TSTP Solution File: SEU137+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n027.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 16:17:44 EDT 2023
% Result : Theorem 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 23:35:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 % File :CSE---1.6
% 0.19/0.69 % Problem :theBenchmark
% 0.19/0.69 % Transform :cnf
% 0.19/0.69 % Format :tptp:raw
% 0.19/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.69
% 0.19/0.69 % Result :Theorem 0.050000s
% 0.19/0.69 % Output :CNFRefutation 0.050000s
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 % File : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% 0.19/0.69 % Domain : Set theory
% 0.19/0.69 % Problem : MPTP chainy problem t45_xboole_1
% 0.19/0.69 % Version : [Urb07] axioms : Especial.
% 0.19/0.69 % English :
% 0.19/0.69
% 0.19/0.69 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.19/0.69 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.19/0.69 % Source : [Urb07]
% 0.19/0.69 % Names : chainy-t45_xboole_1 [Urb07]
% 0.19/0.69
% 0.19/0.69 % Status : Theorem
% 0.19/0.69 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.20 v3.5.0, 0.21 v3.3.0
% 0.19/0.69 % Syntax : Number of formulae : 50 ( 22 unt; 0 def)
% 0.19/0.69 % Number of atoms : 97 ( 25 equ)
% 0.19/0.69 % Maximal formula atoms : 6 ( 1 avg)
% 0.19/0.69 % Number of connectives : 66 ( 19 ~; 1 |; 17 &)
% 0.19/0.69 % ( 13 <=>; 16 =>; 0 <=; 0 <~>)
% 0.19/0.69 % Maximal formula depth : 9 ( 4 avg)
% 0.19/0.69 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.69 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.19/0.69 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.19/0.69 % Number of variables : 98 ( 94 !; 4 ?)
% 0.19/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.69
% 0.19/0.69 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.69 % library, www.mizar.org
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.69 ! [A,B] :
% 0.19/0.69 ( in(A,B)
% 0.19/0.70 => ~ in(B,A) ) ).
% 0.19/0.70
% 0.19/0.70 fof(commutativity_k2_xboole_0,axiom,
% 0.19/0.70 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.19/0.70
% 0.19/0.70 fof(commutativity_k3_xboole_0,axiom,
% 0.19/0.70 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.19/0.70
% 0.19/0.70 fof(d10_xboole_0,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( A = B
% 0.19/0.70 <=> ( subset(A,B)
% 0.19/0.70 & subset(B,A) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d1_xboole_0,axiom,
% 0.19/0.70 ! [A] :
% 0.19/0.70 ( A = empty_set
% 0.19/0.70 <=> ! [B] : ~ in(B,A) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d2_xboole_0,axiom,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( C = set_union2(A,B)
% 0.19/0.70 <=> ! [D] :
% 0.19/0.70 ( in(D,C)
% 0.19/0.70 <=> ( in(D,A)
% 0.19/0.70 | in(D,B) ) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d3_tarski,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 <=> ! [C] :
% 0.19/0.70 ( in(C,A)
% 0.19/0.70 => in(C,B) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d3_xboole_0,axiom,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( C = set_intersection2(A,B)
% 0.19/0.70 <=> ! [D] :
% 0.19/0.70 ( in(D,C)
% 0.19/0.70 <=> ( in(D,A)
% 0.19/0.70 & in(D,B) ) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d4_xboole_0,axiom,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( C = set_difference(A,B)
% 0.19/0.70 <=> ! [D] :
% 0.19/0.70 ( in(D,C)
% 0.19/0.70 <=> ( in(D,A)
% 0.19/0.70 & ~ in(D,B) ) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(d7_xboole_0,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( disjoint(A,B)
% 0.19/0.70 <=> set_intersection2(A,B) = empty_set ) ).
% 0.19/0.70
% 0.19/0.70 fof(dt_k1_xboole_0,axiom,
% 0.19/0.70 $true ).
% 0.19/0.70
% 0.19/0.70 fof(dt_k2_xboole_0,axiom,
% 0.19/0.70 $true ).
% 0.19/0.70
% 0.19/0.70 fof(dt_k3_xboole_0,axiom,
% 0.19/0.70 $true ).
% 0.19/0.70
% 0.19/0.70 fof(dt_k4_xboole_0,axiom,
% 0.19/0.70 $true ).
% 0.19/0.70
% 0.19/0.70 fof(fc1_xboole_0,axiom,
% 0.19/0.70 empty(empty_set) ).
% 0.19/0.70
% 0.19/0.70 fof(fc2_xboole_0,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( ~ empty(A)
% 0.19/0.70 => ~ empty(set_union2(A,B)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(fc3_xboole_0,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( ~ empty(A)
% 0.19/0.70 => ~ empty(set_union2(B,A)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(idempotence_k2_xboole_0,axiom,
% 0.19/0.70 ! [A,B] : set_union2(A,A) = A ).
% 0.19/0.70
% 0.19/0.70 fof(idempotence_k3_xboole_0,axiom,
% 0.19/0.70 ! [A,B] : set_intersection2(A,A) = A ).
% 0.19/0.70
% 0.19/0.70 fof(l32_xboole_1,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( set_difference(A,B) = empty_set
% 0.19/0.70 <=> subset(A,B) ) ).
% 0.19/0.70
% 0.19/0.70 fof(rc1_xboole_0,axiom,
% 0.19/0.70 ? [A] : empty(A) ).
% 0.19/0.70
% 0.19/0.70 fof(rc2_xboole_0,axiom,
% 0.19/0.70 ? [A] : ~ empty(A) ).
% 0.19/0.70
% 0.19/0.70 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.70 ! [A,B] : subset(A,A) ).
% 0.19/0.70
% 0.19/0.70 fof(symmetry_r1_xboole_0,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( disjoint(A,B)
% 0.19/0.70 => disjoint(B,A) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t12_xboole_1,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 => set_union2(A,B) = B ) ).
% 0.19/0.70
% 0.19/0.70 fof(t17_xboole_1,lemma,
% 0.19/0.70 ! [A,B] : subset(set_intersection2(A,B),A) ).
% 0.19/0.70
% 0.19/0.70 fof(t19_xboole_1,lemma,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( ( subset(A,B)
% 0.19/0.70 & subset(A,C) )
% 0.19/0.70 => subset(A,set_intersection2(B,C)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t1_boole,axiom,
% 0.19/0.70 ! [A] : set_union2(A,empty_set) = A ).
% 0.19/0.70
% 0.19/0.70 fof(t1_xboole_1,lemma,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( ( subset(A,B)
% 0.19/0.70 & subset(B,C) )
% 0.19/0.70 => subset(A,C) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t26_xboole_1,lemma,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t28_xboole_1,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 => set_intersection2(A,B) = A ) ).
% 0.19/0.70
% 0.19/0.70 fof(t2_boole,axiom,
% 0.19/0.70 ! [A] : set_intersection2(A,empty_set) = empty_set ).
% 0.19/0.70
% 0.19/0.70 fof(t2_tarski,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( ! [C] :
% 0.19/0.70 ( in(C,A)
% 0.19/0.70 <=> in(C,B) )
% 0.19/0.70 => A = B ) ).
% 0.19/0.70
% 0.19/0.70 fof(t2_xboole_1,lemma,
% 0.19/0.70 ! [A] : subset(empty_set,A) ).
% 0.19/0.70
% 0.19/0.70 fof(t33_xboole_1,lemma,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 => subset(set_difference(A,C),set_difference(B,C)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t36_xboole_1,lemma,
% 0.19/0.70 ! [A,B] : subset(set_difference(A,B),A) ).
% 0.19/0.70
% 0.19/0.70 fof(t37_xboole_1,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( set_difference(A,B) = empty_set
% 0.19/0.70 <=> subset(A,B) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t39_xboole_1,lemma,
% 0.19/0.70 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ).
% 0.19/0.70
% 0.19/0.70 fof(t3_boole,axiom,
% 0.19/0.70 ! [A] : set_difference(A,empty_set) = A ).
% 0.19/0.70
% 0.19/0.70 fof(t3_xboole_0,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( ~ ( ~ disjoint(A,B)
% 0.19/0.70 & ! [C] :
% 0.19/0.70 ~ ( in(C,A)
% 0.19/0.70 & in(C,B) ) )
% 0.19/0.70 & ~ ( ? [C] :
% 0.19/0.70 ( in(C,A)
% 0.19/0.70 & in(C,B) )
% 0.19/0.70 & disjoint(A,B) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t3_xboole_1,lemma,
% 0.19/0.70 ! [A] :
% 0.19/0.70 ( subset(A,empty_set)
% 0.19/0.70 => A = empty_set ) ).
% 0.19/0.70
% 0.19/0.70 fof(t40_xboole_1,lemma,
% 0.19/0.70 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
% 0.19/0.70
% 0.19/0.70 fof(t45_xboole_1,conjecture,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( subset(A,B)
% 0.19/0.70 => B = set_union2(A,set_difference(B,A)) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t4_boole,axiom,
% 0.19/0.70 ! [A] : set_difference(empty_set,A) = empty_set ).
% 0.19/0.70
% 0.19/0.70 fof(t4_xboole_0,lemma,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ( ~ ( ~ disjoint(A,B)
% 0.19/0.70 & ! [C] : ~ in(C,set_intersection2(A,B)) )
% 0.19/0.70 & ~ ( ? [C] : in(C,set_intersection2(A,B))
% 0.19/0.70 & disjoint(A,B) ) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t6_boole,axiom,
% 0.19/0.70 ! [A] :
% 0.19/0.70 ( empty(A)
% 0.19/0.70 => A = empty_set ) ).
% 0.19/0.70
% 0.19/0.70 fof(t7_boole,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ~ ( in(A,B)
% 0.19/0.70 & empty(B) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t7_xboole_1,lemma,
% 0.19/0.70 ! [A,B] : subset(A,set_union2(A,B)) ).
% 0.19/0.70
% 0.19/0.70 fof(t8_boole,axiom,
% 0.19/0.70 ! [A,B] :
% 0.19/0.70 ~ ( empty(A)
% 0.19/0.70 & A != B
% 0.19/0.70 & empty(B) ) ).
% 0.19/0.70
% 0.19/0.70 fof(t8_xboole_1,lemma,
% 0.19/0.70 ! [A,B,C] :
% 0.19/0.70 ( ( subset(A,B)
% 0.19/0.70 & subset(C,B) )
% 0.19/0.70 => subset(set_union2(A,C),B) ) ).
% 0.19/0.70
% 0.19/0.70 %------------------------------------------------------------------------------
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark
% 0.19/0.70 % SZS output start Proof
% 0.19/0.70 %ClaNum:108(EqnAxiom:34)
% 0.19/0.70 %VarNum:380(SingletonVarNum:156)
% 0.19/0.70 %MaxLitNum:4
% 0.19/0.70 %MaxfuncDepth:2
% 0.19/0.70 %SharedTerms:12
% 0.19/0.70 %goalClause: 37 54
% 0.19/0.70 %singleGoalClaCount:2
% 0.19/0.70 [35]P1(a1)
% 0.19/0.70 [36]P1(a2)
% 0.19/0.70 [37]P3(a3,a4)
% 0.19/0.70 [53]~P1(a13)
% 0.19/0.70 [54]~E(f16(a3,f12(a4,a3)),a4)
% 0.19/0.70 [40]P3(a1,x401)
% 0.19/0.70 [43]P3(x431,x431)
% 0.19/0.70 [38]E(f11(x381,a1),a1)
% 0.19/0.70 [39]E(f12(a1,x391),a1)
% 0.19/0.70 [41]E(f16(x411,a1),x411)
% 0.19/0.70 [42]E(f12(x421,a1),x421)
% 0.19/0.70 [44]E(f16(x441,x441),x441)
% 0.19/0.70 [45]E(f11(x451,x451),x451)
% 0.19/0.70 [46]E(f16(x461,x462),f16(x462,x461))
% 0.19/0.70 [47]E(f11(x471,x472),f11(x472,x471))
% 0.19/0.70 [48]P3(x481,f16(x481,x482))
% 0.19/0.70 [49]P3(f11(x491,x492),x491)
% 0.19/0.71 [50]P3(f12(x501,x502),x501)
% 0.19/0.71 [51]E(f16(x511,f12(x512,x511)),f16(x511,x512))
% 0.19/0.71 [52]E(f12(f16(x521,x522),x522),f12(x521,x522))
% 0.19/0.71 [55]~P1(x551)+E(x551,a1)
% 0.19/0.71 [59]~P3(x591,a1)+E(x591,a1)
% 0.19/0.71 [60]P4(f5(x601),x601)+E(x601,a1)
% 0.19/0.71 [58]~E(x581,x582)+P3(x581,x582)
% 0.19/0.71 [61]~P4(x612,x611)+~E(x611,a1)
% 0.19/0.71 [62]~P1(x621)+~P4(x622,x621)
% 0.19/0.71 [69]~P2(x692,x691)+P2(x691,x692)
% 0.19/0.71 [72]~P4(x722,x721)+~P4(x721,x722)
% 0.19/0.71 [63]~P2(x631,x632)+E(f11(x631,x632),a1)
% 0.19/0.71 [65]~P3(x651,x652)+E(f12(x651,x652),a1)
% 0.19/0.71 [67]P3(x671,x672)+~E(f12(x671,x672),a1)
% 0.19/0.71 [68]P2(x681,x682)+~E(f11(x681,x682),a1)
% 0.19/0.71 [70]~P3(x701,x702)+E(f16(x701,x702),x702)
% 0.19/0.71 [71]~P3(x711,x712)+E(f11(x711,x712),x711)
% 0.19/0.71 [74]P1(x741)+~P1(f16(x742,x741))
% 0.19/0.71 [75]P1(x751)+~P1(f16(x751,x752))
% 0.19/0.71 [76]P3(x761,x762)+P4(f7(x761,x762),x761)
% 0.19/0.71 [77]P2(x771,x772)+P4(f14(x771,x772),x772)
% 0.19/0.71 [78]P2(x781,x782)+P4(f14(x781,x782),x781)
% 0.19/0.71 [90]P3(x901,x902)+~P4(f7(x901,x902),x902)
% 0.19/0.71 [91]P2(x911,x912)+P4(f6(x911,x912),f11(x911,x912))
% 0.19/0.71 [96]~P2(x961,x962)+~P4(x963,f11(x961,x962))
% 0.19/0.71 [97]~P3(x971,x973)+P3(f11(x971,x972),f11(x973,x972))
% 0.19/0.71 [98]~P3(x981,x983)+P3(f12(x981,x982),f12(x983,x982))
% 0.19/0.71 [56]~P1(x562)+~P1(x561)+E(x561,x562)
% 0.19/0.71 [73]~P3(x732,x731)+~P3(x731,x732)+E(x731,x732)
% 0.19/0.71 [92]E(x921,x922)+P4(f15(x921,x922),x922)+P4(f15(x921,x922),x921)
% 0.19/0.71 [99]E(x991,x992)+~P4(f15(x991,x992),x992)+~P4(f15(x991,x992),x991)
% 0.19/0.71 [79]~P3(x793,x792)+P4(x791,x792)+~P4(x791,x793)
% 0.19/0.71 [80]~P3(x801,x803)+P3(x801,x802)+~P3(x803,x802)
% 0.19/0.71 [86]~P2(x863,x862)+~P4(x861,x862)+~P4(x861,x863)
% 0.19/0.71 [94]~P3(x941,x943)+~P3(x941,x942)+P3(x941,f11(x942,x943))
% 0.19/0.71 [95]~P3(x952,x953)+~P3(x951,x953)+P3(f16(x951,x952),x953)
% 0.19/0.71 [100]P4(f9(x1002,x1003,x1001),x1001)+P4(f9(x1002,x1003,x1001),x1003)+E(x1001,f11(x1002,x1003))
% 0.19/0.71 [101]P4(f9(x1012,x1013,x1011),x1011)+P4(f9(x1012,x1013,x1011),x1012)+E(x1011,f11(x1012,x1013))
% 0.19/0.71 [102]P4(f10(x1022,x1023,x1021),x1021)+P4(f10(x1022,x1023,x1021),x1022)+E(x1021,f12(x1022,x1023))
% 0.19/0.71 [103]P4(f10(x1032,x1033,x1031),x1031)+~P4(f10(x1032,x1033,x1031),x1033)+E(x1031,f12(x1032,x1033))
% 0.19/0.71 [105]~P4(f8(x1052,x1053,x1051),x1051)+~P4(f8(x1052,x1053,x1051),x1053)+E(x1051,f16(x1052,x1053))
% 0.19/0.71 [106]~P4(f8(x1062,x1063,x1061),x1061)+~P4(f8(x1062,x1063,x1061),x1062)+E(x1061,f16(x1062,x1063))
% 0.19/0.71 [81]~P4(x811,x814)+P4(x811,x812)+~E(x812,f16(x813,x814))
% 0.19/0.71 [82]~P4(x821,x823)+P4(x821,x822)+~E(x822,f16(x823,x824))
% 0.19/0.71 [83]~P4(x831,x833)+P4(x831,x832)+~E(x833,f11(x834,x832))
% 0.19/0.71 [84]~P4(x841,x843)+P4(x841,x842)+~E(x843,f11(x842,x844))
% 0.19/0.71 [85]~P4(x851,x853)+P4(x851,x852)+~E(x853,f12(x852,x854))
% 0.19/0.71 [87]~P4(x874,x873)+~P4(x874,x871)+~E(x871,f12(x872,x873))
% 0.19/0.71 [104]P4(f8(x1042,x1043,x1041),x1041)+P4(f8(x1042,x1043,x1041),x1043)+P4(f8(x1042,x1043,x1041),x1042)+E(x1041,f16(x1042,x1043))
% 0.19/0.71 [107]P4(f10(x1072,x1073,x1071),x1073)+~P4(f10(x1072,x1073,x1071),x1071)+~P4(f10(x1072,x1073,x1071),x1072)+E(x1071,f12(x1072,x1073))
% 0.19/0.71 [108]~P4(f9(x1082,x1083,x1081),x1081)+~P4(f9(x1082,x1083,x1081),x1083)+~P4(f9(x1082,x1083,x1081),x1082)+E(x1081,f11(x1082,x1083))
% 0.19/0.71 [88]~P4(x881,x884)+P4(x881,x882)+P4(x881,x883)+~E(x882,f12(x884,x883))
% 0.19/0.71 [89]~P4(x891,x894)+P4(x891,x892)+P4(x891,x893)+~E(x894,f16(x893,x892))
% 0.19/0.71 [93]~P4(x931,x934)+~P4(x931,x933)+P4(x931,x932)+~E(x932,f11(x933,x934))
% 0.19/0.71 %EqnAxiom
% 0.19/0.71 [1]E(x11,x11)
% 0.19/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.71 [4]~E(x41,x42)+E(f11(x41,x43),f11(x42,x43))
% 0.19/0.71 [5]~E(x51,x52)+E(f11(x53,x51),f11(x53,x52))
% 0.19/0.71 [6]~E(x61,x62)+E(f12(x61,x63),f12(x62,x63))
% 0.19/0.71 [7]~E(x71,x72)+E(f12(x73,x71),f12(x73,x72))
% 0.19/0.71 [8]~E(x81,x82)+E(f16(x81,x83),f16(x82,x83))
% 0.19/0.71 [9]~E(x91,x92)+E(f16(x93,x91),f16(x93,x92))
% 0.19/0.71 [10]~E(x101,x102)+E(f10(x101,x103,x104),f10(x102,x103,x104))
% 0.19/0.71 [11]~E(x111,x112)+E(f10(x113,x111,x114),f10(x113,x112,x114))
% 0.19/0.71 [12]~E(x121,x122)+E(f10(x123,x124,x121),f10(x123,x124,x122))
% 0.19/0.71 [13]~E(x131,x132)+E(f8(x131,x133,x134),f8(x132,x133,x134))
% 0.19/0.71 [14]~E(x141,x142)+E(f8(x143,x141,x144),f8(x143,x142,x144))
% 0.19/0.71 [15]~E(x151,x152)+E(f8(x153,x154,x151),f8(x153,x154,x152))
% 0.19/0.71 [16]~E(x161,x162)+E(f9(x161,x163,x164),f9(x162,x163,x164))
% 0.19/0.71 [17]~E(x171,x172)+E(f9(x173,x171,x174),f9(x173,x172,x174))
% 0.19/0.71 [18]~E(x181,x182)+E(f9(x183,x184,x181),f9(x183,x184,x182))
% 0.19/0.71 [19]~E(x191,x192)+E(f5(x191),f5(x192))
% 0.19/0.71 [20]~E(x201,x202)+E(f15(x201,x203),f15(x202,x203))
% 0.19/0.71 [21]~E(x211,x212)+E(f15(x213,x211),f15(x213,x212))
% 0.19/0.71 [22]~E(x221,x222)+E(f7(x221,x223),f7(x222,x223))
% 0.19/0.71 [23]~E(x231,x232)+E(f7(x233,x231),f7(x233,x232))
% 0.19/0.71 [24]~E(x241,x242)+E(f6(x241,x243),f6(x242,x243))
% 0.19/0.71 [25]~E(x251,x252)+E(f6(x253,x251),f6(x253,x252))
% 0.19/0.71 [26]~E(x261,x262)+E(f14(x261,x263),f14(x262,x263))
% 0.19/0.71 [27]~E(x271,x272)+E(f14(x273,x271),f14(x273,x272))
% 0.19/0.71 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.19/0.71 [29]P4(x292,x293)+~E(x291,x292)+~P4(x291,x293)
% 0.19/0.71 [30]P4(x303,x302)+~E(x301,x302)+~P4(x303,x301)
% 0.19/0.71 [31]P3(x312,x313)+~E(x311,x312)+~P3(x311,x313)
% 0.19/0.71 [32]P3(x323,x322)+~E(x321,x322)+~P3(x323,x321)
% 0.19/0.71 [33]P2(x332,x333)+~E(x331,x332)+~P2(x331,x333)
% 0.19/0.71 [34]P2(x343,x342)+~E(x341,x342)+~P2(x343,x341)
% 0.19/0.71
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 cnf(112,plain,
% 0.19/0.71 (~P4(x1121,f16(a1,a1))),
% 0.19/0.71 inference(scs_inference,[],[35,44,2,62,61])).
% 0.19/0.71 cnf(113,plain,
% 0.19/0.71 (E(f16(x1131,x1131),x1131)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(126,plain,
% 0.19/0.71 (E(f16(x1261,x1261),x1261)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(128,plain,
% 0.19/0.71 (E(f16(x1281,x1281),x1281)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(137,plain,
% 0.19/0.71 (E(f16(x1371,x1371),x1371)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(140,plain,
% 0.19/0.71 (E(f16(x1401,x1401),x1401)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(143,plain,
% 0.19/0.71 (E(f16(x1431,x1431),x1431)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(146,plain,
% 0.19/0.71 (E(f16(x1461,x1461),x1461)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(184,plain,
% 0.19/0.71 (~P4(x1841,f11(a1,x1842))),
% 0.19/0.71 inference(scs_inference,[],[37,43,40,35,36,53,54,44,113,126,128,137,140,143,146,48,49,41,38,2,62,61,78,77,68,33,32,31,28,3,80,73,85,84,83,89,58,55,75,74,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,98,97,96])).
% 0.19/0.71 cnf(188,plain,
% 0.19/0.71 (E(f16(a3,a4),a4)),
% 0.19/0.71 inference(scs_inference,[],[37,43,40,35,36,53,54,44,113,126,128,137,140,143,146,48,49,41,38,2,62,61,78,77,68,33,32,31,28,3,80,73,85,84,83,89,58,55,75,74,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,98,97,96,71,70])).
% 0.19/0.71 cnf(195,plain,
% 0.19/0.71 (E(f16(x1951,x1951),x1951)),
% 0.19/0.71 inference(rename_variables,[],[44])).
% 0.19/0.71 cnf(196,plain,
% 0.19/0.71 (~P4(f16(f14(a1,x1961),f14(a1,x1961)),f16(f12(a1,x1962),f12(a1,x1962)))),
% 0.19/0.71 inference(scs_inference,[],[37,43,40,35,36,53,54,44,113,126,128,137,140,143,146,195,48,49,41,38,2,62,61,78,77,68,33,32,31,28,3,80,73,85,84,83,89,58,55,75,74,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,98,97,96,71,70,65,63,30,29])).
% 0.19/0.71 cnf(229,plain,
% 0.19/0.71 (~P4(x2291,f11(a1,x2292))),
% 0.19/0.71 inference(rename_variables,[],[184])).
% 0.19/0.71 cnf(230,plain,
% 0.19/0.71 (~P4(x2301,f11(a1,x2302))),
% 0.19/0.71 inference(rename_variables,[],[184])).
% 0.19/0.71 cnf(242,plain,
% 0.19/0.71 ($false),
% 0.19/0.71 inference(scs_inference,[],[37,51,46,36,54,53,196,184,230,229,112,188,104,94,92,81,28,3]),
% 0.19/0.71 ['proof']).
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time :0.050000s
%------------------------------------------------------------------------------