TSTP Solution File: SET902+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET902+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 : 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 : Thu Aug 31 14:31:37 EDT 2023
% Result : Theorem 90.94s 91.00s
% Output : CNFRefutation 91.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 10:10:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 90.94/90.99 %-------------------------------------------
% 90.94/90.99 % File :CSE---1.6
% 90.94/90.99 % Problem :theBenchmark
% 90.94/90.99 % Transform :cnf
% 90.94/90.99 % Format :tptp:raw
% 90.94/90.99 % Command :java -jar mcs_scs.jar %d %s
% 90.94/90.99
% 90.94/90.99 % Result :Theorem 90.380000s
% 90.94/90.99 % Output :CNFRefutation 90.380000s
% 90.94/90.99 %-------------------------------------------
% 90.94/90.99 %------------------------------------------------------------------------------
% 90.94/91.00 % File : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 90.94/91.00 % Domain : Set theory
% 90.94/91.00 % Problem : Basic properties of sets, theorem 43
% 90.94/91.00 % Version : [Urb06] axioms : Especial.
% 90.94/91.00 % English : ~ ( singleton(A) = set_union2(B,C) & ~ ( B = singleton(A) &
% 90.94/91.00 % C = singleton(A) ) & ~ ( B = empty_set & C = singleton(A) ) &
% 90.94/91.00 % ~ ( B = singleton(A) & C = empty_set ) )
% 90.94/91.00
% 90.94/91.00 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 90.94/91.00 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 90.94/91.00 % Source : [Urb06]
% 90.94/91.00 % Names : zfmisc_1__t43_zfmisc_1 [Urb06]
% 90.94/91.00
% 90.94/91.00 % Status : Theorem
% 90.94/91.00 % Rating : 0.17 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.17 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.10 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.05 v3.4.0, 0.21 v3.3.0, 0.14 v3.2.0
% 90.94/91.00 % Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% 90.94/91.00 % Number of atoms : 22 ( 12 equ)
% 90.94/91.00 % Maximal formula atoms : 7 ( 1 avg)
% 90.94/91.00 % Number of connectives : 20 ( 10 ~; 1 |; 6 &)
% 90.94/91.00 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 90.94/91.00 % Maximal formula depth : 10 ( 4 avg)
% 90.94/91.00 % Maximal term depth : 2 ( 1 avg)
% 90.94/91.00 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 90.94/91.00 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 90.94/91.00 % Number of variables : 20 ( 18 !; 2 ?)
% 90.94/91.00 % SPC : FOF_THM_RFO_SEQ
% 90.94/91.00
% 90.94/91.00 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 90.94/91.00 % library, www.mizar.org
% 90.94/91.00 %------------------------------------------------------------------------------
% 90.94/91.00 fof(commutativity_k2_xboole_0,axiom,
% 90.94/91.00 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 90.94/91.00
% 90.94/91.00 fof(fc1_xboole_0,axiom,
% 90.94/91.00 empty(empty_set) ).
% 90.94/91.00
% 90.94/91.00 fof(fc2_xboole_0,axiom,
% 90.94/91.00 ! [A,B] :
% 90.94/91.00 ( ~ empty(A)
% 90.94/91.00 => ~ empty(set_union2(A,B)) ) ).
% 90.94/91.00
% 90.94/91.00 fof(fc3_xboole_0,axiom,
% 90.94/91.00 ! [A,B] :
% 90.94/91.00 ( ~ empty(A)
% 90.94/91.00 => ~ empty(set_union2(B,A)) ) ).
% 90.94/91.00
% 90.94/91.00 fof(idempotence_k2_xboole_0,axiom,
% 90.94/91.00 ! [A,B] : set_union2(A,A) = A ).
% 90.94/91.00
% 90.94/91.00 fof(l1_zfmisc_1,axiom,
% 90.94/91.00 ! [A] : singleton(A) != empty_set ).
% 90.94/91.00
% 90.94/91.00 fof(l4_zfmisc_1,axiom,
% 90.94/91.00 ! [A,B] :
% 90.94/91.00 ( subset(A,singleton(B))
% 90.94/91.00 <=> ( A = empty_set
% 90.94/91.00 | A = singleton(B) ) ) ).
% 90.94/91.00
% 90.94/91.00 fof(rc1_xboole_0,axiom,
% 90.94/91.00 ? [A] : empty(A) ).
% 90.94/91.00
% 90.94/91.00 fof(rc2_xboole_0,axiom,
% 90.94/91.00 ? [A] : ~ empty(A) ).
% 90.94/91.00
% 90.94/91.00 fof(reflexivity_r1_tarski,axiom,
% 90.94/91.00 ! [A,B] : subset(A,A) ).
% 90.94/91.00
% 90.94/91.00 fof(t43_zfmisc_1,conjecture,
% 90.94/91.00 ! [A,B,C] :
% 90.94/91.00 ~ ( singleton(A) = set_union2(B,C)
% 90.94/91.00 & ~ ( B = singleton(A)
% 90.94/91.00 & C = singleton(A) )
% 90.94/91.00 & ~ ( B = empty_set
% 90.94/91.00 & C = singleton(A) )
% 90.94/91.00 & ~ ( B = singleton(A)
% 90.94/91.00 & C = empty_set ) ) ).
% 90.94/91.00
% 90.94/91.00 fof(t7_xboole_1,axiom,
% 90.94/91.00 ! [A,B] : subset(A,set_union2(A,B)) ).
% 90.94/91.00
% 90.94/91.00 %------------------------------------------------------------------------------
% 90.94/91.00 %-------------------------------------------
% 90.94/91.00 % Proof found
% 90.94/91.00 % SZS status Theorem for theBenchmark
% 90.94/91.00 % SZS output start Proof
% 90.94/91.00 %ClaNum:26(EqnAxiom:9)
% 90.94/91.00 %VarNum:31(SingletonVarNum:17)
% 90.94/91.00 %MaxLitNum:3
% 90.94/91.00 %MaxfuncDepth:1
% 90.94/91.00 %SharedTerms:16
% 90.94/91.00 %goalClause: 12 19 20 21
% 90.94/91.00 %singleGoalClaCount:1
% 90.94/91.00 [10]P1(a1)
% 90.94/91.00 [11]P1(a2)
% 90.94/91.00 [17]~P1(a5)
% 90.94/91.00 [12]E(f7(a3,a6),f8(a4))
% 90.94/91.00 [13]P2(x131,x131)
% 90.94/91.00 [14]E(f7(x141,x141),x141)
% 90.94/91.00 [18]~E(f8(x181),a1)
% 90.94/91.00 [15]E(f7(x151,x152),f7(x152,x151))
% 90.94/91.00 [16]P2(x161,f7(x161,x162))
% 90.94/91.00 [19]~E(a3,a1)+~E(f8(a4),a6)
% 90.94/91.00 [20]~E(a6,a1)+~E(f8(a4),a3)
% 90.94/91.00 [21]~E(f8(a4),a3)+~E(f8(a4),a6)
% 90.94/91.00 [22]~E(x221,a1)+P2(x221,f8(x222))
% 90.94/91.00 [23]P2(x231,f8(x232))+~E(x231,f8(x232))
% 90.94/91.00 [25]P1(x251)+~P1(f7(x252,x251))
% 90.94/91.00 [26]P1(x261)+~P1(f7(x261,x262))
% 90.94/91.00 [24]E(x241,a1)+E(x241,f8(x242))+~P2(x241,f8(x242))
% 90.94/91.00 %EqnAxiom
% 90.94/91.00 [1]E(x11,x11)
% 90.94/91.00 [2]E(x22,x21)+~E(x21,x22)
% 90.94/91.00 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 90.94/91.00 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 90.94/91.00 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 90.94/91.00 [6]~E(x61,x62)+E(f8(x61),f8(x62))
% 90.94/91.00 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 90.94/91.00 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 90.94/91.00 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 90.94/91.00
% 90.94/91.00 %-------------------------------------------
% 91.01/91.01 cnf(27,plain,
% 91.01/91.01 (E(f8(a4),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[12,2])).
% 91.01/91.01 cnf(28,plain,
% 91.01/91.01 (P2(f7(a1,a1),f8(x281))),
% 91.01/91.01 inference(scs_inference,[],[12,14,2,22])).
% 91.01/91.01 cnf(29,plain,
% 91.01/91.01 (E(f7(x291,x291),x291)),
% 91.01/91.01 inference(rename_variables,[],[14])).
% 91.01/91.01 cnf(31,plain,
% 91.01/91.01 (P2(f7(a3,a6),f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[12,13,14,2,22,9])).
% 91.01/91.01 cnf(32,plain,
% 91.01/91.01 (P2(f8(a4),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[12,13,14,2,22,9,8])).
% 91.01/91.01 cnf(34,plain,
% 91.01/91.01 (E(f7(x341,x341),x341)),
% 91.01/91.01 inference(rename_variables,[],[14])).
% 91.01/91.01 cnf(35,plain,
% 91.01/91.01 (E(f7(f7(a3,a6),f7(a3,a6)),f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,2,22,9,8,7,3])).
% 91.01/91.01 cnf(36,plain,
% 91.01/91.01 (E(f7(x361,x361),x361)),
% 91.01/91.01 inference(rename_variables,[],[14])).
% 91.01/91.01 cnf(37,plain,
% 91.01/91.01 (~P1(f7(a5,x371))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,2,22,9,8,7,3,26])).
% 91.01/91.01 cnf(39,plain,
% 91.01/91.01 (~P1(f7(x391,a5))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,2,22,9,8,7,3,26,25])).
% 91.01/91.01 cnf(41,plain,
% 91.01/91.01 (E(f8(f7(x411,x411)),f8(x411))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,36,2,22,9,8,7,3,26,25,6])).
% 91.01/91.01 cnf(42,plain,
% 91.01/91.01 (E(f7(x421,f7(x422,x422)),f7(x421,x422))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,36,2,22,9,8,7,3,26,25,6,5])).
% 91.01/91.01 cnf(43,plain,
% 91.01/91.01 (E(f7(f7(x431,x431),x432),f7(x431,x432))),
% 91.01/91.01 inference(scs_inference,[],[12,13,17,14,29,34,36,2,22,9,8,7,3,26,25,6,5,4])).
% 91.01/91.01 cnf(47,plain,
% 91.01/91.01 (~E(a1,f8(x471))),
% 91.01/91.01 inference(scs_inference,[],[18,2])).
% 91.01/91.01 cnf(48,plain,
% 91.01/91.01 (~E(a1,a5)),
% 91.01/91.01 inference(scs_inference,[],[10,18,17,2,7])).
% 91.01/91.01 cnf(49,plain,
% 91.01/91.01 (~E(a1,f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[12,10,18,17,2,7,3])).
% 91.01/91.01 cnf(50,plain,
% 91.01/91.01 (P2(f8(a4),f7(f7(a3,a6),x501))),
% 91.01/91.01 inference(scs_inference,[],[12,10,16,18,17,2,7,3,8])).
% 91.01/91.01 cnf(51,plain,
% 91.01/91.01 (P2(x511,f7(x511,x512))),
% 91.01/91.01 inference(rename_variables,[],[16])).
% 91.01/91.01 cnf(52,plain,
% 91.01/91.01 (P2(a3,f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[12,10,16,51,18,17,2,7,3,8,9])).
% 91.01/91.01 cnf(54,plain,
% 91.01/91.01 (E(x541,f7(x541,x541))),
% 91.01/91.01 inference(scs_inference,[],[14,2])).
% 91.01/91.01 cnf(55,plain,
% 91.01/91.01 (E(f8(a4),f7(a6,a3))),
% 91.01/91.01 inference(scs_inference,[],[27,15,14,2,3])).
% 91.01/91.01 cnf(57,plain,
% 91.01/91.01 (E(a3,f8(a4))+E(a3,a1)),
% 91.01/91.01 inference(scs_inference,[],[27,15,14,52,2,3,24])).
% 91.01/91.01 cnf(60,plain,
% 91.01/91.01 (~E(f7(a3,a6),a1)),
% 91.01/91.01 inference(scs_inference,[],[49,2])).
% 91.01/91.01 cnf(61,plain,
% 91.01/91.01 (~E(a1,f7(a6,a3))),
% 91.01/91.01 inference(scs_inference,[],[15,49,2,3])).
% 91.01/91.01 cnf(65,plain,
% 91.01/91.01 (E(f8(x651),f8(f7(x651,x651)))),
% 91.01/91.01 inference(scs_inference,[],[14,41,37,7,2])).
% 91.01/91.01 cnf(66,plain,
% 91.01/91.01 (~E(f7(a1,a1),f7(a6,a3))),
% 91.01/91.01 inference(scs_inference,[],[14,41,54,61,37,7,2,3])).
% 91.01/91.01 cnf(67,plain,
% 91.01/91.01 (E(x671,f7(x671,x671))),
% 91.01/91.01 inference(rename_variables,[],[54])).
% 91.01/91.01 cnf(72,plain,
% 91.01/91.01 (E(f7(x721,x722),f7(x721,f7(x722,x722)))),
% 91.01/91.01 inference(scs_inference,[],[14,41,54,67,61,37,7,2,3,25,26,5])).
% 91.01/91.01 cnf(73,plain,
% 91.01/91.01 (E(f7(x731,x732),f7(f7(x731,x731),x732))),
% 91.01/91.01 inference(scs_inference,[],[14,41,54,67,61,37,7,2,3,25,26,5,4])).
% 91.01/91.01 cnf(78,plain,
% 91.01/91.01 (P2(f7(a1,a1),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[28,27,16,8,9])).
% 91.01/91.01 cnf(80,plain,
% 91.01/91.01 (P1(f7(a2,a2))),
% 91.01/91.01 inference(scs_inference,[],[11,28,27,16,54,8,9,7])).
% 91.01/91.01 cnf(82,plain,
% 91.01/91.01 (~E(f7(a6,a3),f7(a1,a1))),
% 91.01/91.01 inference(scs_inference,[],[11,28,27,16,66,54,8,9,7,2])).
% 91.01/91.01 cnf(83,plain,
% 91.01/91.01 (E(f7(f8(a4),f8(a4)),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[11,28,27,16,14,66,54,8,9,7,2,3])).
% 91.01/91.01 cnf(85,plain,
% 91.01/91.01 (~E(f7(a2,a2),a5)),
% 91.01/91.01 inference(scs_inference,[],[17,80,7])).
% 91.01/91.01 cnf(86,plain,
% 91.01/91.01 (E(f7(a3,a6),f7(f8(a4),f8(a4)))),
% 91.01/91.01 inference(scs_inference,[],[17,83,80,7,2])).
% 91.01/91.01 cnf(87,plain,
% 91.01/91.01 (~E(f8(x871),f7(a1,a1))),
% 91.01/91.01 inference(scs_inference,[],[18,17,14,83,80,7,2,3])).
% 91.01/91.01 cnf(88,plain,
% 91.01/91.01 (E(f7(x881,x881),x881)),
% 91.01/91.01 inference(rename_variables,[],[14])).
% 91.01/91.01 cnf(89,plain,
% 91.01/91.01 (P2(f7(x891,x892),f7(x892,x891))),
% 91.01/91.01 inference(scs_inference,[],[13,18,15,17,14,83,80,7,2,3,8])).
% 91.01/91.01 cnf(90,plain,
% 91.01/91.01 (P2(x901,x901)),
% 91.01/91.01 inference(rename_variables,[],[13])).
% 91.01/91.01 cnf(91,plain,
% 91.01/91.01 (P2(f7(x911,x911),x911)),
% 91.01/91.01 inference(scs_inference,[],[13,90,18,15,17,14,88,83,80,7,2,3,8,9])).
% 91.01/91.01 cnf(94,plain,
% 91.01/91.01 (~E(f7(a3,a6),f7(a1,a1))),
% 91.01/91.01 inference(scs_inference,[],[27,87,2,3])).
% 91.01/91.01 cnf(97,plain,
% 91.01/91.01 (E(f7(x971,x971),x971)),
% 91.01/91.01 inference(rename_variables,[],[14])).
% 91.01/91.01 cnf(99,plain,
% 91.01/91.01 (E(f7(f7(x991,x992),f7(x991,x992)),f7(x992,x991))),
% 91.01/91.01 inference(scs_inference,[],[14,97,15,55,39,7,2,3])).
% 91.01/91.01 cnf(103,plain,
% 91.01/91.01 (~P1(f7(x1031,f7(x1032,a5)))),
% 91.01/91.01 inference(scs_inference,[],[14,97,15,65,55,39,7,2,3,23,25])).
% 91.01/91.01 cnf(105,plain,
% 91.01/91.01 (~P1(f7(f7(x1051,a5),x1052))),
% 91.01/91.01 inference(scs_inference,[],[14,97,15,65,55,39,7,2,3,23,25,26])).
% 91.01/91.01 cnf(107,plain,
% 91.01/91.01 (P1(f7(a2,f7(a2,a2)))),
% 91.01/91.01 inference(scs_inference,[],[72,80,7])).
% 91.01/91.01 cnf(109,plain,
% 91.01/91.01 (~E(f7(a1,a1),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[72,94,80,7,2])).
% 91.01/91.01 cnf(110,plain,
% 91.01/91.01 (~E(f7(a6,a3),f7(f7(a1,a1),f7(a1,a1)))),
% 91.01/91.01 inference(scs_inference,[],[99,72,82,94,80,7,2,3])).
% 91.01/91.01 cnf(113,plain,
% 91.01/91.01 (E(f7(x1131,x1132),f7(x1132,x1131))),
% 91.01/91.01 inference(rename_variables,[],[15])).
% 91.01/91.01 cnf(114,plain,
% 91.01/91.01 (P2(f8(a4),f7(a6,a3))),
% 91.01/91.01 inference(scs_inference,[],[15,113,32,31,8,9])).
% 91.01/91.01 cnf(115,plain,
% 91.01/91.01 (E(f7(x1151,x1152),f7(x1152,x1151))),
% 91.01/91.01 inference(rename_variables,[],[15])).
% 91.01/91.01 cnf(117,plain,
% 91.01/91.01 (E(f8(a4),f7(f7(a3,a6),f7(a3,a6)))),
% 91.01/91.01 inference(scs_inference,[],[15,113,32,35,31,17,107,8,9,7,2])).
% 91.01/91.01 cnf(118,plain,
% 91.01/91.01 (~E(f7(a3,a6),f7(f7(a1,a1),f7(a1,a1)))),
% 91.01/91.01 inference(scs_inference,[],[15,113,115,32,35,31,17,110,107,8,9,7,2,3])).
% 91.01/91.01 cnf(120,plain,
% 91.01/91.01 (~E(f7(f7(a1,a1),f7(a1,a1)),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[118,2])).
% 91.01/91.01 cnf(121,plain,
% 91.01/91.01 (E(f7(x1211,f7(x1212,x1212)),f7(x1212,x1211))),
% 91.01/91.01 inference(scs_inference,[],[15,42,118,2,3])).
% 91.01/91.01 cnf(125,plain,
% 91.01/91.01 (P2(f7(x1251,x1251),f7(x1251,x1252))),
% 91.01/91.01 inference(scs_inference,[],[15,28,16,42,43,73,118,2,3,8,9])).
% 91.01/91.01 cnf(128,plain,
% 91.01/91.01 (P1(f7(f7(a2,a2),a2))),
% 91.01/91.01 inference(scs_inference,[],[15,28,16,42,43,73,118,107,2,3,8,9,7])).
% 91.01/91.01 cnf(134,plain,
% 91.01/91.01 (E(f7(x1341,x1342),f7(x1342,f7(x1341,x1341)))),
% 91.01/91.01 inference(scs_inference,[],[37,121,128,7,2])).
% 91.01/91.01 cnf(145,plain,
% 91.01/91.01 (E(f7(x1451,x1452),f7(f7(x1452,x1451),f7(x1452,x1451)))),
% 91.01/91.01 inference(scs_inference,[],[99,2])).
% 91.01/91.01 cnf(146,plain,
% 91.01/91.01 (E(f8(f7(a4,a4)),f7(a3,a6))),
% 91.01/91.01 inference(scs_inference,[],[27,99,41,2,3])).
% 91.01/91.01 cnf(148,plain,
% 91.01/91.01 (P2(f7(f7(a6,a3),f7(a6,a3)),f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[31,145,8])).
% 91.01/91.01 cnf(149,plain,
% 91.01/91.01 (E(f7(x1491,x1492),f7(f7(x1492,x1491),f7(x1492,x1491)))),
% 91.01/91.01 inference(rename_variables,[],[145])).
% 91.01/91.01 cnf(152,plain,
% 91.01/91.01 (~E(a5,f7(a2,a2))),
% 91.01/91.01 inference(scs_inference,[],[32,31,145,149,85,8,9,2])).
% 91.01/91.01 cnf(153,plain,
% 91.01/91.01 (~E(a1,f7(f7(a3,a6),f7(a3,a6)))),
% 91.01/91.01 inference(scs_inference,[],[32,31,35,145,149,85,47,8,9,2,3])).
% 91.01/91.01 cnf(157,plain,
% 91.01/91.01 (~E(f7(a5,a5),f7(a2,a2))),
% 91.01/91.01 inference(scs_inference,[],[146,152,54,2,3])).
% 91.01/91.01 cnf(165,plain,
% 91.01/91.01 (P2(f7(a1,a1),f7(f7(a3,a6),f7(a3,a6)))),
% 91.01/91.01 inference(scs_inference,[],[28,32,117,146,148,152,65,54,2,3,24,23,8,9])).
% 91.01/91.01 cnf(167,plain,
% 91.01/91.01 (P1(f7(f7(a2,a2),f7(a2,a2)))),
% 91.01/91.01 inference(scs_inference,[],[28,32,117,146,148,152,65,72,128,54,2,3,24,23,8,9,7])).
% 91.01/91.01 cnf(169,plain,
% 91.01/91.01 (~E(f7(f7(a2,a2),f7(a2,a2)),f7(x1691,a5))),
% 91.01/91.01 inference(scs_inference,[],[39,167,7])).
% 91.01/91.01 cnf(170,plain,
% 91.01/91.01 (~E(f7(a2,a2),f7(a5,a5))),
% 91.01/91.01 inference(scs_inference,[],[39,167,157,7,2])).
% 91.01/91.01 cnf(171,plain,
% 91.01/91.01 (E(f7(f7(x1711,x1711),f7(x1712,x1712)),f7(x1712,x1711))),
% 91.01/91.01 inference(scs_inference,[],[42,121,3])).
% 91.01/91.01 cnf(173,plain,
% 91.01/91.01 (E(f7(x1731,x1732),f7(f7(x1732,x1732),f7(x1731,x1731)))),
% 91.01/91.01 inference(scs_inference,[],[42,121,3,2])).
% 91.01/91.01 cnf(175,plain,
% 91.01/91.01 (~E(f7(f7(a1,a1),f7(a1,a1)),f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[27,120,169,2,3])).
% 91.01/91.01 cnf(177,plain,
% 91.01/91.01 (E(f7(x1771,x1772),f7(f7(x1772,x1772),f7(x1771,x1771)))),
% 91.01/91.01 inference(rename_variables,[],[173])).
% 91.01/91.01 cnf(180,plain,
% 91.01/91.01 (~E(f7(a1,f7(a1,a1)),f8(a4))),
% 91.01/91.01 inference(scs_inference,[],[28,43,32,173,177,175,8,9,3])).
% 91.01/91.01 cnf(182,plain,
% 91.01/91.01 (E(f7(f7(a1,a1),f7(a1,a1)),a1)),
% 91.01/91.01 inference(scs_inference,[],[28,43,32,173,177,175,8,9,3,24])).
% 91.01/91.01 cnf(185,plain,
% 91.01/91.01 (E(a1,f7(f7(a1,a1),f7(a1,a1)))),
% 91.01/91.01 inference(scs_inference,[],[182,2])).
% 91.01/91.01 cnf(186,plain,
% 91.01/91.01 (E(f7(f7(x1861,x1861),f7(x1862,x1862)),f7(x1861,x1862))),
% 91.01/91.01 inference(scs_inference,[],[42,43,182,2,3])).
% 91.01/91.01 cnf(187,plain,
% 91.01/91.01 (E(f7(x1871,f7(x1872,x1872)),f7(x1871,x1872))),
% 91.01/91.01 inference(rename_variables,[],[42])).
% 91.01/91.01 cnf(188,plain,
% 91.01/91.01 (P2(f7(x1881,x1882),f7(f7(x1882,x1882),x1881))),
% 91.01/91.01 inference(scs_inference,[],[42,187,43,89,182,2,3,8])).
% 91.01/91.01 cnf(197,plain,
% 91.01/91.01 (~E(f7(a2,a2),f7(a5,f7(a5,a5)))),
% 91.01/91.01 inference(scs_inference,[],[42,37,170,153,167,7,2,3])).
% 91.01/91.01 cnf(199,plain,
% 91.01/91.01 (E(f7(x1991,x1992),f7(f7(x1991,x1991),f7(x1992,x1992)))),
% 91.01/91.01 inference(scs_inference,[],[186,2])).
% 91.01/91.01 cnf(200,plain,
% 91.01/91.01 (~E(f7(f7(a1,a1),f7(a1,a1)),f8(x2001))),
% 91.01/91.01 inference(scs_inference,[],[47,186,185,2,3])).
% 91.01/91.01 cnf(202,plain,
% 91.01/91.01 (E(f8(f7(a4,a4)),f7(a6,a3))),
% 91.01/91.01 inference(scs_inference,[],[48,41,55,2,3])).
% 91.01/91.01 cnf(209,plain,
% 91.01/91.01 (P2(f7(x2091,x2092),f7(f7(x2092,x2092),f7(x2091,x2091)))),
% 91.01/91.01 inference(scs_inference,[],[43,188,8])).
% 91.01/91.01 cnf(214,plain,
% 91.01/91.01 (~E(f7(a2,a2),f7(f7(a5,a5),f7(a5,a5)))),
% 91.01/91.01 inference(scs_inference,[],[32,43,199,188,197,202,8,9,2,3])).
% 91.01/91.01 cnf(226,plain,
% 91.01/91.01 (P1(f7(f7(a1,a1),f7(a1,a1)))),
% 91.01/91.01 inference(scs_inference,[],[48,43,209,200,180,185,10,16,8,9,2,3,24,7])).
% 91.01/91.01 cnf(236,plain,
% 91.01/91.01 (P1(f7(a1,a1))),
% 91.01/91.01 inference(scs_inference,[],[42,39,226,173,7,3,5,26])).
% 91.01/91.01 cnf(238,plain,
% 91.01/91.01 (E(f7(f7(x2381,x2381),x2382),f7(x2382,x2381))),
% 91.01/91.01 inference(scs_inference,[],[42,39,226,173,7,3,5,26,2])).
% 91.01/91.01 cnf(242,plain,
% 91.01/91.01 (~E(f7(f7(a5,a5),f7(a5,a5)),f7(a2,a2))),
% 91.01/91.02 inference(scs_inference,[],[214,2])).
% 91.01/91.02 cnf(250,plain,
% 91.01/91.02 (~E(f7(f7(a5,a5),a5),f7(a2,a2))),
% 91.01/91.02 inference(scs_inference,[],[42,242,3])).
% 91.01/91.02 cnf(252,plain,
% 91.01/91.02 (E(a1,f7(a1,f7(a1,a1)))),
% 91.01/91.02 inference(scs_inference,[],[43,185,3])).
% 91.01/91.02 cnf(254,plain,
% 91.01/91.02 (E(f7(a1,f7(a1,a1)),a1)),
% 91.01/91.02 inference(scs_inference,[],[43,185,3,2])).
% 91.01/91.02 cnf(259,plain,
% 91.01/91.02 (~E(a1,f7(f7(a3,a3),a6))),
% 91.01/91.02 inference(scs_inference,[],[49,43,254,250,22,2,3])).
% 91.01/91.02 cnf(261,plain,
% 91.01/91.02 (P1(f7(f7(a1,a1),a1))),
% 91.01/91.02 inference(scs_inference,[],[49,42,43,254,250,226,22,2,3,7])).
% 91.01/91.02 cnf(299,plain,
% 91.01/91.02 (~E(a2,f7(f7(x2991,a5),x2992))),
% 91.01/91.02 inference(scs_inference,[],[50,55,105,11,8,7])).
% 91.01/91.02 cnf(306,plain,
% 91.01/91.02 (P2(f7(a1,f7(a1,a1)),a1)),
% 91.01/91.02 inference(scs_inference,[],[54,259,252,13,3,8])).
% 91.01/91.02 cnf(317,plain,
% 91.01/91.02 (P2(f7(f7(x3171,x3171),f7(x3171,x3171)),f7(x3171,x3172))),
% 91.01/91.02 inference(scs_inference,[],[54,125,8])).
% 91.01/91.02 cnf(346,plain,
% 91.01/91.02 (~E(f7(a1,a1),f7(f7(a6,a6),f7(a3,a3)))),
% 91.01/91.02 inference(scs_inference,[],[109,171,3])).
% 91.01/91.02 cnf(352,plain,
% 91.01/91.02 (~E(a3,f8(a4))+~E(f8(a4),a6)),
% 91.01/91.02 inference(scs_inference,[],[21,2])).
% 91.01/91.02 cnf(354,plain,
% 91.01/91.02 (E(x3541,f7(x3541,x3541))),
% 91.01/91.02 inference(rename_variables,[],[54])).
% 91.01/91.02 cnf(356,plain,
% 91.01/91.02 (E(x3561,f7(x3561,x3561))),
% 91.01/91.02 inference(rename_variables,[],[54])).
% 91.01/91.02 cnf(358,plain,
% 91.01/91.02 (E(x3581,f7(x3581,f7(x3581,x3581)))),
% 91.01/91.02 inference(scs_inference,[],[54,354,356,72,346,114,306,8,9,2,3])).
% 91.01/91.02 cnf(376,plain,
% 91.01/91.02 (E(f8(a4),f7(a6,f7(a3,a3)))),
% 91.01/91.02 inference(scs_inference,[],[55,72,3])).
% 91.01/91.02 cnf(378,plain,
% 91.01/91.02 (E(f7(a6,f7(a3,a3)),f8(a4))),
% 91.01/91.02 inference(scs_inference,[],[55,72,3,2])).
% 91.01/91.02 cnf(403,plain,
% 91.01/91.02 (P2(f7(f7(a6,a6),f7(a6,a6)),f8(a4))),
% 91.01/91.02 inference(scs_inference,[],[317,261,378,17,7,9])).
% 91.01/91.02 cnf(404,plain,
% 91.01/91.02 (P2(f7(f7(x4041,x4041),f7(x4041,x4041)),f7(x4041,x4042))),
% 91.01/91.02 inference(rename_variables,[],[317])).
% 91.01/91.02 cnf(407,plain,
% 91.01/91.02 (P2(f7(f7(x4071,x4071),x4071),f7(x4071,x4072))),
% 91.01/91.02 inference(scs_inference,[],[72,317,404,261,378,238,182,17,7,9,3,8])).
% 91.01/91.02 cnf(448,plain,
% 91.01/91.02 (E(f7(x4481,x4482),f7(f7(x4481,x4481),x4482))),
% 91.01/91.02 inference(rename_variables,[],[73])).
% 91.01/91.02 cnf(449,plain,
% 91.01/91.02 (E(x4491,f7(f7(x4491,x4491),f7(x4491,x4491)))),
% 91.01/91.02 inference(scs_inference,[],[78,73,448,358,9,3])).
% 91.01/91.02 cnf(452,plain,
% 91.01/91.02 (E(f7(f7(x4521,x4521),f7(x4521,x4521)),x4521)),
% 91.01/91.02 inference(scs_inference,[],[449,2])).
% 91.01/91.02 cnf(456,plain,
% 91.01/91.02 (P2(f7(f7(a6,a6),a6),f8(a4))),
% 91.01/91.02 inference(scs_inference,[],[407,449,299,378,2,3,9])).
% 91.01/91.02 cnf(493,plain,
% 91.01/91.02 (E(f7(f7(x4931,x4931),x4931),x4931)),
% 91.01/91.02 inference(scs_inference,[],[73,86,165,99,54,3,7,9,2])).
% 91.01/91.02 cnf(526,plain,
% 91.01/91.02 (~E(f7(a1,a1),f7(x5261,f7(x5262,a5)))),
% 91.01/91.02 inference(scs_inference,[],[103,236,7])).
% 91.01/91.02 cnf(527,plain,
% 91.01/91.02 (E(f8(a4),f7(f7(a3,a3),f7(a6,a6)))),
% 91.01/91.02 inference(scs_inference,[],[103,134,376,236,7,3])).
% 91.01/91.02 cnf(536,plain,
% 91.01/91.02 (E(a6,f8(a4))+E(a6,a1)),
% 91.01/91.02 inference(scs_inference,[],[526,527,493,456,199,8,2,3,24])).
% 91.01/91.02 cnf(612,plain,
% 91.01/91.02 (~E(a1,f7(f7(x6121,a5),x6122))),
% 91.01/91.02 inference(scs_inference,[],[105,10,7])).
% 91.01/91.02 cnf(639,plain,
% 91.01/91.02 (E(f7(a6,a6),f8(a4))+E(f7(a6,a6),a1)),
% 91.01/91.02 inference(scs_inference,[],[99,403,8,24])).
% 91.01/91.02 cnf(659,plain,
% 91.01/91.02 (E(a3,a1)+~E(f8(a4),a6)),
% 91.01/91.02 inference(scs_inference,[],[352,57])).
% 91.01/91.02 cnf(715,plain,
% 91.01/91.02 (P2(f7(x7151,x7151),f7(x7152,x7151))),
% 91.01/91.02 inference(scs_inference,[],[128,125,121,17,7,9])).
% 91.01/91.02 cnf(738,plain,
% 91.01/91.02 (P2(f7(x7381,f7(x7381,x7381)),f7(x7382,x7381))),
% 91.01/91.02 inference(scs_inference,[],[134,715,8])).
% 91.01/91.02 cnf(767,plain,
% 91.01/91.02 (~E(f7(f7(x7671,a5),x7672),a1)),
% 91.01/91.02 inference(scs_inference,[],[612,2])).
% 91.01/91.02 cnf(774,plain,
% 91.01/91.02 (P2(f7(f7(x7741,x7741),f7(x7741,x7741)),f7(x7742,x7741))),
% 91.01/91.02 inference(scs_inference,[],[134,738,8])).
% 91.01/91.02 cnf(786,plain,
% 91.01/91.02 (P2(x7861,f7(x7862,x7861))),
% 91.01/91.02 inference(scs_inference,[],[774,767,452,24,8])).
% 91.01/91.02 cnf(1529,plain,
% 91.01/91.02 (~E(a6,f8(a4))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[19,2])).
% 91.01/91.02 cnf(1532,plain,
% 91.01/91.02 (E(a6,a1)+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1529,536])).
% 91.01/91.02 cnf(1542,plain,
% 91.01/91.02 (E(a1,a6)+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1532,2])).
% 91.01/91.02 cnf(1552,plain,
% 91.01/91.02 (E(f7(x15521,a6),f7(x15521,a1))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1532,5])).
% 91.01/91.02 cnf(1553,plain,
% 91.01/91.02 (E(f7(x15531,a1),f7(x15531,a6))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1552,2])).
% 91.01/91.02 cnf(1587,plain,
% 91.01/91.02 (P2(a6,f8(x15871))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1532,22])).
% 91.01/91.02 cnf(1588,plain,
% 91.01/91.02 (P2(f7(a6,a6),f8(x15881))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[54,1587,8])).
% 91.01/91.02 cnf(1598,plain,
% 91.01/91.02 (E(f7(a6,a6),a1)+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[14,1532,3])).
% 91.01/91.02 cnf(1599,plain,
% 91.01/91.02 (E(a1,f7(a6,a6))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1598,2])).
% 91.01/91.02 cnf(1601,plain,
% 91.01/91.02 (~E(f7(a3,a6),a6)+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[60,1532,3])).
% 91.01/91.02 cnf(1602,plain,
% 91.01/91.02 (~E(a6,f7(a3,a6))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1601,2])).
% 91.01/91.02 cnf(1603,plain,
% 91.01/91.02 (E(a3,f8(a4))+~E(a6,f7(a3,a6))),
% 91.01/91.02 inference(scs_inference,[],[1602,57])).
% 91.01/91.02 cnf(1700,plain,
% 91.01/91.02 (P2(a6,f7(x17001,a1))+~E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[786,1542,8])).
% 91.01/91.02 cnf(1729,plain,
% 91.01/91.02 (~E(f8(a4),a6)),
% 91.01/91.02 inference(scs_inference,[],[19,659])).
% 91.01/91.02 cnf(1732,plain,
% 91.01/91.02 (E(a6,a1)),
% 91.01/91.02 inference(scs_inference,[],[1729,2,536])).
% 91.01/91.02 cnf(1746,plain,
% 91.01/91.02 (~E(f8(a4),a3)),
% 91.01/91.02 inference(scs_inference,[],[1729,54,91,786,2,536,3,8,5,4,6,639,7,9,23,20])).
% 91.01/91.02 cnf(1764,plain,
% 91.01/91.02 (E(a3,a1)),
% 91.01/91.02 inference(scs_inference,[],[1746,2,57])).
% 91.01/91.02 cnf(1770,plain,
% 91.01/91.02 (~E(a6,f7(a3,a6))),
% 91.01/91.02 inference(scs_inference,[],[1746,60,1732,2,57,3,1553,1588,1599,1700,1603])).
% 91.01/91.02 cnf(1788,plain,
% 91.01/91.02 (E(a1,a3)),
% 91.01/91.02 inference(scs_inference,[],[1764,2])).
% 91.01/91.02 cnf(1789,plain,
% 91.01/91.02 (~E(f7(a6,a6),f7(a3,a6))),
% 91.01/91.02 inference(scs_inference,[],[54,1764,1770,2,3])).
% 91.01/91.02 cnf(1791,plain,
% 91.01/91.02 (~E(a6,a3)),
% 91.01/91.02 inference(scs_inference,[],[54,1764,1770,2,3,4])).
% 91.01/91.02 cnf(1796,plain,
% 91.01/91.02 (E(a3,f7(a1,a1))),
% 91.01/91.02 inference(scs_inference,[],[54,1764,1791,2,4,3])).
% 91.01/91.02 cnf(1818,plain,
% 91.01/91.02 (~E(f7(a6,a6),a3)),
% 91.01/91.02 inference(scs_inference,[],[54,1791,1789,2,3])).
% 91.01/91.02 cnf(1826,plain,
% 91.01/91.02 (E(a1,f7(a3,a3))),
% 91.01/91.02 inference(scs_inference,[],[54,1788,1796,2,3])).
% 91.01/91.02 cnf(1847,plain,
% 91.01/91.02 (E(f7(a3,a3),a1)),
% 91.01/91.02 inference(scs_inference,[],[1826,2])).
% 91.01/91.02 cnf(1855,plain,
% 91.01/91.02 (E(f7(a3,a3),f7(a1,a1))),
% 91.01/91.02 inference(scs_inference,[],[54,1847,1818,2,3])).
% 91.01/91.02 cnf(1862,plain,
% 91.01/91.02 ($false),
% 91.01/91.02 inference(scs_inference,[],[1788,1791,1732,1855,2,3]),
% 91.01/91.02 ['proof']).
% 91.01/91.02 % SZS output end Proof
% 91.01/91.02 % Total time :90.380000s
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