TSTP Solution File: SEU187+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% 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 %s %d
% Computer : n029.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 16:18:14 EDT 2023
% Result : Theorem 0.19s 0.87s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU187+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n029.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 19:11:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.85 %-------------------------------------------
% 0.19/0.85 % File :CSE---1.6
% 0.19/0.85 % Problem :theBenchmark
% 0.19/0.85 % Transform :cnf
% 0.19/0.85 % Format :tptp:raw
% 0.19/0.85 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.85
% 0.19/0.85 % Result :Theorem 0.240000s
% 0.19/0.85 % Output :CNFRefutation 0.240000s
% 0.19/0.85 %-------------------------------------------
% 0.19/0.86 %------------------------------------------------------------------------------
% 0.19/0.86 % File : SEU187+1 : TPTP v8.1.2. Released v3.3.0.
% 0.19/0.86 % Domain : Set theory
% 0.19/0.86 % Problem : MPTP bushy problem t60_relat_1
% 0.19/0.86 % Version : [Urb07] axioms : Especial.
% 0.19/0.86 % English :
% 0.19/0.86
% 0.19/0.86 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.19/0.86 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.19/0.86 % Source : [Urb07]
% 0.19/0.86 % Names : bushy-t60_relat_1 [Urb07]
% 0.19/0.86
% 0.19/0.86 % Status : Theorem
% 0.19/0.86 % Rating : 0.25 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.21 v3.3.0
% 0.19/0.86 % Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% 0.19/0.86 % Number of atoms : 57 ( 9 equ)
% 0.19/0.86 % Maximal formula atoms : 4 ( 1 avg)
% 0.19/0.86 % Number of connectives : 38 ( 13 ~; 1 |; 9 &)
% 0.19/0.86 % ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% 0.19/0.86 % Maximal formula depth : 8 ( 3 avg)
% 0.19/0.86 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.86 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.19/0.86 % Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% 0.19/0.86 % Number of variables : 40 ( 33 !; 7 ?)
% 0.19/0.86 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.86
% 0.19/0.86 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.86 % library, www.mizar.org
% 0.19/0.86 %------------------------------------------------------------------------------
% 0.19/0.86 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.86 ! [A,B] :
% 0.19/0.86 ( in(A,B)
% 0.19/0.86 => ~ in(B,A) ) ).
% 0.19/0.86
% 0.19/0.86 fof(cc1_relat_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( empty(A)
% 0.19/0.86 => relation(A) ) ).
% 0.19/0.86
% 0.19/0.86 fof(commutativity_k2_tarski,axiom,
% 0.19/0.86 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.19/0.86
% 0.19/0.86 fof(d4_relat_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( relation(A)
% 0.19/0.86 => ! [B] :
% 0.19/0.86 ( B = relation_dom(A)
% 0.19/0.86 <=> ! [C] :
% 0.19/0.86 ( in(C,B)
% 0.19/0.86 <=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).
% 0.19/0.86
% 0.19/0.86 fof(d5_relat_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( relation(A)
% 0.19/0.86 => ! [B] :
% 0.19/0.86 ( B = relation_rng(A)
% 0.19/0.86 <=> ! [C] :
% 0.19/0.86 ( in(C,B)
% 0.19/0.86 <=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ).
% 0.19/0.86
% 0.19/0.86 fof(d5_tarski,axiom,
% 0.19/0.86 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k1_relat_1,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k1_tarski,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k1_xboole_0,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k2_relat_1,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k2_tarski,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_k4_tarski,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(dt_m1_subset_1,axiom,
% 0.19/0.86 $true ).
% 0.19/0.86
% 0.19/0.86 fof(existence_m1_subset_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ? [B] : element(B,A) ).
% 0.19/0.86
% 0.19/0.86 fof(fc1_xboole_0,axiom,
% 0.19/0.86 empty(empty_set) ).
% 0.19/0.86
% 0.19/0.86 fof(fc1_zfmisc_1,axiom,
% 0.19/0.86 ! [A,B] : ~ empty(ordered_pair(A,B)) ).
% 0.19/0.86
% 0.19/0.86 fof(fc2_subset_1,axiom,
% 0.19/0.86 ! [A] : ~ empty(singleton(A)) ).
% 0.19/0.86
% 0.19/0.86 fof(fc3_subset_1,axiom,
% 0.19/0.86 ! [A,B] : ~ empty(unordered_pair(A,B)) ).
% 0.19/0.86
% 0.19/0.86 fof(fc4_relat_1,axiom,
% 0.19/0.86 ( empty(empty_set)
% 0.19/0.86 & relation(empty_set) ) ).
% 0.19/0.86
% 0.19/0.86 fof(fc5_relat_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( ( ~ empty(A)
% 0.19/0.86 & relation(A) )
% 0.19/0.86 => ~ empty(relation_dom(A)) ) ).
% 0.19/0.86
% 0.19/0.86 fof(fc6_relat_1,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( ( ~ empty(A)
% 0.19/0.86 & relation(A) )
% 0.19/0.86 => ~ empty(relation_rng(A)) ) ).
% 0.19/0.86
% 0.19/0.86 fof(rc1_relat_1,axiom,
% 0.19/0.86 ? [A] :
% 0.19/0.86 ( empty(A)
% 0.19/0.86 & relation(A) ) ).
% 0.19/0.86
% 0.19/0.86 fof(rc1_xboole_0,axiom,
% 0.19/0.86 ? [A] : empty(A) ).
% 0.19/0.86
% 0.19/0.86 fof(rc2_relat_1,axiom,
% 0.19/0.86 ? [A] :
% 0.19/0.86 ( ~ empty(A)
% 0.19/0.86 & relation(A) ) ).
% 0.19/0.86
% 0.19/0.86 fof(rc2_xboole_0,axiom,
% 0.19/0.86 ? [A] : ~ empty(A) ).
% 0.19/0.86
% 0.19/0.86 fof(t1_subset,axiom,
% 0.19/0.86 ! [A,B] :
% 0.19/0.86 ( in(A,B)
% 0.19/0.86 => element(A,B) ) ).
% 0.19/0.86
% 0.19/0.86 fof(t2_subset,axiom,
% 0.19/0.86 ! [A,B] :
% 0.19/0.86 ( element(A,B)
% 0.19/0.86 => ( empty(B)
% 0.19/0.86 | in(A,B) ) ) ).
% 0.19/0.86
% 0.19/0.86 fof(t2_tarski,axiom,
% 0.19/0.86 ! [A,B] :
% 0.19/0.86 ( ! [C] :
% 0.19/0.86 ( in(C,A)
% 0.19/0.86 <=> in(C,B) )
% 0.19/0.86 => A = B ) ).
% 0.19/0.86
% 0.19/0.86 fof(t60_relat_1,conjecture,
% 0.19/0.86 ( relation_dom(empty_set) = empty_set
% 0.19/0.86 & relation_rng(empty_set) = empty_set ) ).
% 0.19/0.86
% 0.19/0.86 fof(t6_boole,axiom,
% 0.19/0.86 ! [A] :
% 0.19/0.86 ( empty(A)
% 0.19/0.86 => A = empty_set ) ).
% 0.19/0.86
% 0.19/0.86 fof(t7_boole,axiom,
% 0.19/0.87 ! [A,B] :
% 0.19/0.87 ~ ( in(A,B)
% 0.19/0.87 & empty(B) ) ).
% 0.19/0.87
% 0.19/0.87 fof(t8_boole,axiom,
% 0.19/0.87 ! [A,B] :
% 0.19/0.87 ~ ( empty(A)
% 0.19/0.87 & A != B
% 0.19/0.87 & empty(B) ) ).
% 0.19/0.87
% 0.19/0.87 %------------------------------------------------------------------------------
% 0.19/0.87 %-------------------------------------------
% 0.19/0.87 % Proof found
% 0.19/0.87 % SZS status Theorem for theBenchmark
% 0.19/0.87 % SZS output start Proof
% 0.19/0.87 %ClaNum:65(EqnAxiom:31)
% 0.19/0.87 %VarNum:146(SingletonVarNum:48)
% 0.19/0.87 %MaxLitNum:4
% 0.19/0.87 %MaxfuncDepth:3
% 0.19/0.87 %SharedTerms:17
% 0.19/0.87 %goalClause: 47
% 0.19/0.87 [33]P1(a1)
% 0.19/0.87 [34]P1(a2)
% 0.19/0.87 [35]P1(a13)
% 0.19/0.87 [36]P3(a1)
% 0.19/0.87 [37]P3(a2)
% 0.19/0.87 [38]P3(a3)
% 0.19/0.87 [41]~P1(a3)
% 0.19/0.87 [42]~P1(a5)
% 0.19/0.87 [39]P2(f4(x391),x391)
% 0.19/0.87 [43]~P1(f15(x431))
% 0.19/0.87 [40]E(f14(x401,x402),f14(x402,x401))
% 0.19/0.87 [44]~P1(f14(x441,x442))
% 0.19/0.87 [47]~E(f16(a1),a1)+~E(f17(a1),a1)
% 0.19/0.87 [46]~P1(x461)+E(x461,a1)
% 0.19/0.87 [48]~P1(x481)+P3(x481)
% 0.19/0.87 [52]~P1(x521)+~P4(x522,x521)
% 0.19/0.87 [53]~P4(x531,x532)+P2(x531,x532)
% 0.19/0.87 [55]~P4(x552,x551)+~P4(x551,x552)
% 0.19/0.87 [50]~P3(x501)+P1(x501)+~P1(f16(x501))
% 0.19/0.87 [51]~P3(x511)+P1(x511)+~P1(f17(x511))
% 0.19/0.87 [49]~P1(x492)+~P1(x491)+E(x491,x492)
% 0.19/0.87 [54]~P2(x542,x541)+P1(x541)+P4(x542,x541)
% 0.19/0.87 [56]E(x561,x562)+P4(f6(x561,x562),x562)+P4(f6(x561,x562),x561)
% 0.19/0.87 [57]E(x571,x572)+~P4(f6(x571,x572),x572)+~P4(f6(x571,x572),x571)
% 0.19/0.87 [61]~P3(x612)+P4(f8(x612,x611),x611)+E(x611,f16(x612))+P4(f14(f14(f8(x612,x611),f10(x612,x611)),f15(f8(x612,x611))),x612)
% 0.19/0.87 [62]~P3(x622)+P4(f7(x622,x621),x621)+E(x621,f17(x622))+P4(f14(f14(f12(x622,x621),f7(x622,x621)),f15(f12(x622,x621))),x622)
% 0.19/0.87 [60]~P3(x602)+~P4(f7(x602,x601),x601)+E(x601,f17(x602))+~P4(f14(f14(x603,f7(x602,x601)),f15(x603)),x602)
% 0.19/0.87 [64]~P3(x642)+~P4(x641,x643)+~E(x643,f16(x642))+P4(f14(f14(x641,f9(x642,x643,x641)),f15(x641)),x642)
% 0.19/0.87 [63]~P3(x632)+~P4(f8(x632,x631),x631)+E(x631,f16(x632))+~P4(f14(f14(f8(x632,x631),x633),f15(f8(x632,x631))),x632)
% 0.19/0.87 [65]~P3(x651)+~P4(x653,x652)+~E(x652,f17(x651))+P4(f14(f14(f11(x651,x652,x653),x653),f15(f11(x651,x652,x653))),x651)
% 0.19/0.87 [58]~P3(x583)+P4(x581,x582)+~E(x582,f17(x583))+~P4(f14(f14(x584,x581),f15(x584)),x583)
% 0.19/0.87 [59]~P3(x593)+P4(x591,x592)+~E(x592,f16(x593))+~P4(f14(f14(x591,x594),f15(x591)),x593)
% 0.19/0.87 %EqnAxiom
% 0.19/0.87 [1]E(x11,x11)
% 0.19/0.87 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.87 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.87 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.19/0.87 [5]~E(x51,x52)+E(f14(x51,x53),f14(x52,x53))
% 0.19/0.87 [6]~E(x61,x62)+E(f14(x63,x61),f14(x63,x62))
% 0.19/0.87 [7]~E(x71,x72)+E(f17(x71),f17(x72))
% 0.19/0.87 [8]~E(x81,x82)+E(f15(x81),f15(x82))
% 0.19/0.87 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93))
% 0.19/0.87 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102))
% 0.19/0.87 [11]~E(x111,x112)+E(f11(x111,x113,x114),f11(x112,x113,x114))
% 0.19/0.87 [12]~E(x121,x122)+E(f11(x123,x121,x124),f11(x123,x122,x124))
% 0.19/0.87 [13]~E(x131,x132)+E(f11(x133,x134,x131),f11(x133,x134,x132))
% 0.19/0.87 [14]~E(x141,x142)+E(f16(x141),f16(x142))
% 0.19/0.87 [15]~E(x151,x152)+E(f8(x151,x153),f8(x152,x153))
% 0.19/0.87 [16]~E(x161,x162)+E(f8(x163,x161),f8(x163,x162))
% 0.19/0.87 [17]~E(x171,x172)+E(f12(x171,x173),f12(x172,x173))
% 0.19/0.87 [18]~E(x181,x182)+E(f12(x183,x181),f12(x183,x182))
% 0.19/0.87 [19]~E(x191,x192)+E(f6(x191,x193),f6(x192,x193))
% 0.19/0.87 [20]~E(x201,x202)+E(f6(x203,x201),f6(x203,x202))
% 0.19/0.87 [21]~E(x211,x212)+E(f9(x211,x213,x214),f9(x212,x213,x214))
% 0.19/0.87 [22]~E(x221,x222)+E(f9(x223,x221,x224),f9(x223,x222,x224))
% 0.19/0.87 [23]~E(x231,x232)+E(f9(x233,x234,x231),f9(x233,x234,x232))
% 0.19/0.87 [24]~E(x241,x242)+E(f10(x241,x243),f10(x242,x243))
% 0.19/0.87 [25]~E(x251,x252)+E(f10(x253,x251),f10(x253,x252))
% 0.19/0.87 [26]~P1(x261)+P1(x262)+~E(x261,x262)
% 0.19/0.87 [27]P4(x272,x273)+~E(x271,x272)+~P4(x271,x273)
% 0.19/0.87 [28]P4(x283,x282)+~E(x281,x282)+~P4(x283,x281)
% 0.19/0.87 [29]~P3(x291)+P3(x292)+~E(x291,x292)
% 0.19/0.87 [30]P2(x302,x303)+~E(x301,x302)+~P2(x301,x303)
% 0.19/0.87 [31]P2(x313,x312)+~E(x311,x312)+~P2(x313,x311)
% 0.19/0.87
% 0.19/0.87 %-------------------------------------------
% 0.19/0.87 cnf(66,plain,
% 0.19/0.87 (~P4(x661,a1)),
% 0.19/0.87 inference(scs_inference,[],[33,52])).
% 0.19/0.87 cnf(67,plain,
% 0.19/0.87 (P2(f4(f14(x671,x672)),f14(x672,x671))),
% 0.19/0.87 inference(scs_inference,[],[33,39,40,52,31])).
% 0.19/0.87 cnf(68,plain,
% 0.19/0.87 (P2(f4(x681),x681)),
% 0.19/0.87 inference(rename_variables,[],[39])).
% 0.19/0.87 cnf(69,plain,
% 0.19/0.87 (P4(f4(a3),a3)),
% 0.19/0.87 inference(scs_inference,[],[33,41,39,68,40,52,31,54])).
% 0.19/0.87 cnf(72,plain,
% 0.19/0.87 (~E(a3,f16(a1))),
% 0.19/0.87 inference(scs_inference,[],[33,36,41,39,68,40,52,31,54,64])).
% 0.19/0.87 cnf(74,plain,
% 0.19/0.87 (~E(f16(a1),a3)),
% 0.19/0.87 inference(scs_inference,[],[33,36,41,39,68,40,52,31,54,64,2])).
% 0.19/0.87 cnf(75,plain,
% 0.19/0.87 (~P4(a3,f4(a3))),
% 0.19/0.87 inference(scs_inference,[],[33,36,41,39,68,40,52,31,54,64,2,55])).
% 0.19/0.87 cnf(77,plain,
% 0.19/0.87 (P3(a13)),
% 0.19/0.87 inference(scs_inference,[],[33,35,36,41,39,68,40,52,31,54,64,2,55,48])).
% 0.19/0.87 cnf(79,plain,
% 0.19/0.87 (E(a2,a1)),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46])).
% 0.19/0.87 cnf(81,plain,
% 0.19/0.87 (E(f10(x811,f14(x812,x813)),f10(x811,f14(x813,x812)))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25])).
% 0.19/0.87 cnf(96,plain,
% 0.19/0.87 (E(f7(x961,f14(x962,x963)),f7(x961,f14(x963,x962)))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10])).
% 0.19/0.87 cnf(98,plain,
% 0.19/0.87 (E(f15(f14(x981,x982)),f15(f14(x982,x981)))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8])).
% 0.19/0.87 cnf(102,plain,
% 0.19/0.87 (E(f4(f14(x1021,x1022)),f4(f14(x1022,x1021)))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4])).
% 0.19/0.87 cnf(103,plain,
% 0.19/0.87 (~E(a1,x1031)+P3(x1031)),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,29])).
% 0.19/0.87 cnf(104,plain,
% 0.19/0.87 (~E(a1,a3)),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,29,26])).
% 0.19/0.87 cnf(110,plain,
% 0.19/0.87 (~P4(x1101,f14(x1102,x1103))+P4(x1101,f14(x1103,x1102))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,38,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,29,26,51,50,30,28])).
% 0.19/0.87 cnf(112,plain,
% 0.19/0.87 (~E(a1,x1121)+E(a2,x1121)+P4(a1,f14(x1122,x1123))),
% 0.19/0.87 inference(scs_inference,[],[33,34,35,36,38,41,39,68,40,52,31,54,64,2,55,48,46,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,29,26,51,50,30,28,27,3])).
% 0.19/0.87 cnf(119,plain,
% 0.19/0.87 (~E(a3,f17(a1))),
% 0.19/0.87 inference(scs_inference,[],[36,66,69,65])).
% 0.19/0.87 cnf(120,plain,
% 0.19/0.87 (~P4(x1201,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(122,plain,
% 0.19/0.87 (P4(f7(a1,a3),a3)),
% 0.19/0.87 inference(scs_inference,[],[36,66,120,69,65,62])).
% 0.19/0.87 cnf(123,plain,
% 0.19/0.87 (~P4(x1231,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(126,plain,
% 0.19/0.87 (~P4(x1261,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(128,plain,
% 0.19/0.87 (P2(f7(a1,a3),a3)),
% 0.19/0.87 inference(scs_inference,[],[36,66,120,123,69,72,65,62,61,53])).
% 0.19/0.87 cnf(130,plain,
% 0.19/0.87 (~P4(a3,f7(a1,a3))),
% 0.19/0.87 inference(scs_inference,[],[36,66,120,123,69,72,65,62,61,53,55])).
% 0.19/0.87 cnf(132,plain,
% 0.19/0.87 (~E(a1,a5)),
% 0.19/0.87 inference(scs_inference,[],[33,42,36,66,120,123,69,72,65,62,61,53,55,26])).
% 0.19/0.87 cnf(133,plain,
% 0.19/0.87 (~E(a3,a1)),
% 0.19/0.87 inference(scs_inference,[],[33,42,36,66,120,123,126,69,72,65,62,61,53,55,26,28])).
% 0.19/0.87 cnf(135,plain,
% 0.19/0.87 (E(a1,a2)),
% 0.19/0.87 inference(scs_inference,[],[33,42,36,66,120,123,126,79,69,72,65,62,61,53,55,26,28,2])).
% 0.19/0.87 cnf(136,plain,
% 0.19/0.87 (P4(f4(f14(x1361,x1362)),f14(x1362,x1361))),
% 0.19/0.87 inference(scs_inference,[],[33,42,44,36,67,66,120,123,126,79,69,72,65,62,61,53,55,26,28,2,54])).
% 0.19/0.87 cnf(139,plain,
% 0.19/0.87 (~E(a2,a3)),
% 0.19/0.87 inference(scs_inference,[],[33,42,44,36,67,66,120,123,126,79,69,72,75,104,65,62,61,53,55,26,28,2,54,27,3])).
% 0.19/0.87 cnf(140,plain,
% 0.19/0.87 (P2(f4(f10(x1401,f14(x1402,x1403))),f10(x1401,f14(x1403,x1402)))),
% 0.19/0.87 inference(scs_inference,[],[33,42,44,39,36,67,81,66,120,123,126,79,69,72,75,104,65,62,61,53,55,26,28,2,54,27,3,31])).
% 0.19/0.87 cnf(152,plain,
% 0.19/0.87 (P4(f4(f14(x1521,x1522)),f14(x1521,x1522))),
% 0.19/0.87 inference(scs_inference,[],[136,110])).
% 0.19/0.87 cnf(153,plain,
% 0.19/0.87 (~E(f14(x1531,x1532),f17(a1))),
% 0.19/0.87 inference(scs_inference,[],[66,36,136,110,65])).
% 0.19/0.87 cnf(154,plain,
% 0.19/0.87 (~P4(x1541,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(156,plain,
% 0.19/0.87 (P4(f6(a1,a5),a5)),
% 0.19/0.87 inference(scs_inference,[],[66,154,36,136,132,110,65,56])).
% 0.19/0.87 cnf(157,plain,
% 0.19/0.87 (~P4(x1571,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(161,plain,
% 0.19/0.87 (~P4(x1611,a2)),
% 0.19/0.87 inference(scs_inference,[],[66,154,157,36,136,132,79,110,65,56,55,28])).
% 0.19/0.87 cnf(163,plain,
% 0.19/0.87 (~E(f14(x1631,x1632),f16(a2))),
% 0.19/0.87 inference(scs_inference,[],[37,66,154,157,36,136,119,132,79,110,65,56,55,28,2,64])).
% 0.19/0.87 cnf(167,plain,
% 0.19/0.87 (P4(x1671,a3)+~E(f7(a1,a3),x1671)),
% 0.19/0.87 inference(scs_inference,[],[37,66,154,157,36,136,119,130,122,132,79,110,65,56,55,28,2,64,54,27])).
% 0.19/0.87 cnf(171,plain,
% 0.19/0.87 (P4(f8(a2,f14(x1711,x1712)),f14(x1711,x1712))),
% 0.19/0.87 inference(scs_inference,[],[37,163,161,61])).
% 0.19/0.87 cnf(172,plain,
% 0.19/0.87 (~P4(x1721,a2)),
% 0.19/0.87 inference(rename_variables,[],[161])).
% 0.19/0.87 cnf(174,plain,
% 0.19/0.87 (~E(f14(x1741,x1742),f16(a1))),
% 0.19/0.87 inference(scs_inference,[],[37,66,36,152,163,161,61,64])).
% 0.19/0.87 cnf(175,plain,
% 0.19/0.87 (~P4(x1751,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(177,plain,
% 0.19/0.87 (P4(f7(a1,f14(x1771,x1772)),f14(x1771,x1772))),
% 0.19/0.87 inference(scs_inference,[],[37,66,175,36,152,153,163,161,61,64,62])).
% 0.19/0.87 cnf(180,plain,
% 0.19/0.87 (P4(f4(f15(x1801)),f15(x1801))),
% 0.19/0.87 inference(scs_inference,[],[43,37,66,175,39,36,152,153,163,161,61,64,62,54])).
% 0.19/0.87 cnf(184,plain,
% 0.19/0.87 (~P4(x1841,a2)),
% 0.19/0.87 inference(rename_variables,[],[161])).
% 0.19/0.87 cnf(188,plain,
% 0.19/0.87 (~E(a2,f15(x1881))),
% 0.19/0.87 inference(scs_inference,[],[34,43,37,66,175,39,36,152,153,163,161,172,139,61,64,62,54,56,55,26])).
% 0.19/0.87 cnf(189,plain,
% 0.19/0.87 (P4(f4(f15(f14(x1891,x1892))),f15(f14(x1892,x1891)))),
% 0.19/0.87 inference(scs_inference,[],[34,43,37,66,175,39,36,152,153,163,161,172,139,98,61,64,62,54,56,55,26,28])).
% 0.19/0.87 cnf(190,plain,
% 0.19/0.87 (~E(f14(x1901,x1902),f17(a2))),
% 0.19/0.87 inference(scs_inference,[],[34,43,37,66,175,39,36,152,153,163,161,172,184,139,98,61,64,62,54,56,55,26,28,65])).
% 0.19/0.87 cnf(201,plain,
% 0.19/0.87 (~P4(x2011,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(203,plain,
% 0.19/0.87 (P4(f7(a2,f14(x2031,x2032)),f14(x2031,x2032))),
% 0.19/0.87 inference(scs_inference,[],[66,37,36,174,190,161,61,62])).
% 0.19/0.87 cnf(204,plain,
% 0.19/0.87 (~P4(x2041,a2)),
% 0.19/0.87 inference(rename_variables,[],[161])).
% 0.19/0.87 cnf(207,plain,
% 0.19/0.87 (~P4(f15(x2071),f4(f15(x2071)))),
% 0.19/0.87 inference(scs_inference,[],[66,37,36,180,171,174,190,161,61,62,110,55])).
% 0.19/0.87 cnf(211,plain,
% 0.19/0.87 (~E(a13,a5)),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,37,36,180,171,177,174,190,96,161,61,62,110,55,27,26])).
% 0.19/0.87 cnf(213,plain,
% 0.19/0.87 (~P4(x2131,a1)),
% 0.19/0.87 inference(rename_variables,[],[66])).
% 0.19/0.87 cnf(217,plain,
% 0.19/0.87 (E(f10(a1,x2171),f10(a2,x2171))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24])).
% 0.19/0.87 cnf(218,plain,
% 0.19/0.87 (E(f9(x2181,x2182,a1),f9(x2181,x2182,a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23])).
% 0.19/0.87 cnf(219,plain,
% 0.19/0.87 (E(f11(x2191,x2192,a1),f11(x2191,x2192,a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13])).
% 0.19/0.87 cnf(220,plain,
% 0.19/0.87 (E(f11(x2201,a1,x2202),f11(x2201,a2,x2202))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12])).
% 0.19/0.87 cnf(221,plain,
% 0.19/0.87 (E(f14(a1,x2211),f14(a2,x2211))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5])).
% 0.19/0.87 cnf(222,plain,
% 0.19/0.87 (E(f4(a1),f4(a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4])).
% 0.19/0.87 cnf(223,plain,
% 0.19/0.87 (E(f9(x2231,a1,x2232),f9(x2231,a2,x2232))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22])).
% 0.19/0.87 cnf(224,plain,
% 0.19/0.87 (E(f9(a1,x2241,x2242),f9(a2,x2241,x2242))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21])).
% 0.19/0.87 cnf(230,plain,
% 0.19/0.87 (E(f8(a1,x2301),f8(a2,x2301))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15])).
% 0.19/0.87 cnf(231,plain,
% 0.19/0.87 (E(f16(a1),f16(a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14])).
% 0.19/0.87 cnf(232,plain,
% 0.19/0.87 (E(f11(a1,x2321,x2322),f11(a2,x2321,x2322))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11])).
% 0.19/0.87 cnf(234,plain,
% 0.19/0.87 (E(f7(a1,x2341),f7(a2,x2341))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9])).
% 0.19/0.87 cnf(235,plain,
% 0.19/0.87 (E(f15(a1),f15(a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8])).
% 0.19/0.87 cnf(236,plain,
% 0.19/0.87 (E(f17(a1),f17(a2))),
% 0.19/0.87 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,135,161,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8,7])).
% 0.19/0.87 cnf(239,plain,
% 0.19/0.88 (~P4(x2391,f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,133,135,161,204,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8,7,6,3,64])).
% 0.19/0.88 cnf(240,plain,
% 0.19/0.88 (~P4(x2401,a2)),
% 0.19/0.88 inference(rename_variables,[],[161])).
% 0.19/0.88 cnf(242,plain,
% 0.19/0.88 (~P4(x2421,f17(a1))),
% 0.19/0.88 inference(scs_inference,[],[35,42,66,201,37,36,180,171,177,174,190,96,133,135,161,204,240,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8,7,6,3,64,65])).
% 0.19/0.88 cnf(247,plain,
% 0.19/0.88 (E(a1,f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[35,42,66,201,213,37,36,140,180,171,177,174,190,96,133,135,161,204,240,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8,7,6,3,64,65,54,56])).
% 0.19/0.88 cnf(252,plain,
% 0.19/0.88 (~P4(x2521,a13)),
% 0.19/0.88 inference(scs_inference,[],[35,42,66,201,213,37,36,140,180,171,177,174,190,96,133,135,161,204,240,61,62,110,55,27,26,28,46,25,24,23,13,12,5,4,22,21,20,19,18,17,16,15,14,11,10,9,8,7,6,3,64,65,54,56,2,167,52])).
% 0.19/0.88 cnf(256,plain,
% 0.19/0.88 (P3(f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[247,103])).
% 0.19/0.88 cnf(257,plain,
% 0.19/0.88 (~E(f15(f14(x2571,x2572)),f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[66,36,189,247,103,64])).
% 0.19/0.88 cnf(258,plain,
% 0.19/0.88 (~P4(x2581,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(260,plain,
% 0.19/0.88 (~E(a5,f17(a1))),
% 0.19/0.88 inference(scs_inference,[],[66,258,36,189,247,156,103,64,65])).
% 0.19/0.88 cnf(261,plain,
% 0.19/0.88 (~P4(x2611,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(266,plain,
% 0.19/0.88 (P1(f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[39,66,258,36,189,217,234,239,128,247,156,140,103,64,65,30,31,54])).
% 0.19/0.88 cnf(278,plain,
% 0.19/0.88 (P4(f7(a2,f14(x2781,x2782)),f14(x2782,x2781))),
% 0.19/0.88 inference(scs_inference,[],[39,66,258,261,36,189,203,218,223,217,234,239,128,247,156,140,104,96,103,64,65,30,31,54,3,56,55,27])).
% 0.19/0.88 cnf(282,plain,
% 0.19/0.88 (~E(f15(f14(x2821,x2822)),f17(a1))),
% 0.19/0.88 inference(scs_inference,[],[39,66,258,261,36,189,203,218,223,217,234,239,242,188,128,247,156,140,104,96,103,64,65,30,31,54,3,56,55,27,2,28])).
% 0.19/0.88 cnf(295,plain,
% 0.19/0.88 (P4(f8(a1,f15(f14(x2951,x2952))),f15(f14(x2951,x2952)))),
% 0.19/0.88 inference(scs_inference,[],[36,66,257,61])).
% 0.19/0.88 cnf(296,plain,
% 0.19/0.88 (~P4(x2961,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(298,plain,
% 0.19/0.88 (~E(a3,f17(a13))),
% 0.19/0.88 inference(scs_inference,[],[36,69,66,257,252,77,61,65])).
% 0.19/0.88 cnf(307,plain,
% 0.19/0.88 (P4(f6(f15(f14(x3071,x3072)),f16(a1)),f15(f14(x3071,x3072)))),
% 0.19/0.88 inference(scs_inference,[],[36,69,66,296,37,257,282,252,77,239,161,61,65,64,62,56])).
% 0.19/0.88 cnf(310,plain,
% 0.19/0.88 (P4(f4(a5),a5)),
% 0.19/0.88 inference(scs_inference,[],[36,42,69,39,66,296,37,257,282,252,77,239,161,61,65,64,62,56,54])).
% 0.19/0.88 cnf(311,plain,
% 0.19/0.88 (P2(f4(x3111),x3111)),
% 0.19/0.88 inference(rename_variables,[],[39])).
% 0.19/0.88 cnf(314,plain,
% 0.19/0.88 (~P4(f14(x3141,x3142),f7(a2,f14(x3142,x3141)))),
% 0.19/0.88 inference(scs_inference,[],[36,42,69,39,66,296,37,278,257,282,252,74,77,239,161,231,61,65,64,62,56,54,3,55])).
% 0.19/0.88 cnf(319,plain,
% 0.19/0.88 (P4(f7(a2,f14(x3191,a1)),f14(a2,x3191))),
% 0.19/0.88 inference(scs_inference,[],[36,42,69,39,66,296,37,207,278,219,221,257,282,235,252,74,77,239,161,231,61,65,64,62,56,54,3,55,27,2,28])).
% 0.19/0.88 cnf(320,plain,
% 0.19/0.88 (E(f14(a1,x3201),f14(a2,x3201))),
% 0.19/0.88 inference(rename_variables,[],[221])).
% 0.19/0.88 cnf(325,plain,
% 0.19/0.88 (P2(f4(f14(x3251,a1)),f14(a2,x3251))),
% 0.19/0.88 inference(scs_inference,[],[36,44,67,42,69,39,311,66,296,37,207,278,219,221,320,257,282,222,235,252,266,74,77,239,188,161,231,61,65,64,62,56,54,3,55,27,2,28,26,112,30,31])).
% 0.19/0.88 cnf(328,plain,
% 0.19/0.88 (E(a1,f16(a13))),
% 0.19/0.88 inference(scs_inference,[],[66,252,77,61])).
% 0.19/0.88 cnf(330,plain,
% 0.19/0.88 (~P4(x3301,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(332,plain,
% 0.19/0.88 (~E(a5,f16(a1))),
% 0.19/0.88 inference(scs_inference,[],[36,66,330,310,252,77,61,64])).
% 0.19/0.88 cnf(333,plain,
% 0.19/0.88 (~P4(x3331,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(336,plain,
% 0.19/0.88 (~P4(x3361,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(338,plain,
% 0.19/0.88 (~E(a3,f17(f16(a1)))),
% 0.19/0.88 inference(scs_inference,[],[36,69,66,330,333,310,260,256,252,77,239,61,64,62,65])).
% 0.19/0.88 cnf(343,plain,
% 0.19/0.88 (~P4(x3431,a1)),
% 0.19/0.88 inference(rename_variables,[],[66])).
% 0.19/0.88 cnf(347,plain,
% 0.19/0.88 (P4(f4(f14(x3471,a1)),f14(a2,x3471))),
% 0.19/0.88 inference(scs_inference,[],[36,44,69,66,330,333,336,307,325,310,260,256,252,242,77,239,61,64,62,65,56,55,54])).
% 0.19/0.88 cnf(352,plain,
% 0.19/0.88 (P4(f8(a2,f15(f14(x3521,x3522))),f15(f14(x3521,x3522)))),
% 0.19/0.88 inference(scs_inference,[],[36,44,69,66,330,333,336,307,295,220,232,325,230,310,260,256,252,242,77,239,61,64,62,65,56,55,54,3,27])).
% 0.19/0.88 cnf(355,plain,
% 0.19/0.88 (~E(f14(a2,x3551),a1)),
% 0.19/0.88 inference(scs_inference,[],[36,44,69,66,330,333,336,343,307,295,220,232,325,230,319,298,310,260,256,252,242,77,239,61,64,62,65,56,55,54,3,27,2,28])).
% 0.19/0.88 cnf(374,plain,
% 0.19/0.88 (P1(f17(a1))),
% 0.19/0.88 inference(scs_inference,[],[39,66,338,328,332,256,242,239,36,103,61,62,54])).
% 0.19/0.88 cnf(394,plain,
% 0.19/0.88 (E(f16(a1),a1)),
% 0.19/0.88 inference(scs_inference,[],[39,66,40,352,224,347,236,338,355,328,332,211,314,102,234,256,266,252,242,239,36,103,61,62,54,56,55,3,27,2,28,26,48,46])).
% 0.19/0.88 cnf(426,plain,
% 0.19/0.88 (~E(f17(a1),a1)),
% 0.19/0.88 inference(scs_inference,[],[394,47])).
% 0.19/0.88 cnf(453,plain,
% 0.19/0.88 ($false),
% 0.19/0.88 inference(scs_inference,[],[426,374,33,49]),
% 0.19/0.88 ['proof']).
% 0.19/0.88 % SZS output end Proof
% 0.19/0.88 % Total time :0.240000s
%------------------------------------------------------------------------------