TSTP Solution File: NUM410+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n031.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 10:21:57 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 09:56:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 % File : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.63 % Domain : Number Theory (Ordinals)
% 0.20/0.63 % Problem : Ordinal numbers, theorem 46
% 0.20/0.63 % Version : [Urb06] axioms : Especial.
% 0.20/0.63 % English :
% 0.20/0.63
% 0.20/0.63 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 0.20/0.63 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.63 % Source : [Urb06]
% 0.20/0.63 % Names : ordinal1__t46_ordinal1 [Urb06]
% 0.20/0.63
% 0.20/0.63 % Status : Theorem
% 0.20/0.63 % Rating : 0.08 v8.1.0, 0.03 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.1, 0.17 v3.7.0, 0.05 v3.3.0, 0.00 v3.2.0
% 0.20/0.63 % Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% 0.20/0.63 % Number of atoms : 131 ( 2 equ)
% 0.20/0.63 % Maximal formula atoms : 8 ( 2 avg)
% 0.20/0.63 % Number of connectives : 98 ( 12 ~; 1 |; 61 &)
% 0.20/0.63 % ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% 0.20/0.63 % Maximal formula depth : 8 ( 4 avg)
% 0.20/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.63 % Number of predicates : 16 ( 15 usr; 0 prp; 1-2 aty)
% 0.20/0.63 % Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% 0.20/0.63 % Number of variables : 56 ( 40 !; 16 ?)
% 0.20/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.63
% 0.20/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.63 % library, www.mizar.org
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( in(A,B)
% 0.20/0.63 => ~ in(B,A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc1_funct_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 => function(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc1_ordinal1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ordinal(A)
% 0.20/0.63 => ( epsilon_transitive(A)
% 0.20/0.63 & epsilon_connected(A) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc1_relat_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 => relation(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc2_funct_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( relation(A)
% 0.20/0.63 & empty(A)
% 0.20/0.63 & function(A) )
% 0.20/0.63 => ( relation(A)
% 0.20/0.63 & function(A)
% 0.20/0.63 & one_to_one(A) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc2_ordinal1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( epsilon_transitive(A)
% 0.20/0.63 & epsilon_connected(A) )
% 0.20/0.63 => ordinal(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(cc3_ordinal1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 => ( epsilon_transitive(A)
% 0.20/0.63 & epsilon_connected(A)
% 0.20/0.63 & ordinal(A) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(d7_ordinal1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( relation(A)
% 0.20/0.63 & function(A) )
% 0.20/0.63 => ( transfinite_sequence(A)
% 0.20/0.63 <=> ordinal(relation_dom(A)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(d8_ordinal1,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( ( relation(B)
% 0.20/0.63 & function(B)
% 0.20/0.63 & transfinite_sequence(B) )
% 0.20/0.63 => ( transfinite_sequence_of(B,A)
% 0.20/0.63 <=> subset(relation_rng(B),A) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(dt_m1_ordinal1,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( transfinite_sequence_of(B,A)
% 0.20/0.63 => ( relation(B)
% 0.20/0.63 & function(B)
% 0.20/0.63 & transfinite_sequence(B) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(existence_m1_ordinal1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ? [B] : transfinite_sequence_of(B,A) ).
% 0.20/0.63
% 0.20/0.63 fof(existence_m1_subset_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ? [B] : element(B,A) ).
% 0.20/0.63
% 0.20/0.63 fof(fc12_relat_1,axiom,
% 0.20/0.63 ( empty(empty_set)
% 0.20/0.63 & relation(empty_set)
% 0.20/0.63 & relation_empty_yielding(empty_set) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc1_xboole_0,axiom,
% 0.20/0.63 empty(empty_set) ).
% 0.20/0.63
% 0.20/0.63 fof(fc2_ordinal1,axiom,
% 0.20/0.63 ( relation(empty_set)
% 0.20/0.63 & relation_empty_yielding(empty_set)
% 0.20/0.63 & function(empty_set)
% 0.20/0.63 & one_to_one(empty_set)
% 0.20/0.63 & empty(empty_set)
% 0.20/0.63 & epsilon_transitive(empty_set)
% 0.20/0.63 & epsilon_connected(empty_set)
% 0.20/0.63 & ordinal(empty_set) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc4_relat_1,axiom,
% 0.20/0.63 ( empty(empty_set)
% 0.20/0.63 & relation(empty_set) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc5_relat_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( ~ empty(A)
% 0.20/0.63 & relation(A) )
% 0.20/0.63 => ~ empty(relation_dom(A)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc6_funct_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( relation(A)
% 0.20/0.63 & relation_non_empty(A)
% 0.20/0.63 & function(A) )
% 0.20/0.63 => with_non_empty_elements(relation_rng(A)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc6_relat_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( ( ~ empty(A)
% 0.20/0.63 & relation(A) )
% 0.20/0.63 => ~ empty(relation_rng(A)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc7_relat_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 => ( empty(relation_dom(A))
% 0.20/0.63 & relation(relation_dom(A)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc8_relat_1,axiom,
% 0.20/0.63 ! [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 => ( empty(relation_rng(A))
% 0.20/0.63 & relation(relation_rng(A)) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(rc1_funct_1,axiom,
% 0.20/0.63 ? [A] :
% 0.20/0.63 ( relation(A)
% 0.20/0.63 & function(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(rc1_ordinal1,axiom,
% 0.20/0.63 ? [A] :
% 0.20/0.63 ( epsilon_transitive(A)
% 0.20/0.63 & epsilon_connected(A)
% 0.20/0.63 & ordinal(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(rc1_relat_1,axiom,
% 0.20/0.63 ? [A] :
% 0.20/0.63 ( empty(A)
% 0.20/0.63 & relation(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(rc1_xboole_0,axiom,
% 0.20/0.63 ? [A] : empty(A) ).
% 0.20/0.63
% 0.20/0.63 fof(rc2_funct_1,axiom,
% 0.20/0.63 ? [A] :
% 0.20/0.63 ( relation(A)
% 0.20/0.63 & empty(A)
% 0.20/0.63 & function(A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(rc2_ordinal1,axiom,
% 0.20/0.63 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & function(A)
% 0.20/0.64 & one_to_one(A)
% 0.20/0.64 & empty(A)
% 0.20/0.64 & epsilon_transitive(A)
% 0.20/0.64 & epsilon_connected(A)
% 0.20/0.64 & ordinal(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc2_relat_1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( ~ empty(A)
% 0.20/0.64 & relation(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc2_xboole_0,axiom,
% 0.20/0.64 ? [A] : ~ empty(A) ).
% 0.20/0.64
% 0.20/0.64 fof(rc3_funct_1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & function(A)
% 0.20/0.64 & one_to_one(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc3_ordinal1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( ~ empty(A)
% 0.20/0.64 & epsilon_transitive(A)
% 0.20/0.64 & epsilon_connected(A)
% 0.20/0.64 & ordinal(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc3_relat_1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & relation_empty_yielding(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc4_funct_1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & relation_empty_yielding(A)
% 0.20/0.64 & function(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc4_ordinal1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & function(A)
% 0.20/0.64 & transfinite_sequence(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc5_funct_1,axiom,
% 0.20/0.64 ? [A] :
% 0.20/0.64 ( relation(A)
% 0.20/0.64 & relation_non_empty(A)
% 0.20/0.64 & function(A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(reflexivity_r1_tarski,axiom,
% 0.20/0.64 ! [A,B] : subset(A,A) ).
% 0.20/0.64
% 0.20/0.64 fof(t1_subset,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( in(A,B)
% 0.20/0.64 => element(A,B) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t2_subset,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( element(A,B)
% 0.20/0.64 => ( empty(B)
% 0.20/0.64 | in(A,B) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t3_subset,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( element(A,powerset(B))
% 0.20/0.64 <=> subset(A,B) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t46_ordinal1,conjecture,
% 0.20/0.64 ! [A] :
% 0.20/0.64 ( ( relation(A)
% 0.20/0.64 & function(A) )
% 0.20/0.64 => ( ordinal(relation_dom(A))
% 0.20/0.64 => transfinite_sequence_of(A,relation_rng(A)) ) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t4_subset,axiom,
% 0.20/0.64 ! [A,B,C] :
% 0.20/0.64 ( ( in(A,B)
% 0.20/0.64 & element(B,powerset(C)) )
% 0.20/0.64 => element(A,C) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t5_subset,axiom,
% 0.20/0.64 ! [A,B,C] :
% 0.20/0.64 ~ ( in(A,B)
% 0.20/0.64 & element(B,powerset(C))
% 0.20/0.64 & empty(C) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t6_boole,axiom,
% 0.20/0.64 ! [A] :
% 0.20/0.64 ( empty(A)
% 0.20/0.64 => A = empty_set ) ).
% 0.20/0.64
% 0.20/0.64 fof(t7_boole,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ~ ( in(A,B)
% 0.20/0.64 & empty(B) ) ).
% 0.20/0.64
% 0.20/0.64 fof(t8_boole,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ~ ( empty(A)
% 0.20/0.64 & A != B
% 0.20/0.64 & empty(B) ) ).
% 0.20/0.64
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:120(EqnAxiom:27)
% 0.20/0.64 %VarNum:117(SingletonVarNum:52)
% 0.20/0.64 %MaxLitNum:5
% 0.20/0.64 %MaxfuncDepth:1
% 0.20/0.64 %SharedTerms:69
% 0.20/0.64 %goalClause: 44 70 80 87
% 0.20/0.64 %singleGoalClaCount:4
% 0.20/0.64 [31]P1(a1)
% 0.20/0.64 [32]P1(a2)
% 0.20/0.64 [33]P1(a15)
% 0.20/0.64 [34]P1(a16)
% 0.20/0.64 [35]P1(a17)
% 0.20/0.64 [36]P3(a1)
% 0.20/0.64 [37]P3(a3)
% 0.20/0.64 [38]P3(a16)
% 0.20/0.64 [39]P3(a17)
% 0.20/0.64 [40]P3(a4)
% 0.20/0.64 [41]P3(a6)
% 0.20/0.64 [42]P3(a9)
% 0.20/0.64 [43]P3(a10)
% 0.20/0.64 [44]P3(a11)
% 0.20/0.64 [45]P6(a1)
% 0.20/0.64 [46]P6(a14)
% 0.20/0.64 [47]P6(a17)
% 0.20/0.64 [48]P6(a7)
% 0.20/0.64 [49]P4(a1)
% 0.20/0.64 [50]P4(a14)
% 0.20/0.64 [51]P4(a17)
% 0.20/0.64 [52]P4(a7)
% 0.20/0.64 [53]P5(a1)
% 0.20/0.64 [54]P5(a14)
% 0.20/0.64 [55]P5(a17)
% 0.20/0.64 [56]P5(a7)
% 0.20/0.64 [59]P9(a1)
% 0.20/0.64 [60]P9(a3)
% 0.20/0.64 [61]P9(a2)
% 0.20/0.64 [62]P9(a16)
% 0.20/0.64 [63]P9(a17)
% 0.20/0.64 [64]P9(a18)
% 0.20/0.64 [65]P9(a4)
% 0.20/0.64 [66]P9(a8)
% 0.20/0.64 [67]P9(a6)
% 0.20/0.64 [68]P9(a9)
% 0.20/0.64 [69]P9(a10)
% 0.20/0.64 [70]P9(a11)
% 0.20/0.64 [71]P7(a1)
% 0.20/0.64 [72]P7(a17)
% 0.20/0.64 [73]P7(a4)
% 0.20/0.64 [74]P10(a9)
% 0.20/0.64 [76]P11(a1)
% 0.20/0.64 [77]P11(a8)
% 0.20/0.64 [78]P11(a6)
% 0.20/0.64 [79]P12(a10)
% 0.20/0.64 [84]~P1(a18)
% 0.20/0.64 [85]~P1(a5)
% 0.20/0.64 [86]~P1(a7)
% 0.20/0.64 [80]P6(f19(a11))
% 0.20/0.64 [87]~P14(a11,f21(a11))
% 0.20/0.64 [81]P13(x811,x811)
% 0.20/0.64 [82]P14(f12(x821),x821)
% 0.20/0.64 [83]P2(f13(x831),x831)
% 0.20/0.64 [88]~P1(x881)+E(x881,a1)
% 0.20/0.64 [89]~P1(x891)+P3(x891)
% 0.20/0.64 [90]~P1(x901)+P6(x901)
% 0.20/0.64 [91]~P1(x911)+P4(x911)
% 0.20/0.64 [92]~P6(x921)+P4(x921)
% 0.20/0.64 [93]~P1(x931)+P5(x931)
% 0.20/0.64 [94]~P6(x941)+P5(x941)
% 0.20/0.64 [95]~P1(x951)+P9(x951)
% 0.20/0.64 [97]~P1(x971)+P1(f19(x971))
% 0.20/0.64 [98]~P1(x981)+P1(f21(x981))
% 0.20/0.64 [99]~P1(x991)+P9(f19(x991))
% 0.20/0.64 [100]~P1(x1001)+P9(f21(x1001))
% 0.20/0.64 [103]P3(x1031)+~P14(x1031,x1032)
% 0.20/0.64 [104]P9(x1041)+~P14(x1041,x1042)
% 0.20/0.64 [105]P10(x1051)+~P14(x1051,x1052)
% 0.20/0.64 [108]~P1(x1081)+~P8(x1082,x1081)
% 0.20/0.64 [112]~P8(x1121,x1122)+P2(x1121,x1122)
% 0.20/0.64 [115]~P8(x1152,x1151)+~P8(x1151,x1152)
% 0.20/0.64 [114]~P13(x1141,x1142)+P2(x1141,f20(x1142))
% 0.20/0.64 [116]P13(x1161,x1162)+~P2(x1161,f20(x1162))
% 0.20/0.64 [101]~P4(x1011)+~P5(x1011)+P6(x1011)
% 0.20/0.64 [106]~P9(x1061)+P1(x1061)+~P1(f19(x1061))
% 0.20/0.64 [107]~P9(x1071)+P1(x1071)+~P1(f21(x1071))
% 0.20/0.64 [96]~P1(x962)+~P1(x961)+E(x961,x962)
% 0.20/0.64 [113]~P2(x1132,x1131)+P1(x1131)+P8(x1132,x1131)
% 0.20/0.64 [117]~P1(x1171)+~P8(x1172,x1173)+~P2(x1173,f20(x1171))
% 0.20/0.64 [120]P2(x1201,x1202)+~P8(x1201,x1203)+~P2(x1203,f20(x1202))
% 0.20/0.64 [102]~P1(x1021)+~P3(x1021)+~P9(x1021)+P7(x1021)
% 0.20/0.64 [109]~P3(x1091)+~P9(x1091)+~P10(x1091)+P6(f19(x1091))
% 0.20/0.64 [110]~P3(x1101)+~P9(x1101)+~P12(x1101)+P15(f21(x1101))
% 0.20/0.64 [111]~P3(x1111)+~P9(x1111)+P10(x1111)+~P6(f19(x1111))
% 0.20/0.64 [118]~P3(x1181)+~P9(x1181)+~P10(x1181)+~P14(x1181,x1182)+P13(f21(x1181),x1182)
% 0.20/0.64 [119]~P3(x1191)+~P9(x1191)+~P10(x1191)+P14(x1191,x1192)+~P13(f21(x1191),x1192)
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f19(x41),f19(x42))
% 0.20/0.64 [5]~E(x51,x52)+E(f12(x51),f12(x52))
% 0.20/0.64 [6]~E(x61,x62)+E(f13(x61),f13(x62))
% 0.20/0.64 [7]~E(x71,x72)+E(f21(x71),f21(x72))
% 0.20/0.64 [8]~E(x81,x82)+E(f20(x81),f20(x82))
% 0.20/0.64 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.20/0.64 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 0.20/0.64 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 0.20/0.64 [12]P8(x122,x123)+~E(x121,x122)+~P8(x121,x123)
% 0.20/0.64 [13]P8(x133,x132)+~E(x131,x132)+~P8(x133,x131)
% 0.20/0.64 [14]~P9(x141)+P9(x142)+~E(x141,x142)
% 0.20/0.64 [15]P13(x152,x153)+~E(x151,x152)+~P13(x151,x153)
% 0.20/0.64 [16]P13(x163,x162)+~E(x161,x162)+~P13(x163,x161)
% 0.20/0.64 [17]~P10(x171)+P10(x172)+~E(x171,x172)
% 0.20/0.64 [18]~P6(x181)+P6(x182)+~E(x181,x182)
% 0.20/0.64 [19]~P3(x191)+P3(x192)+~E(x191,x192)
% 0.20/0.64 [20]P14(x202,x203)+~E(x201,x202)+~P14(x201,x203)
% 0.20/0.64 [21]P14(x213,x212)+~E(x211,x212)+~P14(x213,x211)
% 0.20/0.64 [22]~P4(x221)+P4(x222)+~E(x221,x222)
% 0.20/0.64 [23]~P5(x231)+P5(x232)+~E(x231,x232)
% 0.20/0.64 [24]~P12(x241)+P12(x242)+~E(x241,x242)
% 0.20/0.64 [25]~P11(x251)+P11(x252)+~E(x251,x252)
% 0.20/0.64 [26]~P7(x261)+P7(x262)+~E(x261,x262)
% 0.20/0.64 [27]~P15(x271)+P15(x272)+~E(x271,x272)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(123,plain,
% 0.20/0.64 (P2(f13(x1231),x1231)),
% 0.20/0.64 inference(rename_variables,[],[83])).
% 0.20/0.64 cnf(128,plain,
% 0.20/0.64 (P2(f13(x1281),x1281)),
% 0.20/0.64 inference(rename_variables,[],[83])).
% 0.20/0.64 cnf(137,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[44,81,70,31,34,38,62,84,87,80,82,83,123,128,108,116,20,113,117,102,111,119]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------