type(D_112,relation_type(B_106,C_110))
| ~ ilf_type(C_110,set_type)
| ~ ilf_type(B_106,set_type) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_1809,plain,
! [B_374,C_375,D_376] :
( ( range(B_374,C_375,D_376) = range_of(D_376) )
| ~ ilf_type(D_376,relation_type(B_374,C_375)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_78]) ).
tff(c_1817,plain,
range('#skF_11','#skF_12','#skF_13') = range_of('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_1809]) ).
tff(c_509,plain,
! [E_212,B_213,C_214] :
( ilf_type(E_212,subset_type(cross_product(B_213,C_214)))
| ~ ilf_type(E_212,relation_type(B_213,C_214)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_6]) ).
tff(c_524,plain,
! [E_215,B_216,C_217] :
( relation_like(E_215)
| ~ ilf_type(E_215,relation_type(B_216,C_217)) ),
inference(resolution,[status(thm)],[c_509,c_112]) ).
tff(c_532,plain,
relation_like('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_524]) ).
tff(c_54,plain,
! [B_54] :
( ~ empty(power_set(B_54))
| ~ ilf_type(B_54,set_type) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_128,plain,
! [B_54] : ~ empty(power_set(B_54)),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_54]) ).
tff(c_40,plain,
! [C_41,B_39] :
( ilf_type(C_41,member_type(power_set(B_39)))
| ~ ilf_type(C_41,subset_type(B_39))
| ~ ilf_type(C_41,set_type)
| ~ ilf_type(B_39,set_type) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_265,plain,
! [C_177,B_178] :
( ilf_type(C_177,member_type(power_set(B_178)))
| ~ ilf_type(C_177,subset_type(B_178)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_40]) ).
tff(c_14,plain,
! [B_24,C_26] :
( member(B_24,C_26)
| ~ ilf_type(B_24,member_type(C_26))
| ~ ilf_type(C_26,set_type)
| empty(C_26)
| ~ ilf_type(B_24,set_type) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_162,plain,
! [B_24,C_26] :
( member(B_24,C_26)
| ~ ilf_type(B_24,member_type(C_26))
| empty(C_26) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_14]) ).
tff(c_268,plain,
! [C_177,B_178] :
( member(C_177,power_set(B_178))
| empty(power_set(B_178))
| ~ ilf_type(C_177,subset_type(B_178)) ),
inference(resolution,[status(thm)],[c_265,c_162]) ).
tff(c_271,plain,
! [C_177,B_178] :
( member(C_177,power_set(B_178))
| ~ ilf_type(C_177,subset_type(B_178)) ),
inference(negUnitSimplification,[status(thm)],[c_128,c_268]) ).
tff(c_58,plain,
! [B_55] :
( member('#skF_10'(B_55),B_55)
| relation_like(B_55)
| ~ ilf_type(B_55,set_type) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_124,plain,
! [B_55] :
( member('#skF_10'(B_55),B_55)
| relation_like(B_55) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_58]) ).
tff(c_44,plain,
! [D_53,C_50,B_44] :
( member(D_53,C_50)
| ~ member(D_53,B_44)
| ~ ilf_type(D_53,set_type)
| ~ member(B_44,power_set(C_50))
| ~ ilf_type(C_50,set_type)
| ~ ilf_type(B_44,set_type) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_393,plain,
! [D_199,C_200,B_201] :
( member(D_199,C_200)
| ~ member(D_199,B_201)
| ~ member(B_201,power_set(C_200)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_82,c_44]) ).
tff(c_418,plain,
! [B_55,C_200] :
( member('#skF_10'(B_55),C_200)
| ~ member(B_55,power_set(C_200))
| relation_like(B_55) ),
inference(resolution,[status(thm)],[c_124,c_393]) ).
tff(c_606,plain,
! [B_225,C_226,D_227] :
( ( range(B_225,C_226,D_227) = range_of(D_227) )
| ~ ilf_type(D_227,relation_type(B_225,C_226)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_78]) ).
tff(c_614,plain,
range('#skF_11','#skF_12','#skF_13') = range_of('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_606]) ).
tff(c_94,plain,
~ empty('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_12,plain,
! [B_24,C_26] :
( ilf_type(B_24,member_type(C_26))
| ~ member(B_24,C_26)
| ~ ilf_type(C_26,set_type)
| empty(C_26)
| ~ ilf_type(B_24,set_type) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_164,plain,
! [B_24,C_26] :
( ilf_type(B_24,member_type(C_26))
| ~ member(B_24,C_26)
| empty(C_26) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_12]) ).
tff(c_206,plain,
! [F_162] :
( ~ member(F_162,range('#skF_11','#skF_12','#skF_13'))
| ~ ilf_type(F_162,member_type('#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_215,plain,
( ~ ilf_type('#skF_10'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12'))
| relation_like(range('#skF_11','#skF_12','#skF_13')) ),
inference(resolution,[status(thm)],[c_124,c_206]) ).
tff(c_336,plain,
~ ilf_type('#skF_10'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12')),
inference(splitLeft,[status(thm)],[c_215]) ).
tff(c_470,plain,
( ~ member('#skF_10'(range('#skF_11','#skF_12','#skF_13')),'#skF_12')
| empty('#skF_12') ),
inference(resolution,[status(thm)],[c_164,c_336]) ).
tff(c_473,plain,
~ member('#skF_10'(range('#skF_11','#skF_12','#skF_13')),'#skF_12'),
inference(negUnitSimplification,[status(thm)],[c_94,c_470]) ).
tff(c_617,plain,
~ member('#skF_10'(range_of('#skF_13')),'#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_614,c_473]) ).
tff(c_629,plain,
( ~ member(range_of('#skF_13'),power_set('#skF_12'))
| relation_like(range_of('#skF_13')) ),
inference(resolution,[status(thm)],[c_418,c_617]) ).
tff(c_889,plain,
~ member(range_of('#skF_13'),power_set('#skF_12')),
inference(splitLeft,[status(thm)],[c_629]) ).
tff(c_896,plain,
~ ilf_type(range_of('#skF_13'),subset_type('#skF_12')),
inference(resolution,[status(thm)],[c_271,c_889]) ).
tff(c_80,plain,
! [B_113,C_117,D_119] :
( ilf_type(range(B_113,C_117,D_119),subset_type(C_117))
| ~ ilf_type(D_119,relation_type(B_113,C_117))
| ~ ilf_type(C_117,set_type)
| ~ ilf_type(B_113,set_type) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_965,plain,
! [B_265,C_266,D_267] :
( ilf_type(range(B_265,C_266,D_267),subset_type(C_266))
| ~ ilf_type(D_267,relation_type(B_265,C_266)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_80]) ).
tff(c_979,plain,
( ilf_type(range_of('#skF_13'),subset_type('#skF_12'))
| ~ ilf_type('#skF_13',relation_type('#skF_11','#skF_12')) ),
inference(superposition,[status(thm),theory(equality)],[c_614,c_965]) ).
tff(c_984,plain,
ilf_type(range_of('#skF_13'),subset_type('#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_979]) ).
tff(c_986,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_896,c_984]) ).
tff(c_988,plain,
member(range_of('#skF_13'),power_set('#skF_12')),
inference(splitRight,[status(thm)],[c_629]) ).
tff(c_20,plain,
! [B_29] :
( member('#skF_4'(B_29),B_29)
| empty(B_29)
| ~ ilf_type(B_29,set_type) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_156,plain,
! [B_29] :
( member('#skF_4'(B_29),B_29)
| empty(B_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_20]) ).
tff(c_1107,plain,
! [B_287,C_288] :
( member('#skF_4'(B_287),C_288)
| ~ member(B_287,power_set(C_288))
| empty(B_287) ),
inference(resolution,[status(thm)],[c_156,c_393]) ).
tff(c_311,plain,
! [B_186,C_187] :
( ilf_type(B_186,member_type(C_187))
| ~ member(B_186,C_187)
| empty(C_187) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_12]) ).
tff(c_216,plain,
( ~ ilf_type('#skF_4'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12'))
| empty(range('#skF_11','#skF_12','#skF_13')) ),
inference(resolution,[status(thm)],[c_156,c_206]) ).
tff(c_272,plain,
~ ilf_type('#skF_4'(range('#skF_11','#skF_12','#skF_13')),member_type('#skF_12')),
inference(splitLeft,[status(thm)],[c_216]) ).
tff(c_318,plain,
( ~ member('#skF_4'(range('#skF_11','#skF_12','#skF_13')),'#skF_12')
| empty('#skF_12') ),
inference(resolution,[status(thm)],[c_311,c_272]) ).
tff(c_327,plain,
~ member('#skF_4'(range('#skF_11','#skF_12','#skF_13')),'#skF_12'),
inference(negUnitSimplification,[status(thm)],[c_94,c_318]) ).
tff(c_619,plain,
~ member('#skF_4'(range_of('#skF_13')),'#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_614,c_327]) ).
tff(c_1118,plain,
( ~ member(range_of('#skF_13'),power_set('#skF_12'))
| empty(range_of('#skF_13')) ),
inference(resolution,[status(thm)],[c_1107,c_619]) ).
tff(c_1136,plain,
empty(range_of('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_988,c_1118]) ).
tff(c_74,plain,
! [B_92,C_96,D_98] :
( ( domain(B_92,C_96,D_98) = domain_of(D_98) )
| ~ ilf_type(D_98,relation_type(B_92,C_96))
| ~ ilf_type(C_96,set_type)
| ~ ilf_type(B_92,set_type) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_672,plain,
! [B_230,C_231,D_232] :
( ( domain(B_230,C_231,D_232) = domain_of(D_232) )
| ~ ilf_type(D_232,relation_type(B_230,C_231)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_74]) ).
tff(c_680,plain,
domain('#skF_11','#skF_12','#skF_13') = domain_of('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_672]) ).
tff(c_86,plain,
member('#skF_14',domain('#skF_11','#skF_12','#skF_13')),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_683,plain,
member('#skF_14',domain_of('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_680,c_86]) ).
tff(c_2,plain,
! [B_1,C_5] :
( member('#skF_1'(B_1,C_5),range_of(C_5))
| ~ member(B_1,domain_of(C_5))
| ~ ilf_type(C_5,binary_relation_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_1431,plain,
! [B_318,C_319] :
( member('#skF_1'(B_318,C_319),range_of(C_319))
| ~ member(B_318,domain_of(C_319))
| ~ ilf_type(C_319,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_2]) ).
tff(c_18,plain,
! [C_32,B_29] :
( ~ member(C_32,B_29)
| ~ ilf_type(C_32,set_type)
| ~ empty(B_29)
| ~ ilf_type(B_29,set_type) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_158,plain,
! [C_32,B_29] :
( ~ member(C_32,B_29)
| ~ empty(B_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_18]) ).
tff(c_1472,plain,
! [C_329,B_330] :
( ~ empty(range_of(C_329))
| ~ member(B_330,domain_of(C_329))
| ~ ilf_type(C_329,binary_relation_type) ),
inference(resolution,[status(thm)],[c_1431,c_158]) ).
tff(c_1479,plain,
( ~ empty(range_of('#skF_13'))
| ~ ilf_type('#skF_13',binary_relation_type) ),
inference(resolution,[status(thm)],[c_683,c_1472]) ).
tff(c_1503,plain,
~ ilf_type('#skF_13',binary_relation_type),
inference(demodulation,[status(thm),theory(equality)],[c_1136,c_1479]) ).
tff(c_1511,plain,
~ relation_like('#skF_13'),
inference(resolution,[status(thm)],[c_148,c_1503]) ).
tff(c_1515,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_532,c_1511]) ).
tff(c_1516,plain,
empty(range('#skF_11','#skF_12','#skF_13')),
inference(splitRight,[status(thm)],[c_216]) ).
tff(c_1822,plain,
empty(range_of('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_1817,c_1516]) ).
tff(c_2076,plain,
! [B_396,C_397,D_398] :
( ( domain(B_396,C_397,D_398) = domain_of(D_398) )
| ~ ilf_type(D_398,relation_type(B_396,C_397)) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_82,c_74]) ).
tff(c_2096,plain,
domain('#skF_11','#skF_12','#skF_13') = domain_of('#skF_13'),
inference(resolution,[status(thm)],[c_90,c_2076]) ).
tff(c_2120,plain,
member('#skF_14',domain_of('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_2096,c_86]) ).
tff(c_2373,plain,
! [B_428,C_429] :
( member('#skF_1'(B_428,C_429),range_of(C_429))
| ~ member(B_428,domain_of(C_429))
| ~ ilf_type(C_429,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_2]) ).
tff(c_2637,plain,
! [C_458,B_459] :
( ~ empty(range_of(C_458))
| ~ member(B_459,domain_of(C_458))
| ~ ilf_type(C_458,binary_relation_type) ),
inference(resolution,[status(thm)],[c_2373,c_158]) ).
tff(c_2648,plain,
( ~ empty(range_of('#skF_13'))
| ~ ilf_type('#skF_13',binary_relation_type) ),
inference(resolution,[status(thm)],[c_2120,c_2637]) ).
tff(c_2673,plain,
~ ilf_type('#skF_13',binary_relation_type),
inference(demodulation,[status(thm),theory(equality)],[c_1822,c_2648]) ).
tff(c_2681,plain,
~ relation_like('#skF_13'),
inference(resolution,[status(thm)],[c_148,c_2673]) ).
tff(c_2685,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_2681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET682+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n025.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
% 0.13/0.35 % DateTime : Thu Aug 3 17:15:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.22/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.22/2.50
% 6.22/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.22/2.54
% 6.22/2.54 Inference rules
% 6.22/2.54 ----------------------
% 6.22/2.54 #Ref : 0
% 6.22/2.54 #Sup : 508
% 6.22/2.54 #Fact : 0
% 6.22/2.54 #Define : 0
% 6.22/2.54 #Split : 6
% 6.22/2.54 #Chain : 0
% 6.22/2.54 #Close : 0
% 6.22/2.54
% 6.22/2.54 Ordering : KBO
% 6.22/2.54
% 6.22/2.54 Simplification rules
% 6.22/2.54 ----------------------
% 6.22/2.54 #Subsume : 101
% 6.22/2.54 #Demod : 169
% 6.22/2.54 #Tautology : 101
% 6.22/2.54 #SimpNegUnit : 41
% 6.22/2.54 #BackRed : 19
% 6.22/2.54
% 6.22/2.54 #Partial instantiations: 0
% 6.22/2.54 #Strategies tried : 1
% 6.22/2.54
% 6.22/2.54 Timing (in seconds)
% 6.22/2.54 ----------------------
% 6.52/2.54 Preprocessing : 0.60
% 6.52/2.54 Parsing : 0.32
% 6.52/2.54 CNF conversion : 0.05
% 6.52/2.54 Main loop : 0.85
% 6.52/2.54 Inferencing : 0.34
% 6.52/2.54 Reduction : 0.25
% 6.52/2.54 Demodulation : 0.18
% 6.52/2.54 BG Simplification : 0.04
% 6.52/2.54 Subsumption : 0.15
% 6.52/2.54 Abstraction : 0.03
% 6.52/2.54 MUC search : 0.00
% 6.52/2.54 Cooper : 0.00
% 6.52/2.54 Total : 1.52
% 6.52/2.54 Index Insertion : 0.00
% 6.52/2.54 Index Deletion : 0.00
% 6.52/2.54 Index Matching : 0.00
% 6.52/2.54 BG Taut test : 0.00
%------------------------------------------------------------------------------