0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.16/0.16 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.0n4sOPdWLq 0.16/0.37 % Computer : n008.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1200 0.16/0.37 % DateTime : Tue Jul 13 10:58:59 EDT 2021 0.16/0.37 % CPUTime : 0.16/0.37 % Running portfolio for 120 s 0.16/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.54/0.65 % Estimated wc time : 1286 0.54/0.65 % Estimated cpu time (7 cpus) : 183.71428571428572 0.57/0.74 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 70.61/10.92 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 105.06/15.87 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.06/16.04 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 144.70/21.78 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 146.31/22.01 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 179.66/26.88 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 186.81/27.94 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 191.01/28.65 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 262.26/38.86 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 269.77/39.99 % Solved by lams/c_ic.sh. 269.77/39.99 % Running : timeout 32 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.0n4sOPdWLq/e_inputc1d798 --cpu-limit=30 --auto-schedule -s -p. 269.77/39.99 % done 2153 iterations in 11.275s 269.77/39.99 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 269.77/39.99 % SZS output start Refutation 269.77/39.99 tff(inIntersectImpInIntersectUnions, axiom, 269.77/39.99 inIntersectImpInIntersectUnions <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Z]: 269.77/39.99 (in(Z,powerset(A)) => 269.77/39.99 (![Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (in(Xx,binintersect(X,Y)) => 269.77/39.99 in(Xx,binintersect(binunion(X,Z),binunion(Y,Z))))))))))))). 269.77/39.99 tff('0', plain, 269.77/39.99 inIntersectImpInIntersectUnions = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,powerset(X4)) => 269.77/39.99 (![X12]: 269.77/39.99 (in(X12,X4) => 269.77/39.99 (in(X12,binintersect(X6,X8)) => 269.77/39.99 in(X12,binintersect(binunion(X6,X10),binunion(X8,X10)))))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Z]: 269.77/39.99 (in(Z,powerset(A)) => 269.77/39.99 (![Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (in(Xx,binintersect(X,Y)) => in(Xx,binunion(Y,Z)))))))))))). 269.77/39.99 tff('1', plain, 269.77/39.99 inIntersectImpInUnion2 = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,powerset(X4)) => 269.77/39.99 (![X12]: 269.77/39.99 (in(X12,X4) => 269.77/39.99 (in(X12,binintersect(X6,X8)) => in(X12,binunion(X8,X10))))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(inIntersectImpInUnion, axiom, inIntersectImpInUnion <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Z]: 269.77/39.99 (in(Z,powerset(A)) => 269.77/39.99 (![Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (in(Xx,binintersect(X,Y)) => in(Xx,binunion(X,Z)))))))))))). 269.77/39.99 tff('2', plain, 269.77/39.99 inIntersectImpInUnion = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,powerset(X4)) => 269.77/39.99 (![X12]: 269.77/39.99 (in(X12,X4) => 269.77/39.99 (in(X12,binintersect(X6,X8)) => in(X12,binunion(X6,X10))))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionTIRcontra, axiom, binunionTIRcontra <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: (in(Xx,A) => ((~in(Xx,binunion(X,Y))) => (~in(Xx,Y)))))))))). 269.77/39.99 tff('3', plain, 269.77/39.99 binunionTIRcontra = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => ((~in(X10,binunion(X6,X8))) => (~in(X10,X8))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionTILcontra, axiom, binunionTILcontra <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: (in(Xx,A) => ((~in(Xx,binunion(X,Y))) => (~in(Xx,X)))))))))). 269.77/39.99 tff('4', plain, 269.77/39.99 binunionTILcontra = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => ((~in(X10,binunion(X6,X8))) => (~in(X10,X6))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(complementInPowersetComplementIntersect, axiom, 269.77/39.99 complementInPowersetComplementIntersect <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 in(setminus(A,X),powerset(setminus(A,binintersect(X,Y))))))))). 269.77/39.99 tff('5', plain, 269.77/39.99 complementInPowersetComplementIntersect = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 in(setminus(X4,X6),powerset(setminus(X4,binintersect(X6,X8)))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(complementSubsetComplementIntersect, axiom, 269.77/39.99 complementSubsetComplementIntersect <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 subset(setminus(A,X),setminus(A,binintersect(X,Y)))))))). 269.77/39.99 tff('6', plain, 269.77/39.99 complementSubsetComplementIntersect = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 subset(setminus(X4,X6),setminus(X4,binintersect(X6,X8))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(complementImpComplementIntersect, axiom, 269.77/39.99 complementImpComplementIntersect <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (in(Xx,setminus(A,X)) => in(Xx,setminus(A,binintersect(X,Y))))))))))). 269.77/39.99 tff('7', plain, 269.77/39.99 complementImpComplementIntersect = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => 269.77/39.99 (in(X10,setminus(X4,X6)) => 269.77/39.99 in(X10,setminus(X4,binintersect(X6,X8)))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(complementTnotintersectT, axiom, complementTnotintersectT <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (in(Xx,setminus(A,X)) => (~in(Xx,binintersect(X,Y))))))))))). 269.77/39.99 tff('8', plain, 269.77/39.99 complementTnotintersectT = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => 269.77/39.99 (in(X10,setminus(X4,X6)) => (~in(X10,binintersect(X6,X8)))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectTERcontra, axiom, binintersectTERcontra <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: (in(Xx,A) => ((~in(Xx,Y)) => (~in(Xx,binintersect(X,Y))))))))))). 269.77/39.99 tff('9', plain, 269.77/39.99 binintersectTERcontra = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => 269.77/39.99 ((~in(X10,X8)) => (~in(X10,binintersect(X6,X8)))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectTELcontra, axiom, binintersectTELcontra <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: (in(Xx,A) => ((~in(Xx,X)) => (~in(Xx,binintersect(X,Y))))))))))). 269.77/39.99 tff('10', plain, 269.77/39.99 binintersectTELcontra = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => 269.77/39.99 ((~in(X10,X6)) => (~in(X10,binintersect(X6,X8)))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetTE1, axiom, powersetTE1 <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 (![Xx]: (in(Xx,A) => (in(X,powerset(Y)) => (in(Xx,X) => in(Xx,Y)))))))))). 269.77/39.99 tff('11', plain, 269.77/39.99 powersetTE1 = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X4) => 269.77/39.99 (in(X6,powerset(X8)) => (in(X10,X6) => in(X10,X8))))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetTI1, axiom, powersetTI1 <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) => in(X,powerset(Y)))))))). 269.77/39.99 tff('12', plain, 269.77/39.99 powersetTI1 = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 ((![X10]: (in(X10,X4) => (in(X10,X6) => in(X10,X8)))) => 269.77/39.99 in(X6,powerset(X8))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(setextT, axiom, setextT <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in(Y,powerset(A)) => 269.77/39.99 ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) => 269.77/39.99 ((![Xx]: (in(Xx,A) => (in(Xx,Y) => in(Xx,X)))) => (X = Y)))))))). 269.77/39.99 tff('13', plain, 269.77/39.99 setextT = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: 269.77/39.99 (in(X8,powerset(X4)) => 269.77/39.99 ((![X10]: (in(X10,X4) => (in(X10,X6) => in(X10,X8)))) => 269.77/39.99 ((![X12]: (in(X12,X4) => (in(X12,X8) => in(X12,X6)))) => 269.77/39.99 (X6 = X8))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetT_lem, axiom, powersetT_lem <=> 269.77/39.99 (![A,X]: (in(X,powerset(A)) => in(powerset(X),powerset(powerset(A)))))). 269.77/39.99 tff('14', plain, 269.77/39.99 powersetT_lem = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => in(powerset(X6),powerset(powerset(X4))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionT_lem, axiom, binunionT_lem <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: (in(Y,powerset(A)) => in(binunion(X,Y),powerset(A))))))). 269.77/39.99 tff('15', plain, 269.77/39.99 binunionT_lem = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: (in(X8,powerset(X4)) => in(binunion(X6,X8),powerset(X4)))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectT_lem, axiom, binintersectT_lem <=> 269.77/39.99 (![A,X]: 269.77/39.99 (in(X,powerset(A)) => 269.77/39.99 (![Y]: (in(Y,powerset(A)) => in(binintersect(X,Y),powerset(A))))))). 269.77/39.99 tff('16', plain, 269.77/39.99 binintersectT_lem = 269.77/39.99 (![X4,X6]: 269.77/39.99 (in(X6,powerset(X4)) => 269.77/39.99 (![X8]: (in(X8,powerset(X4)) => in(binintersect(X6,X8),powerset(X4)))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (![Xy]: 269.77/39.99 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 269.77/39.99 tff('17', plain, 269.77/39.99 ubforcartprodlem3 = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X6) => 269.77/39.99 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (![Xy]: 269.77/39.99 (in(Xy,B) => 269.77/39.99 in(setadjoin(setadjoin(Xx,emptyset), 269.77/39.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset(powerset(binunion(A,B))))))))). 269.77/39.99 tff('18', plain, 269.77/39.99 ubforcartprodlem2 = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X6) => 269.77/39.99 in(setadjoin(setadjoin(X8,emptyset), 269.77/39.99 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset(powerset(binunion(X4,X6)))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (![Xy]: 269.77/39.99 (in(Xy,B) => 269.77/39.99 subset(setadjoin(setadjoin(Xx,emptyset), 269.77/39.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset(binunion(A,B)))))))). 269.77/39.99 tff('19', plain, 269.77/39.99 ubforcartprodlem1 = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X6) => 269.77/39.99 subset(setadjoin(setadjoin(X8,emptyset), 269.77/39.99 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset(binunion(X4,X6))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(upairinpowunion, axiom, upairinpowunion <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (![Xy]: 269.77/39.99 (in(Xy,B) => 269.77/39.99 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 269.77/39.99 tff('20', plain, 269.77/39.99 upairinpowunion = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X6) => 269.77/39.99 in(setadjoin(X8,setadjoin(X10,emptyset)), 269.77/39.99 powerset(binunion(X4,X6))))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(upairsubunion, axiom, upairsubunion <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => 269.77/39.99 (![Xy]: 269.77/39.99 (in(Xy,B) => 269.77/39.99 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 269.77/39.99 tff('21', plain, 269.77/39.99 upairsubunion = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => 269.77/39.99 (![X10]: 269.77/39.99 (in(X10,X6) => 269.77/39.99 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(singletoninpowunion, axiom, singletoninpowunion <=> 269.77/39.99 (![A,B,Xx]: 269.77/39.99 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 269.77/39.99 tff('22', plain, 269.77/39.99 singletoninpowunion = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(bs114d, axiom, bs114d <=> 269.77/39.99 (![A,B,C]: 269.77/39.99 (binintersect(A,binunion(B,C)) = 269.77/39.99 binunion(binintersect(A,B),binintersect(A,C))))). 269.77/39.99 tff('23', plain, 269.77/39.99 bs114d = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (binintersect(X4,binunion(X6,X8)) = 269.77/39.99 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 269.77/39.99 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 269.77/39.99 tff('24', plain, 269.77/39.99 binintersectSubset1 = 269.77/39.99 (![X4,X6]: ((binintersect(X4,X6) = X4) => subset(X4,X6))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 269.77/39.99 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 269.77/39.99 tff('25', plain, 269.77/39.99 binintersectSubset4 = 269.77/39.99 (![X4,X6]: (subset(X6,X4) => (binintersect(X4,X6) = X6))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectRsub, axiom, binintersectRsub <=> 269.77/39.99 (![A,B]: subset(binintersect(A,B),B))). 269.77/39.99 tff('26', plain, 269.77/39.99 binintersectRsub = (![X4,X6]: subset(binintersect(X4,X6),X6)), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 269.77/39.99 (![A,B]: 269.77/39.99 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 269.77/39.99 tff('27', plain, 269.77/39.99 disjointsetsI1 = 269.77/39.99 (![X4,X6]: 269.77/39.99 ((~(?[X8]: (in(X8,X6) & in(X8,X4)))) => 269.77/39.99 (binintersect(X4,X6) = emptyset))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectER, axiom, binintersectER <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 269.77/39.99 tff('28', plain, 269.77/39.99 binintersectER = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X6))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 269.77/39.99 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 269.77/39.99 tff('29', plain, 269.77/39.99 binintersectSubset3 = 269.77/39.99 (![X4,X6]: ((binintersect(X4,X6) = X6) => subset(X6,X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 269.77/39.99 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 269.77/39.99 tff('30', plain, 269.77/39.99 binintersectSubset2 = 269.77/39.99 (![X4,X6]: (subset(X4,X6) => (binintersect(X4,X6) = X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectLsub, axiom, binintersectLsub <=> 269.77/39.99 (![A,B]: subset(binintersect(A,B),A))). 269.77/39.99 tff('31', plain, 269.77/39.99 binintersectLsub = (![X4,X6]: subset(binintersect(X4,X6),X4)), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectEL, axiom, binintersectEL <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 269.77/39.99 tff('32', plain, 269.77/39.99 binintersectEL = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 269.77/39.99 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 269.77/39.99 tff('33', plain, 269.77/39.99 binintersectSubset5 = 269.77/39.99 (![X4,X6,X8]: 269.77/39.99 (subset(X8,X4) => (subset(X8,X6) => subset(X8,binintersect(X4,X6))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binintersectI, axiom, binintersectI <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 269.77/39.99 tff('34', plain, 269.77/39.99 binintersectI = 269.77/39.99 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => in(X8,binintersect(X4,X6))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 269.77/39.99 tff('35', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 269.77/39.99 tff('36', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionE, axiom, binunionE <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 269.77/39.99 tff('37', plain, 269.77/39.99 binunionE = 269.77/39.99 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionEcases, axiom, binunionEcases <=> 269.77/39.99 (![A,B,Xx,Xphi:$o]: 269.77/39.99 (in(Xx,binunion(A,B)) => 269.77/39.99 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 269.77/39.99 tff('38', plain, 269.77/39.99 binunionEcases = 269.77/39.99 (![X4,X6,X8,X10:$o]: 269.77/39.99 (in(X8,binunion(X4,X6)) => 269.77/39.99 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionIR, axiom, binunionIR <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 269.77/39.99 tff('39', plain, 269.77/39.99 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(binunionIL, axiom, binunionIL <=> 269.77/39.99 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 269.77/39.99 tff('40', plain, 269.77/39.99 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 269.77/39.99 tff('41', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powerset__Cong, axiom, powerset__Cong <=> 269.77/39.99 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 269.77/39.99 tff('42', plain, 269.77/39.99 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetE, axiom, powersetE <=> 269.77/39.99 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 269.77/39.99 tff('43', plain, 269.77/39.99 powersetE = 269.77/39.99 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(emptyInPowerset, axiom, emptyInPowerset <=> 269.77/39.99 (![A]: in(emptyset,powerset(A)))). 269.77/39.99 tff('44', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(emptyinPowerset, axiom, emptyinPowerset <=> 269.77/39.99 (![A]: in(emptyset,powerset(A)))). 269.77/39.99 tff('45', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetI, axiom, powersetI <=> 269.77/39.99 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 269.77/39.99 tff('46', plain, 269.77/39.99 powersetI = 269.77/39.99 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(powersetAx, axiom, powersetAx <=> 269.77/39.99 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 269.77/39.99 tff('47', plain, 269.77/39.99 powersetAx = 269.77/39.99 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 269.77/39.99 define([status(thm)])). 269.77/39.99 tff(intersectInPowersetIntersectUnions, conjecture, 269.77/39.99 (setextAx => 269.77/39.99 (emptysetAx => 269.77/39.99 (setadjoinAx => 269.77/39.99 (powersetAx => 269.77/39.99 (setunionAx => 269.77/39.99 (omega0Ax => 269.77/39.99 (omegaSAx => 269.77/39.99 (omegaIndAx => 269.77/39.99 (replAx => 269.77/39.99 (foundationAx => 269.77/39.99 (wellorderingAx => 269.77/39.99 (descrp => 269.77/39.99 (dsetconstrI => 269.77/39.99 (dsetconstrEL => 269.77/39.99 (dsetconstrER => 269.77/39.99 (exuE1 => 269.77/39.99 (prop2setE => 269.77/39.99 (emptysetE => 269.77/39.99 (emptysetimpfalse => 269.77/39.99 (notinemptyset => 269.77/39.99 (exuE3e => 269.77/39.99 (setext => 269.77/39.99 (emptyI => 269.77/39.99 (noeltsimpempty => 269.77/39.99 (setbeta => 269.77/39.99 (nonemptyE1 => 269.77/39.99 (nonemptyI => 269.77/39.99 (nonemptyI1 => 269.77/39.99 (setadjoinIL => 269.77/39.99 (emptyinunitempty => 269.77/39.99 (setadjoinIR => 269.77/39.99 (setadjoinE => 269.77/39.99 (setadjoinOr => 269.77/39.99 (setoftrueEq => 269.77/39.99 (powersetI => 269.77/39.99 (emptyinPowerset => 269.77/39.99 (emptyInPowerset => 269.77/39.99 (powersetE => 269.77/39.99 (setunionI => 269.77/39.99 (setunionE => 269.77/39.99 (subPowSU => 269.77/39.99 (exuE2 => 269.77/39.99 (nonemptyImpWitness => 269.77/39.99 (uniqinunit => 269.77/39.99 (notinsingleton => 269.77/39.99 (eqinunit => 269.77/39.99 (singletonsswitch => 269.77/39.99 (upairsetE => 269.77/39.99 (upairsetIL => 269.77/39.99 (upairsetIR => 269.77/39.99 (emptyE1 => 269.77/39.99 (vacuousDall => 269.77/39.99 (quantDeMorgan1 => 269.77/39.99 (quantDeMorgan2 => 269.77/39.99 (quantDeMorgan3 => 269.77/39.99 (quantDeMorgan4 => 269.77/39.99 (prop2setI => 269.77/39.99 (prop2set2propI => 269.77/39.99 (notdexE => 269.77/39.99 (notdallE => 269.77/39.99 (exuI1 => 269.77/39.99 (exuI3 => 269.77/39.99 (exuI2 => 269.77/39.99 (inCongP => 269.77/39.99 (in__Cong => 269.77/39.99 (exuE3u => 269.77/39.99 ( 269.77/39.99 exu__Cong => 269.77/39.99 ( 269.77/39.99 emptyset__Cong => 269.77/39.99 ( 269.77/39.99 setadjoin__Cong => 269.77/39.99 ( 269.77/39.99 powerset__Cong => 269.77/39.99 ( 269.77/39.99 setunion__Cong => 269.77/39.99 ( 269.77/39.99 omega__Cong => 269.77/39.99 ( 269.77/39.99 exuEu => 269.77/39.99 ( 269.77/39.99 descr__Cong => 269.77/39.99 ( 269.77/39.99 dsetconstr__Cong => 269.77/39.99 ( 269.77/39.99 subsetI1 => 269.77/39.99 ( 269.77/39.99 eqimpsubset2 => 269.77/39.99 ( 269.77/39.99 eqimpsubset1 => 269.77/39.99 ( 269.77/39.99 subsetI2 => 269.77/39.99 ( 269.77/39.99 emptysetsubset => 269.77/39.99 ( 269.77/39.99 subsetE => 269.77/39.99 ( 269.77/39.99 subsetE2 => 269.77/39.99 ( 269.77/39.99 notsubsetI => 269.77/39.99 ( 269.77/39.99 notequalI1 => 269.77/39.99 ( 269.77/39.99 notequalI2 => 269.77/39.99 ( 269.77/39.99 subsetRefl => 269.77/39.99 ( 269.77/39.99 subsetTrans => 269.77/39.99 ( 269.77/39.99 setadjoinSub => 269.77/39.99 ( 269.77/39.99 setadjoinSub2 => 269.77/39.99 ( 269.77/39.99 subset2powerset => 269.77/39.99 ( 269.77/39.99 setextsub => 269.77/39.99 ( 269.77/39.99 subsetemptysetimpeq => 269.77/39.99 ( 269.77/39.99 powersetI1 => 269.77/39.99 ( 269.77/39.99 powersetE1 => 269.77/39.99 ( 269.77/39.99 inPowerset => 269.77/39.99 ( 269.77/39.99 powersetsubset => 269.77/39.99 ( 269.77/39.99 sepInPowerset => 269.77/39.99 ( 269.77/39.99 sepSubset => 269.77/39.99 ( 269.77/39.99 binunionIL => 269.77/39.99 ( 269.77/39.99 upairset2IR => 269.77/39.99 ( 269.77/39.99 binunionIR => 269.77/39.99 ( 269.77/39.99 binunionEcases => 269.77/39.99 ( 269.77/39.99 binunionE => 269.77/39.99 ( 269.77/39.99 binunionLsub => 269.77/39.99 ( 269.77/39.99 binunionRsub => 269.77/39.99 ( 269.77/39.99 binintersectI => 269.77/39.99 ( 269.77/39.99 binintersectSubset5 => 269.77/39.99 ( 269.77/39.99 binintersectEL => 269.77/39.99 ( 269.77/39.99 binintersectLsub => 269.77/39.99 ( 269.77/39.99 binintersectSubset2 => 269.77/39.99 ( 269.77/39.99 binintersectSubset3 => 269.77/39.99 ( 269.77/39.99 binintersectER => 269.77/39.99 ( 269.77/39.99 disjointsetsI1 => 269.77/39.99 ( 269.77/39.99 binintersectRsub => 269.77/39.99 ( 269.77/39.99 binintersectSubset4 => 269.77/39.99 ( 269.77/39.99 binintersectSubset1 => 269.77/39.99 ( 269.77/39.99 bs114d => 269.77/39.99 ( 269.77/39.99 setminusI => 269.77/39.99 ( 269.77/39.99 setminusEL => 269.77/39.99 ( 269.77/39.99 setminusER => 269.77/39.99 ( 269.77/39.99 setminusSubset2 => 269.77/39.99 ( 269.77/39.99 setminusERneg => 269.77/39.99 ( 269.77/39.99 setminusELneg => 269.77/39.99 ( 269.77/39.99 setminusILneg => 269.77/39.99 ( 269.77/39.99 setminusIRneg => 269.77/39.99 ( 269.77/39.99 setminusLsub => 269.77/39.99 ( 269.77/39.99 setminusSubset1 => 269.77/39.99 ( 269.77/39.99 symdiffE => 269.77/39.99 ( 269.77/39.99 symdiffI1 => 269.77/39.99 ( 269.77/39.99 symdiffI2 => 269.77/39.99 ( 269.77/39.99 symdiffIneg1 => 269.77/39.99 ( 269.77/39.99 symdiffIneg2 => 269.77/39.99 ( 269.77/39.99 secondinupair => 269.77/39.99 ( 269.77/39.99 setukpairIL => 269.77/39.99 ( 269.77/39.99 setukpairIR => 269.77/39.99 ( 269.77/39.99 kpairiskpair => 269.77/39.99 ( 269.77/39.99 kpairp => 269.77/39.99 ( 269.77/39.99 singletonsubset => 269.77/39.99 ( 269.77/39.99 singletoninpowerset => 269.77/39.99 ( 269.77/39.99 singletoninpowunion => 269.77/39.99 ( 269.77/39.99 upairset2E => 269.77/39.99 ( 269.77/39.99 upairsubunion => 269.77/39.99 ( 269.77/39.99 upairinpowunion => 269.77/39.99 ( 269.77/39.99 ubforcartprodlem1 => 269.77/39.99 ( 269.77/39.99 ubforcartprodlem2 => 269.77/39.99 ( 269.77/39.99 ubforcartprodlem3 => 269.77/39.99 ( 269.77/39.99 cartprodpairin => 269.77/39.99 ( 269.77/39.99 cartprodmempair1 => 269.77/39.99 ( 269.77/39.99 cartprodmempair => 269.77/39.99 ( 269.77/39.99 setunionE2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton1 => 269.77/39.99 ( 269.77/39.99 setunionsingleton2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton => 269.77/39.99 ( 269.77/39.99 singletonprop => 269.77/39.99 ( 269.77/39.99 ex1E1 => 269.77/39.99 ( 269.77/39.99 ex1I => 269.77/39.99 ( 269.77/39.99 ex1I2 => 269.77/39.99 ( 269.77/39.99 singletonsuniq => 269.77/39.99 ( 269.77/39.99 setukpairinjL1 => 269.77/39.99 ( 269.77/39.99 kfstsingleton => 269.77/39.99 ( 269.77/39.99 theprop => 269.77/39.99 ( 269.77/39.99 kfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodfstin => 269.77/39.99 ( 269.77/39.99 setukpairinjL2 => 269.77/39.99 ( 269.77/39.99 setukpairinjL => 269.77/39.99 ( 269.77/39.99 setukpairinjR11 => 269.77/39.99 ( 269.77/39.99 setukpairinjR12 => 269.77/39.99 ( 269.77/39.99 setukpairinjR1 => 269.77/39.99 ( 269.77/39.99 upairequniteq => 269.77/39.99 ( 269.77/39.99 setukpairinjR2 => 269.77/39.99 ( 269.77/39.99 setukpairinjR => 269.77/39.99 ( 269.77/39.99 ksndsingleton => 269.77/39.99 ( 269.77/39.99 ksndpairEq => 269.77/39.99 ( 269.77/39.99 kpairsurjEq => 269.77/39.99 ( 269.77/39.99 cartprodsndin => 269.77/39.99 ( 269.77/39.99 cartprodpairmemEL => 269.77/39.99 ( 269.77/39.99 cartprodpairmemER => 269.77/39.99 ( 269.77/39.99 cartprodmempaircEq => 269.77/39.99 ( 269.77/39.99 cartprodfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodsndpairEq => 269.77/39.99 ( 269.77/39.99 cartprodpairsurjEq => 269.77/39.99 ( 269.77/39.99 dpsetconstrI => 269.77/39.99 ( 269.77/39.99 dpsetconstrSub => 269.77/39.99 ( 269.77/39.99 setOfPairsIsBReln => 269.77/39.99 ( 269.77/39.99 dpsetconstrERa => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL1 => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL2 => 269.77/39.99 ( 269.77/39.99 dpsetconstrER => 269.77/39.99 ( 269.77/39.99 funcImageSingleton => 269.77/39.99 ( 269.77/39.99 apProp => 269.77/39.99 ( 269.77/39.99 app => 269.77/39.99 ( 269.77/39.99 infuncsetfunc => 269.77/39.99 ( 269.77/39.99 ap2p => 269.77/39.99 ( 269.77/39.99 funcinfuncset => 269.77/39.99 ( 269.77/39.99 lamProp => 269.77/39.99 ( 269.77/39.99 lamp => 269.77/39.99 ( 269.77/39.99 lam2p => 269.77/39.99 ( 269.77/39.99 brelnall1 => 269.77/39.99 ( 269.77/39.99 brelnall2 => 269.77/39.99 ( 269.77/39.99 ex1E2 => 269.77/39.99 ( 269.77/39.99 funcGraphProp1 => 269.77/39.99 ( 269.77/39.99 funcGraphProp3 => 269.77/39.99 ( 269.77/39.99 funcGraphProp2 => 269.77/39.99 ( 269.77/39.99 funcextLem => 269.77/39.99 ( 269.77/39.99 funcGraphProp4 => 269.77/39.99 ( 269.77/39.99 subbreln => 269.77/39.99 ( 269.77/39.99 eqbreln => 269.77/39.99 ( 269.77/39.99 funcext => 269.77/39.99 ( 269.77/39.99 funcext2 => 269.77/39.99 ( 269.77/39.99 ap2apEq1 => 269.77/39.99 ( 269.77/39.99 ap2apEq2 => 269.77/39.99 ( 269.77/39.99 beta1 => 269.77/39.99 ( 269.77/39.99 eta1 => 269.77/39.99 ( 269.77/39.99 lam2lamEq => 269.77/39.99 ( 269.77/39.99 beta2 => 269.77/39.99 ( 269.77/39.99 eta2 => 269.77/39.99 ( 269.77/39.99 iffalseProp1 => 269.77/39.99 ( 269.77/39.99 iffalseProp2 => 269.77/39.99 ( 269.77/39.99 iftrueProp1 => 269.77/39.99 ( 269.77/39.99 iftrueProp2 => 269.77/39.99 ( 269.77/39.99 ifSingleton => 269.77/39.99 ( 269.77/39.99 ifp => 269.77/39.99 ( 269.77/39.99 theeq => 269.77/39.99 ( 269.77/39.99 iftrue => 269.77/39.99 ( 269.77/39.99 iffalse => 269.77/39.99 ( 269.77/39.99 iftrueorfalse => 269.77/39.99 ( 269.77/39.99 binintersectT_lem => 269.77/39.99 ( 269.77/39.99 binunionT_lem => 269.77/39.99 ( 269.77/39.99 powersetT_lem => 269.77/39.99 ( 269.77/39.99 setminusT_lem => 269.77/39.99 ( 269.77/39.99 complementT_lem => 269.77/39.99 ( 269.77/39.99 setextT => 269.77/39.99 ( 269.77/39.99 subsetTI => 269.77/39.99 ( 269.77/39.99 powersetTI1 => 269.77/39.99 ( 269.77/39.99 powersetTE1 => 269.77/39.99 ( 269.77/39.99 complementTI1 => 269.77/39.99 ( 269.77/39.99 complementTE1 => 269.77/39.99 ( 269.77/39.99 binintersectTELcontra => 269.77/39.99 ( 269.77/39.99 binintersectTERcontra => 269.77/39.99 ( 269.77/39.99 contrasubsetT => 269.77/39.99 ( 269.77/39.99 contrasubsetT1 => 269.77/39.99 ( 269.77/39.99 contrasubsetT2 => 269.77/39.99 ( 269.77/39.99 contrasubsetT3 => 269.77/39.99 ( 269.77/39.99 doubleComplementI1 => 269.77/39.99 ( 269.77/39.99 doubleComplementE1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub2 => 269.77/39.99 ( 269.77/39.99 doubleComplementEq => 269.77/39.99 ( 269.77/39.99 complementTnotintersectT => 269.77/39.99 ( 269.77/39.99 complementImpComplementIntersect => 269.77/39.99 ( 269.77/39.99 complementSubsetComplementIntersect => 269.77/39.99 ( 269.77/39.99 complementInPowersetComplementIntersect => 269.77/39.99 ( 269.77/39.99 contraSubsetComplement => 269.77/39.99 ( 269.77/39.99 complementTcontraSubset => 269.77/39.99 ( 269.77/39.99 binunionTILcontra => 269.77/39.99 ( 269.77/39.99 binunionTIRcontra => 269.77/39.99 ( 269.77/39.99 inIntersectImpInUnion => 269.77/39.99 ( 269.77/39.99 inIntersectImpInUnion2 => 269.77/39.99 ( 269.77/39.99 inIntersectImpInIntersectUnions => 269.77/39.99 ( 269.77/39.99 ![A,X]: 269.77/39.99 (in( 269.77/39.99 X, 269.77/39.99 powerset( 269.77/39.99 A)) => 269.77/39.99 (![Y]: 269.77/39.99 (in( 269.77/39.99 Y, 269.77/39.99 powerset( 269.77/39.99 A)) => 269.77/39.99 (![Z]: 269.77/39.99 (in( 269.77/39.99 Z, 269.77/39.99 powerset( 269.77/39.99 A)) => 269.77/39.99 in( 269.77/39.99 binintersect( 269.77/39.99 X,Y), 269.77/39.99 powerset( 269.77/39.99 binintersect( 269.77/39.99 binunion( 269.77/39.99 X,Z), 269.77/39.99 binunion( 269.77/39.99 Y,Z)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 269.77/39.99 tff(zf_stmt_0, conjecture, 269.77/39.99 (setextAx => 269.77/39.99 (emptysetAx => 269.77/39.99 (setadjoinAx => 269.77/39.99 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))) => 269.77/39.99 (setunionAx => 269.77/39.99 (omega0Ax => 269.77/39.99 (omegaSAx => 269.77/39.99 (omegaIndAx => 269.77/39.99 (replAx => 269.77/39.99 (foundationAx => 269.77/39.99 (wellorderingAx => 269.77/39.99 (descrp => 269.77/39.99 (dsetconstrI => 269.77/39.99 (dsetconstrEL => 269.77/39.99 (dsetconstrER => 269.77/39.99 (exuE1 => 269.77/39.99 (prop2setE => 269.77/39.99 (emptysetE => 269.77/39.99 (emptysetimpfalse => 269.77/39.99 (notinemptyset => 269.77/39.99 (exuE3e => 269.77/39.99 (setext => 269.77/39.99 (emptyI => 269.77/39.99 (noeltsimpempty => 269.77/39.99 (setbeta => 269.77/39.99 (nonemptyE1 => 269.77/39.99 (nonemptyI => 269.77/39.99 (nonemptyI1 => 269.77/39.99 (setadjoinIL => 269.77/39.99 (emptyinunitempty => 269.77/39.99 (setadjoinIR => 269.77/39.99 (setadjoinE => 269.77/39.99 (setadjoinOr => 269.77/39.99 (setoftrueEq => 269.77/39.99 ((![X10,X12]: 269.77/39.99 ((![X14]: 269.77/39.99 (in(X14,X12) => in(X14,X10))) => 269.77/39.99 in(X12,powerset(X10)))) => 269.77/39.99 ((![X16]: in(emptyset,powerset(X16))) => 269.77/39.99 ((![X18]: in(emptyset,powerset(X18))) => 269.77/39.99 ((![X20,X22,X24]: 269.77/39.99 (in(X22,powerset(X20)) => 269.77/39.99 (in(X24,X22) => in(X24,X20)))) => 269.77/39.99 (setunionI => 269.77/39.99 (setunionE => 269.77/39.99 (subPowSU => 269.77/39.99 (exuE2 => 269.77/39.99 (nonemptyImpWitness => 269.77/39.99 (uniqinunit => 269.77/39.99 (notinsingleton => 269.77/39.99 (eqinunit => 269.77/39.99 (singletonsswitch => 269.77/39.99 (upairsetE => 269.77/39.99 (upairsetIL => 269.77/39.99 (upairsetIR => 269.77/39.99 (emptyE1 => 269.77/39.99 (vacuousDall => 269.77/39.99 (quantDeMorgan1 => 269.77/39.99 (quantDeMorgan2 => 269.77/39.99 (quantDeMorgan3 => 269.77/39.99 (quantDeMorgan4 => 269.77/39.99 (prop2setI => 269.77/39.99 (prop2set2propI => 269.77/39.99 (notdexE => 269.77/39.99 (notdallE => 269.77/39.99 (exuI1 => 269.77/39.99 (exuI3 => 269.77/39.99 (exuI2 => 269.77/39.99 (inCongP => 269.77/39.99 (in__Cong => 269.77/39.99 (exuE3u => 269.77/39.99 ( 269.77/39.99 exu__Cong => 269.77/39.99 ( 269.77/39.99 emptyset__Cong => 269.77/39.99 ( 269.77/39.99 setadjoin__Cong => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X26,X28]: 269.77/39.99 (( 269.77/39.99 X26 = X28) => 269.77/39.99 (powerset( 269.77/39.99 X26) = 269.77/39.99 powerset( 269.77/39.99 X28)))) => 269.77/39.99 ( 269.77/39.99 setunion__Cong => 269.77/39.99 ( 269.77/39.99 omega__Cong => 269.77/39.99 ( 269.77/39.99 exuEu => 269.77/39.99 ( 269.77/39.99 descr__Cong => 269.77/39.99 ( 269.77/39.99 dsetconstr__Cong => 269.77/39.99 ( 269.77/39.99 subsetI1 => 269.77/39.99 ( 269.77/39.99 eqimpsubset2 => 269.77/39.99 ( 269.77/39.99 eqimpsubset1 => 269.77/39.99 ( 269.77/39.99 subsetI2 => 269.77/39.99 ( 269.77/39.99 emptysetsubset => 269.77/39.99 ( 269.77/39.99 subsetE => 269.77/39.99 ( 269.77/39.99 subsetE2 => 269.77/39.99 ( 269.77/39.99 notsubsetI => 269.77/39.99 ( 269.77/39.99 notequalI1 => 269.77/39.99 ( 269.77/39.99 notequalI2 => 269.77/39.99 ( 269.77/39.99 subsetRefl => 269.77/39.99 ( 269.77/39.99 subsetTrans => 269.77/39.99 ( 269.77/39.99 setadjoinSub => 269.77/39.99 ( 269.77/39.99 setadjoinSub2 => 269.77/39.99 ( 269.77/39.99 subset2powerset => 269.77/39.99 ( 269.77/39.99 setextsub => 269.77/39.99 ( 269.77/39.99 subsetemptysetimpeq => 269.77/39.99 ( 269.77/39.99 powersetI1 => 269.77/39.99 ( 269.77/39.99 powersetE1 => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X30]: 269.77/39.99 in( 269.77/39.99 X30, 269.77/39.99 powerset( 269.77/39.99 X30))) => 269.77/39.99 ( 269.77/39.99 powersetsubset => 269.77/39.99 ( 269.77/39.99 sepInPowerset => 269.77/39.99 ( 269.77/39.99 sepSubset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X32, 269.77/39.99 X34,X36]: 269.77/39.99 (in( 269.77/39.99 X36,X32) => 269.77/39.99 in( 269.77/39.99 X36, 269.77/39.99 binunion( 269.77/39.99 X32,X34)))) => 269.77/39.99 ( 269.77/39.99 upairset2IR => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X38, 269.77/39.99 X40,X42]: 269.77/39.99 (in( 269.77/39.99 X42,X40) => 269.77/39.99 in( 269.77/39.99 X42, 269.77/39.99 binunion( 269.77/39.99 X38,X40)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X44, 269.77/39.99 X46,X48, 269.77/39.99 X50:$o]: 269.77/39.99 (in( 269.77/39.99 X48, 269.77/39.99 binunion( 269.77/39.99 X44,X46)) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X44) => 269.77/39.99 X50) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X46) => 269.77/39.99 X50) => 269.77/39.99 X50)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X52, 269.77/39.99 X54,X56]: 269.77/39.99 (in( 269.77/39.99 X56, 269.77/39.99 binunion( 269.77/39.99 X52,X54)) => 269.77/39.99 (in( 269.77/39.99 X56,X54) | 269.77/39.99 in( 269.77/39.99 X56,X52)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X58,X60]: 269.77/39.99 subset( 269.77/39.99 X58, 269.77/39.99 binunion( 269.77/39.99 X58,X60))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X62,X64]: 269.77/39.99 subset( 269.77/39.99 X64, 269.77/39.99 binunion( 269.77/39.99 X62,X64))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X66, 269.77/39.99 X68,X70]: 269.77/39.99 (in( 269.77/39.99 X70,X66) => 269.77/39.99 (in( 269.77/39.99 X70,X68) => 269.77/39.99 in( 269.77/39.99 X70, 269.77/39.99 binintersect( 269.77/39.99 X66,X68))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X72, 269.77/39.99 X74,X76]: 269.77/39.99 (subset( 269.77/39.99 X76,X72) => 269.77/39.99 (subset( 269.77/39.99 X76,X74) => 269.77/39.99 subset( 269.77/39.99 X76, 269.77/39.99 binintersect( 269.77/39.99 X72,X74))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X78, 269.77/39.99 X80,X82]: 269.77/39.99 (in( 269.77/39.99 X82, 269.77/39.99 binintersect( 269.77/39.99 X78,X80)) => 269.77/39.99 in( 269.77/39.99 X82,X78))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X84,X86]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X84,X86), 269.77/39.99 X84)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X88,X90]: 269.77/39.99 (subset( 269.77/39.99 X88,X90) => 269.77/39.99 (binintersect( 269.77/39.99 X88,X90) = 269.77/39.99 X88))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X92,X94]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X92,X94) = 269.77/39.99 X94) => 269.77/39.99 subset( 269.77/39.99 X94,X92))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X96, 269.77/39.99 X98,X100]: 269.77/39.99 (in( 269.77/39.99 X100, 269.77/39.99 binintersect( 269.77/39.99 X96,X98)) => 269.77/39.99 in( 269.77/39.99 X100,X98))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X102, 269.77/39.99 X104]: 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 ( 269.77/39.99 ?[X106]: 269.77/39.99 (in( 269.77/39.99 X106,X102) & 269.77/39.99 in( 269.77/39.99 X106,X104)))) => 269.77/39.99 (binintersect( 269.77/39.99 X102,X104) = 269.77/39.99 emptyset))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X108, 269.77/39.99 X110]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X108,X110), 269.77/39.99 X110)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X112, 269.77/39.99 X114]: 269.77/39.99 (subset( 269.77/39.99 X114,X112) => 269.77/39.99 (binintersect( 269.77/39.99 X112,X114) = 269.77/39.99 X114))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X116, 269.77/39.99 X118]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X116,X118) = 269.77/39.99 X116) => 269.77/39.99 subset( 269.77/39.99 X116,X118))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X120, 269.77/39.99 X122,X124]: 269.77/39.99 (binintersect( 269.77/39.99 X120, 269.77/39.99 binunion( 269.77/39.99 X122,X124)) = 269.77/39.99 binunion( 269.77/39.99 binintersect( 269.77/39.99 X120,X122), 269.77/39.99 binintersect( 269.77/39.99 X120,X124)))) => 269.77/39.99 ( 269.77/39.99 setminusI => 269.77/39.99 ( 269.77/39.99 setminusEL => 269.77/39.99 ( 269.77/39.99 setminusER => 269.77/39.99 ( 269.77/39.99 setminusSubset2 => 269.77/39.99 ( 269.77/39.99 setminusERneg => 269.77/39.99 ( 269.77/39.99 setminusELneg => 269.77/39.99 ( 269.77/39.99 setminusILneg => 269.77/39.99 ( 269.77/39.99 setminusIRneg => 269.77/39.99 ( 269.77/39.99 setminusLsub => 269.77/39.99 ( 269.77/39.99 setminusSubset1 => 269.77/39.99 ( 269.77/39.99 symdiffE => 269.77/39.99 ( 269.77/39.99 symdiffI1 => 269.77/39.99 ( 269.77/39.99 symdiffI2 => 269.77/39.99 ( 269.77/39.99 symdiffIneg1 => 269.77/39.99 ( 269.77/39.99 symdiffIneg2 => 269.77/39.99 ( 269.77/39.99 secondinupair => 269.77/39.99 ( 269.77/39.99 setukpairIL => 269.77/39.99 ( 269.77/39.99 setukpairIR => 269.77/39.99 ( 269.77/39.99 kpairiskpair => 269.77/39.99 ( 269.77/39.99 kpairp => 269.77/39.99 ( 269.77/39.99 singletonsubset => 269.77/39.99 ( 269.77/39.99 singletoninpowerset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X126, 269.77/39.99 X128,X130]: 269.77/39.99 (in( 269.77/39.99 X130,X126) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X130, 269.77/39.99 emptyset), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X126,X128))))) => 269.77/39.99 ( 269.77/39.99 upairset2E => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X132, 269.77/39.99 X134,X136]: 269.77/39.99 (in( 269.77/39.99 X136,X132) => 269.77/39.99 (![X138]: 269.77/39.99 (in( 269.77/39.99 X138,X134) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 X136, 269.77/39.99 setadjoin( 269.77/39.99 X138, 269.77/39.99 emptyset)), 269.77/39.99 binunion( 269.77/39.99 X132,X134)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X140, 269.77/39.99 X142,X144]: 269.77/39.99 (in( 269.77/39.99 X144,X140) => 269.77/39.99 (![X146]: 269.77/39.99 (in( 269.77/39.99 X146,X142) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X144, 269.77/39.99 setadjoin( 269.77/39.99 X146, 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X140,X142))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X148, 269.77/39.99 X150,X152]: 269.77/39.99 (in( 269.77/39.99 X152,X148) => 269.77/39.99 (![X154]: 269.77/39.99 (in( 269.77/39.99 X154,X150) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 setadjoin( 269.77/39.99 X154, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X148,X150))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X156, 269.77/39.99 X158,X160]: 269.77/39.99 (in( 269.77/39.99 X160,X156) => 269.77/39.99 (![X162]: 269.77/39.99 (in( 269.77/39.99 X162,X158) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 setadjoin( 269.77/39.99 X162, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X156,X158)))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X164, 269.77/39.99 X166,X168]: 269.77/39.99 (in( 269.77/39.99 X168,X164) => 269.77/39.99 (![X170]: 269.77/39.99 (in( 269.77/39.99 X170,X166) => 269.77/39.99 in( 269.77/39.99 kpair( 269.77/39.99 X168,X170), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X164,X166)))))))) => 269.77/39.99 ( 269.77/39.99 cartprodpairin => 269.77/39.99 ( 269.77/39.99 cartprodmempair1 => 269.77/39.99 ( 269.77/39.99 cartprodmempair => 269.77/39.99 ( 269.77/39.99 setunionE2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton1 => 269.77/39.99 ( 269.77/39.99 setunionsingleton2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton => 269.77/39.99 ( 269.77/39.99 singletonprop => 269.77/39.99 ( 269.77/39.99 ex1E1 => 269.77/39.99 ( 269.77/39.99 ex1I => 269.77/39.99 ( 269.77/39.99 ex1I2 => 269.77/39.99 ( 269.77/39.99 singletonsuniq => 269.77/39.99 ( 269.77/39.99 setukpairinjL1 => 269.77/39.99 ( 269.77/39.99 kfstsingleton => 269.77/39.99 ( 269.77/39.99 theprop => 269.77/39.99 ( 269.77/39.99 kfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodfstin => 269.77/39.99 ( 269.77/39.99 setukpairinjL2 => 269.77/39.99 ( 269.77/39.99 setukpairinjL => 269.77/39.99 ( 269.77/39.99 setukpairinjR11 => 269.77/39.99 ( 269.77/39.99 setukpairinjR12 => 269.77/39.99 ( 269.77/39.99 setukpairinjR1 => 269.77/39.99 ( 269.77/39.99 upairequniteq => 269.77/39.99 ( 269.77/39.99 setukpairinjR2 => 269.77/39.99 ( 269.77/39.99 setukpairinjR => 269.77/39.99 ( 269.77/39.99 ksndsingleton => 269.77/39.99 ( 269.77/39.99 ksndpairEq => 269.77/39.99 ( 269.77/39.99 kpairsurjEq => 269.77/39.99 ( 269.77/39.99 cartprodsndin => 269.77/39.99 ( 269.77/39.99 cartprodpairmemEL => 269.77/39.99 ( 269.77/39.99 cartprodpairmemER => 269.77/39.99 ( 269.77/39.99 cartprodmempaircEq => 269.77/39.99 ( 269.77/39.99 cartprodfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodsndpairEq => 269.77/39.99 ( 269.77/39.99 cartprodpairsurjEq => 269.77/39.99 ( 269.77/39.99 dpsetconstrI => 269.77/39.99 ( 269.77/39.99 dpsetconstrSub => 269.77/39.99 ( 269.77/39.99 setOfPairsIsBReln => 269.77/39.99 ( 269.77/39.99 dpsetconstrERa => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL1 => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL2 => 269.77/39.99 ( 269.77/39.99 dpsetconstrER => 269.77/39.99 ( 269.77/39.99 funcImageSingleton => 269.77/39.99 ( 269.77/39.99 apProp => 269.77/39.99 ( 269.77/39.99 app => 269.77/39.99 ( 269.77/39.99 infuncsetfunc => 269.77/39.99 ( 269.77/39.99 ap2p => 269.77/39.99 ( 269.77/39.99 funcinfuncset => 269.77/39.99 ( 269.77/39.99 lamProp => 269.77/39.99 ( 269.77/39.99 lamp => 269.77/39.99 ( 269.77/39.99 lam2p => 269.77/39.99 ( 269.77/39.99 brelnall1 => 269.77/39.99 ( 269.77/39.99 brelnall2 => 269.77/39.99 ( 269.77/39.99 ex1E2 => 269.77/39.99 ( 269.77/39.99 funcGraphProp1 => 269.77/39.99 ( 269.77/39.99 funcGraphProp3 => 269.77/39.99 ( 269.77/39.99 funcGraphProp2 => 269.77/39.99 ( 269.77/39.99 funcextLem => 269.77/39.99 ( 269.77/39.99 funcGraphProp4 => 269.77/39.99 ( 269.77/39.99 subbreln => 269.77/39.99 ( 269.77/39.99 eqbreln => 269.77/39.99 ( 269.77/39.99 funcext => 269.77/39.99 ( 269.77/39.99 funcext2 => 269.77/39.99 ( 269.77/39.99 ap2apEq1 => 269.77/39.99 ( 269.77/39.99 ap2apEq2 => 269.77/39.99 ( 269.77/39.99 beta1 => 269.77/39.99 ( 269.77/39.99 eta1 => 269.77/39.99 ( 269.77/39.99 lam2lamEq => 269.77/39.99 ( 269.77/39.99 beta2 => 269.77/39.99 ( 269.77/39.99 eta2 => 269.77/39.99 ( 269.77/39.99 iffalseProp1 => 269.77/39.99 ( 269.77/39.99 iffalseProp2 => 269.77/39.99 ( 269.77/39.99 iftrueProp1 => 269.77/39.99 ( 269.77/39.99 iftrueProp2 => 269.77/39.99 ( 269.77/39.99 ifSingleton => 269.77/39.99 ( 269.77/39.99 ifp => 269.77/39.99 ( 269.77/39.99 theeq => 269.77/39.99 ( 269.77/39.99 iftrue => 269.77/39.99 ( 269.77/39.99 iffalse => 269.77/39.99 ( 269.77/39.99 iftrueorfalse => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X172, 269.77/39.99 X174]: 269.77/39.99 (in( 269.77/39.99 X174, 269.77/39.99 powerset( 269.77/39.99 X172)) => 269.77/39.99 (![X176]: 269.77/39.99 (in( 269.77/39.99 X176, 269.77/39.99 powerset( 269.77/39.99 X172)) => 269.77/39.99 in( 269.77/39.99 binintersect( 269.77/39.99 X174,X176), 269.77/39.99 powerset( 269.77/39.99 X172)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X178, 269.77/39.99 X180]: 269.77/39.99 (in( 269.77/39.99 X180, 269.77/39.99 powerset( 269.77/39.99 X178)) => 269.77/39.99 (![X182]: 269.77/39.99 (in( 269.77/39.99 X182, 269.77/39.99 powerset( 269.77/39.99 X178)) => 269.77/39.99 in( 269.77/39.99 binunion( 269.77/39.99 X180,X182), 269.77/39.99 powerset( 269.77/39.99 X178)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X184, 269.77/39.99 X186]: 269.77/39.99 (in( 269.77/39.99 X186, 269.77/39.99 powerset( 269.77/39.99 X184)) => 269.77/39.99 in( 269.77/39.99 powerset( 269.77/39.99 X186), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 X184))))) => 269.77/39.99 ( 269.77/39.99 setminusT_lem => 269.77/39.99 ( 269.77/39.99 complementT_lem => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X188, 269.77/39.99 X190]: 269.77/39.99 (in( 269.77/39.99 X190, 269.77/39.99 powerset( 269.77/39.99 X188)) => 269.77/39.99 (![X192]: 269.77/39.99 (in( 269.77/39.99 X192, 269.77/39.99 powerset( 269.77/39.99 X188)) => 269.77/39.99 (( 269.77/39.99 ![X194]: 269.77/39.99 (in( 269.77/39.99 X194,X188) => 269.77/39.99 (in( 269.77/39.99 X194,X190) => 269.77/39.99 in( 269.77/39.99 X194,X192)))) => 269.77/39.99 (( 269.77/39.99 ![X196]: 269.77/39.99 (in( 269.77/39.99 X196,X188) => 269.77/39.99 (in( 269.77/39.99 X196,X192) => 269.77/39.99 in( 269.77/39.99 X196,X190)))) => 269.77/39.99 (X190 = 269.77/39.99 X192))))))) => 269.77/39.99 ( 269.77/39.99 subsetTI => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X198, 269.77/39.99 X200]: 269.77/39.99 (in( 269.77/39.99 X200, 269.77/39.99 powerset( 269.77/39.99 X198)) => 269.77/39.99 (![X202]: 269.77/39.99 (in( 269.77/39.99 X202, 269.77/39.99 powerset( 269.77/39.99 X198)) => 269.77/39.99 (( 269.77/39.99 ![X204]: 269.77/39.99 (in( 269.77/39.99 X204,X198) => 269.77/39.99 (in( 269.77/39.99 X204,X200) => 269.77/39.99 in( 269.77/39.99 X204,X202)))) => 269.77/39.99 in( 269.77/39.99 X200, 269.77/39.99 powerset( 269.77/39.99 X202))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X206, 269.77/39.99 X208]: 269.77/39.99 (in( 269.77/39.99 X208, 269.77/39.99 powerset( 269.77/39.99 X206)) => 269.77/39.99 (![X210]: 269.77/39.99 (in( 269.77/39.99 X210, 269.77/39.99 powerset( 269.77/39.99 X206)) => 269.77/39.99 (![X212]: 269.77/39.99 (in( 269.77/39.99 X212,X206) => 269.77/39.99 (in( 269.77/39.99 X208, 269.77/39.99 powerset( 269.77/39.99 X210)) => 269.77/39.99 (in( 269.77/39.99 X212,X208) => 269.77/39.99 in( 269.77/39.99 X212,X210))))))))) => 269.77/39.99 ( 269.77/39.99 complementTI1 => 269.77/39.99 ( 269.77/39.99 complementTE1 => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X214, 269.77/39.99 X216]: 269.77/39.99 (in( 269.77/39.99 X216, 269.77/39.99 powerset( 269.77/39.99 X214)) => 269.77/39.99 (![X218]: 269.77/39.99 (in( 269.77/39.99 X218, 269.77/39.99 powerset( 269.77/39.99 X214)) => 269.77/39.99 (![X220]: 269.77/39.99 (in( 269.77/39.99 X220,X214) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X220,X216)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X220, 269.77/39.99 binintersect( 269.77/39.99 X216,X218)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X222, 269.77/39.99 X224]: 269.77/39.99 (in( 269.77/39.99 X224, 269.77/39.99 powerset( 269.77/39.99 X222)) => 269.77/39.99 (![X226]: 269.77/39.99 (in( 269.77/39.99 X226, 269.77/39.99 powerset( 269.77/39.99 X222)) => 269.77/39.99 (![X228]: 269.77/39.99 (in( 269.77/39.99 X228,X222) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X228,X226)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X228, 269.77/39.99 binintersect( 269.77/39.99 X224,X226)))))))))) => 269.77/39.99 ( 269.77/39.99 contrasubsetT => 269.77/39.99 ( 269.77/39.99 contrasubsetT1 => 269.77/39.99 ( 269.77/39.99 contrasubsetT2 => 269.77/39.99 ( 269.77/39.99 contrasubsetT3 => 269.77/39.99 ( 269.77/39.99 doubleComplementI1 => 269.77/39.99 ( 269.77/39.99 doubleComplementE1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub2 => 269.77/39.99 ( 269.77/39.99 doubleComplementEq => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X230, 269.77/39.99 X232]: 269.77/39.99 (in( 269.77/39.99 X232, 269.77/39.99 powerset( 269.77/39.99 X230)) => 269.77/39.99 (![X234]: 269.77/39.99 (in( 269.77/39.99 X234, 269.77/39.99 powerset( 269.77/39.99 X230)) => 269.77/39.99 (![X236]: 269.77/39.99 (in( 269.77/39.99 X236,X230) => 269.77/39.99 (in( 269.77/39.99 X236, 269.77/39.99 setminus( 269.77/39.99 X230,X232)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X236, 269.77/39.99 binintersect( 269.77/39.99 X232,X234)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X238, 269.77/39.99 X240]: 269.77/39.99 (in( 269.77/39.99 X240, 269.77/39.99 powerset( 269.77/39.99 X238)) => 269.77/39.99 (![X242]: 269.77/39.99 (in( 269.77/39.99 X242, 269.77/39.99 powerset( 269.77/39.99 X238)) => 269.77/39.99 (![X244]: 269.77/39.99 (in( 269.77/39.99 X244,X238) => 269.77/39.99 (in( 269.77/39.99 X244, 269.77/39.99 setminus( 269.77/39.99 X238,X240)) => 269.77/39.99 in( 269.77/39.99 X244, 269.77/39.99 setminus( 269.77/39.99 X238, 269.77/39.99 binintersect( 269.77/39.99 X240,X242)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X246, 269.77/39.99 X248]: 269.77/39.99 (in( 269.77/39.99 X248, 269.77/39.99 powerset( 269.77/39.99 X246)) => 269.77/39.99 (![X250]: 269.77/39.99 (in( 269.77/39.99 X250, 269.77/39.99 powerset( 269.77/39.99 X246)) => 269.77/39.99 subset( 269.77/39.99 setminus( 269.77/39.99 X246,X248), 269.77/39.99 setminus( 269.77/39.99 X246, 269.77/39.99 binintersect( 269.77/39.99 X248,X250))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X252, 269.77/39.99 X254]: 269.77/39.99 (in( 269.77/39.99 X254, 269.77/39.99 powerset( 269.77/39.99 X252)) => 269.77/39.99 (![X256]: 269.77/39.99 (in( 269.77/39.99 X256, 269.77/39.99 powerset( 269.77/39.99 X252)) => 269.77/39.99 in( 269.77/39.99 setminus( 269.77/39.99 X252,X254), 269.77/39.99 powerset( 269.77/39.99 setminus( 269.77/39.99 X252, 269.77/39.99 binintersect( 269.77/39.99 X254,X256)))))))) => 269.77/39.99 ( 269.77/39.99 contraSubsetComplement => 269.77/39.99 ( 269.77/39.99 complementTcontraSubset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X258, 269.77/39.99 X260]: 269.77/39.99 (in( 269.77/39.99 X260, 269.77/39.99 powerset( 269.77/39.99 X258)) => 269.77/39.99 (![X262]: 269.77/39.99 (in( 269.77/39.99 X262, 269.77/39.99 powerset( 269.77/39.99 X258)) => 269.77/39.99 (![X264]: 269.77/39.99 (in( 269.77/39.99 X264,X258) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X264, 269.77/39.99 binunion( 269.77/39.99 X260,X262))) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X264,X260))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X266, 269.77/39.99 X268]: 269.77/39.99 (in( 269.77/39.99 X268, 269.77/39.99 powerset( 269.77/39.99 X266)) => 269.77/39.99 (![X270]: 269.77/39.99 (in( 269.77/39.99 X270, 269.77/39.99 powerset( 269.77/39.99 X266)) => 269.77/39.99 (![X272]: 269.77/39.99 (in( 269.77/39.99 X272,X266) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X272, 269.77/39.99 binunion( 269.77/39.99 X268,X270))) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X272,X270))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X274, 269.77/39.99 X276]: 269.77/39.99 (in( 269.77/39.99 X276, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X278]: 269.77/39.99 (in( 269.77/39.99 X278, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X280]: 269.77/39.99 (in( 269.77/39.99 X280, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X282]: 269.77/39.99 (in( 269.77/39.99 X282,X274) => 269.77/39.99 (in( 269.77/39.99 X282, 269.77/39.99 binintersect( 269.77/39.99 X276,X278)) => 269.77/39.99 in( 269.77/39.99 X282, 269.77/39.99 binunion( 269.77/39.99 X276,X280))))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X284, 269.77/39.99 X286]: 269.77/39.99 (in( 269.77/39.99 X286, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X288]: 269.77/39.99 (in( 269.77/39.99 X288, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X290]: 269.77/39.99 (in( 269.77/39.99 X290, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X292]: 269.77/39.99 (in( 269.77/39.99 X292,X284) => 269.77/39.99 (in( 269.77/39.99 X292, 269.77/39.99 binintersect( 269.77/39.99 X286,X288)) => 269.77/39.99 in( 269.77/39.99 X292, 269.77/39.99 binunion( 269.77/39.99 X288,X290))))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X294, 269.77/39.99 X296]: 269.77/39.99 (in( 269.77/39.99 X296, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X298]: 269.77/39.99 (in( 269.77/39.99 X298, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X300]: 269.77/39.99 (in( 269.77/39.99 X300, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X302]: 269.77/39.99 (in( 269.77/39.99 X302,X294) => 269.77/39.99 (in( 269.77/39.99 X302, 269.77/39.99 binintersect( 269.77/39.99 X296,X298)) => 269.77/39.99 in( 269.77/39.99 X302, 269.77/39.99 binintersect( 269.77/39.99 binunion( 269.77/39.99 X296,X300), 269.77/39.99 binunion( 269.77/39.99 X298,X300)))))))))))) => 269.77/39.99 ( 269.77/39.99 ![X304, 269.77/39.99 X306]: 269.77/39.99 (in( 269.77/39.99 X306, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 (![X308]: 269.77/39.99 (in( 269.77/39.99 X308, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 (![X310]: 269.77/39.99 (in( 269.77/39.99 X310, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 in( 269.77/39.99 binintersect( 269.77/39.99 X306,X308), 269.77/39.99 powerset( 269.77/39.99 binintersect( 269.77/39.99 binunion( 269.77/39.99 X306,X310), 269.77/39.99 binunion( 269.77/39.99 X308,X310)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 269.77/39.99 tff(zf_stmt_1, type, zip_tseitin_0 : ($i * $i * $i) > $o). 269.77/39.99 tff(zf_stmt_2, axiom, (zip_tseitin_0(X8,X6,X4) <=> (in(X8,X6) => in(X8,X4)))). 269.77/39.99 tff(zf_stmt_3, conjecture, 269.77/39.99 (setextAx => 269.77/39.99 (emptysetAx => 269.77/39.99 (setadjoinAx => 269.77/39.99 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 269.77/39.99 (setunionAx => 269.77/39.99 (omega0Ax => 269.77/39.99 (omegaSAx => 269.77/39.99 (omegaIndAx => 269.77/39.99 (replAx => 269.77/39.99 (foundationAx => 269.77/39.99 (wellorderingAx => 269.77/39.99 (descrp => 269.77/39.99 (dsetconstrI => 269.77/39.99 (dsetconstrEL => 269.77/39.99 (dsetconstrER => 269.77/39.99 (exuE1 => 269.77/39.99 (prop2setE => 269.77/39.99 (emptysetE => 269.77/39.99 (emptysetimpfalse => 269.77/39.99 (notinemptyset => 269.77/39.99 (exuE3e => 269.77/39.99 (setext => 269.77/39.99 (emptyI => 269.77/39.99 (noeltsimpempty => 269.77/39.99 (setbeta => 269.77/39.99 (nonemptyE1 => 269.77/39.99 (nonemptyI => 269.77/39.99 (nonemptyI1 => 269.77/39.99 (setadjoinIL => 269.77/39.99 (emptyinunitempty => 269.77/39.99 (setadjoinIR => 269.77/39.99 (setadjoinE => 269.77/39.99 (setadjoinOr => 269.77/39.99 (setoftrueEq => 269.77/39.99 ((![X10,X12]: 269.77/39.99 ((![X14]: 269.77/39.99 (in(X14,X12) => in(X14,X10))) => 269.77/39.99 in(X12,powerset(X10)))) => 269.77/39.99 ((![X16]: in(emptyset,powerset(X16))) => 269.77/39.99 ((![X18]: in(emptyset,powerset(X18))) => 269.77/39.99 ((![X20,X22,X24]: 269.77/39.99 (in(X22,powerset(X20)) => 269.77/39.99 (in(X24,X22) => in(X24,X20)))) => 269.77/39.99 (setunionI => 269.77/39.99 (setunionE => 269.77/39.99 (subPowSU => 269.77/39.99 (exuE2 => 269.77/39.99 (nonemptyImpWitness => 269.77/39.99 (uniqinunit => 269.77/39.99 (notinsingleton => 269.77/39.99 (eqinunit => 269.77/39.99 (singletonsswitch => 269.77/39.99 (upairsetE => 269.77/39.99 (upairsetIL => 269.77/39.99 (upairsetIR => 269.77/39.99 (emptyE1 => 269.77/39.99 (vacuousDall => 269.77/39.99 (quantDeMorgan1 => 269.77/39.99 (quantDeMorgan2 => 269.77/39.99 (quantDeMorgan3 => 269.77/39.99 (quantDeMorgan4 => 269.77/39.99 (prop2setI => 269.77/39.99 (prop2set2propI => 269.77/39.99 (notdexE => 269.77/39.99 (notdallE => 269.77/39.99 (exuI1 => 269.77/39.99 (exuI3 => 269.77/39.99 (exuI2 => 269.77/39.99 (inCongP => 269.77/39.99 (in__Cong => 269.77/39.99 (exuE3u => 269.77/39.99 ( 269.77/39.99 exu__Cong => 269.77/39.99 ( 269.77/39.99 emptyset__Cong => 269.77/39.99 ( 269.77/39.99 setadjoin__Cong => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X26,X28]: 269.77/39.99 (( 269.77/39.99 X26 = X28) => 269.77/39.99 (powerset( 269.77/39.99 X26) = 269.77/39.99 powerset( 269.77/39.99 X28)))) => 269.77/39.99 ( 269.77/39.99 setunion__Cong => 269.77/39.99 ( 269.77/39.99 omega__Cong => 269.77/39.99 ( 269.77/39.99 exuEu => 269.77/39.99 ( 269.77/39.99 descr__Cong => 269.77/39.99 ( 269.77/39.99 dsetconstr__Cong => 269.77/39.99 ( 269.77/39.99 subsetI1 => 269.77/39.99 ( 269.77/39.99 eqimpsubset2 => 269.77/39.99 ( 269.77/39.99 eqimpsubset1 => 269.77/39.99 ( 269.77/39.99 subsetI2 => 269.77/39.99 ( 269.77/39.99 emptysetsubset => 269.77/39.99 ( 269.77/39.99 subsetE => 269.77/39.99 ( 269.77/39.99 subsetE2 => 269.77/39.99 ( 269.77/39.99 notsubsetI => 269.77/39.99 ( 269.77/39.99 notequalI1 => 269.77/39.99 ( 269.77/39.99 notequalI2 => 269.77/39.99 ( 269.77/39.99 subsetRefl => 269.77/39.99 ( 269.77/39.99 subsetTrans => 269.77/39.99 ( 269.77/39.99 setadjoinSub => 269.77/39.99 ( 269.77/39.99 setadjoinSub2 => 269.77/39.99 ( 269.77/39.99 subset2powerset => 269.77/39.99 ( 269.77/39.99 setextsub => 269.77/39.99 ( 269.77/39.99 subsetemptysetimpeq => 269.77/39.99 ( 269.77/39.99 powersetI1 => 269.77/39.99 ( 269.77/39.99 powersetE1 => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X30]: 269.77/39.99 in( 269.77/39.99 X30, 269.77/39.99 powerset( 269.77/39.99 X30))) => 269.77/39.99 ( 269.77/39.99 powersetsubset => 269.77/39.99 ( 269.77/39.99 sepInPowerset => 269.77/39.99 ( 269.77/39.99 sepSubset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X32, 269.77/39.99 X34,X36]: 269.77/39.99 (in( 269.77/39.99 X36,X32) => 269.77/39.99 in( 269.77/39.99 X36, 269.77/39.99 binunion( 269.77/39.99 X32,X34)))) => 269.77/39.99 ( 269.77/39.99 upairset2IR => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X38, 269.77/39.99 X40,X42]: 269.77/39.99 (in( 269.77/39.99 X42,X40) => 269.77/39.99 in( 269.77/39.99 X42, 269.77/39.99 binunion( 269.77/39.99 X38,X40)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X44, 269.77/39.99 X46,X48, 269.77/39.99 X50:$o]: 269.77/39.99 (in( 269.77/39.99 X48, 269.77/39.99 binunion( 269.77/39.99 X44,X46)) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X44) => 269.77/39.99 X50) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X46) => 269.77/39.99 X50) => 269.77/39.99 X50)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X52, 269.77/39.99 X54,X56]: 269.77/39.99 (in( 269.77/39.99 X56, 269.77/39.99 binunion( 269.77/39.99 X52,X54)) => 269.77/39.99 (in( 269.77/39.99 X56,X52) | 269.77/39.99 in( 269.77/39.99 X56,X54)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X58,X60]: 269.77/39.99 subset( 269.77/39.99 X58, 269.77/39.99 binunion( 269.77/39.99 X58,X60))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X62,X64]: 269.77/39.99 subset( 269.77/39.99 X64, 269.77/39.99 binunion( 269.77/39.99 X62,X64))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X66, 269.77/39.99 X68,X70]: 269.77/39.99 (in( 269.77/39.99 X70,X66) => 269.77/39.99 (in( 269.77/39.99 X70,X68) => 269.77/39.99 in( 269.77/39.99 X70, 269.77/39.99 binintersect( 269.77/39.99 X66,X68))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X72, 269.77/39.99 X74,X76]: 269.77/39.99 (subset( 269.77/39.99 X76,X72) => 269.77/39.99 (subset( 269.77/39.99 X76,X74) => 269.77/39.99 subset( 269.77/39.99 X76, 269.77/39.99 binintersect( 269.77/39.99 X72,X74))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X78, 269.77/39.99 X80,X82]: 269.77/39.99 (in( 269.77/39.99 X82, 269.77/39.99 binintersect( 269.77/39.99 X78,X80)) => 269.77/39.99 in( 269.77/39.99 X82,X78))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X84,X86]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X84,X86), 269.77/39.99 X84)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X88,X90]: 269.77/39.99 (subset( 269.77/39.99 X88,X90) => 269.77/39.99 (binintersect( 269.77/39.99 X88,X90) = 269.77/39.99 X88))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X92,X94]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X92,X94) = 269.77/39.99 X94) => 269.77/39.99 subset( 269.77/39.99 X94,X92))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X96, 269.77/39.99 X98,X100]: 269.77/39.99 (in( 269.77/39.99 X100, 269.77/39.99 binintersect( 269.77/39.99 X96,X98)) => 269.77/39.99 in( 269.77/39.99 X100,X98))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X102, 269.77/39.99 X104]: 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 ( 269.77/39.99 ?[X106]: 269.77/39.99 (in( 269.77/39.99 X106,X104) & 269.77/39.99 in( 269.77/39.99 X106,X102)))) => 269.77/39.99 (binintersect( 269.77/39.99 X102,X104) = 269.77/39.99 emptyset))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X108, 269.77/39.99 X110]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X108,X110), 269.77/39.99 X110)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X112, 269.77/39.99 X114]: 269.77/39.99 (subset( 269.77/39.99 X114,X112) => 269.77/39.99 (binintersect( 269.77/39.99 X112,X114) = 269.77/39.99 X114))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X116, 269.77/39.99 X118]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X116,X118) = 269.77/39.99 X116) => 269.77/39.99 subset( 269.77/39.99 X116,X118))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X120, 269.77/39.99 X122,X124]: 269.77/39.99 (binintersect( 269.77/39.99 X120, 269.77/39.99 binunion( 269.77/39.99 X122,X124)) = 269.77/39.99 binunion( 269.77/39.99 binintersect( 269.77/39.99 X120,X122), 269.77/39.99 binintersect( 269.77/39.99 X120,X124)))) => 269.77/39.99 ( 269.77/39.99 setminusI => 269.77/39.99 ( 269.77/39.99 setminusEL => 269.77/39.99 ( 269.77/39.99 setminusER => 269.77/39.99 ( 269.77/39.99 setminusSubset2 => 269.77/39.99 ( 269.77/39.99 setminusERneg => 269.77/39.99 ( 269.77/39.99 setminusELneg => 269.77/39.99 ( 269.77/39.99 setminusILneg => 269.77/39.99 ( 269.77/39.99 setminusIRneg => 269.77/39.99 ( 269.77/39.99 setminusLsub => 269.77/39.99 ( 269.77/39.99 setminusSubset1 => 269.77/39.99 ( 269.77/39.99 symdiffE => 269.77/39.99 ( 269.77/39.99 symdiffI1 => 269.77/39.99 ( 269.77/39.99 symdiffI2 => 269.77/39.99 ( 269.77/39.99 symdiffIneg1 => 269.77/39.99 ( 269.77/39.99 symdiffIneg2 => 269.77/39.99 ( 269.77/39.99 secondinupair => 269.77/39.99 ( 269.77/39.99 setukpairIL => 269.77/39.99 ( 269.77/39.99 setukpairIR => 269.77/39.99 ( 269.77/39.99 kpairiskpair => 269.77/39.99 ( 269.77/39.99 kpairp => 269.77/39.99 ( 269.77/39.99 singletonsubset => 269.77/39.99 ( 269.77/39.99 singletoninpowerset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X126, 269.77/39.99 X128,X130]: 269.77/39.99 (in( 269.77/39.99 X130,X126) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X130, 269.77/39.99 emptyset), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X126,X128))))) => 269.77/39.99 ( 269.77/39.99 upairset2E => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X132, 269.77/39.99 X134,X136]: 269.77/39.99 (in( 269.77/39.99 X136,X132) => 269.77/39.99 (![X138]: 269.77/39.99 (in( 269.77/39.99 X138,X134) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 X136, 269.77/39.99 setadjoin( 269.77/39.99 X138, 269.77/39.99 emptyset)), 269.77/39.99 binunion( 269.77/39.99 X132,X134)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X140, 269.77/39.99 X142,X144]: 269.77/39.99 (in( 269.77/39.99 X144,X140) => 269.77/39.99 (![X146]: 269.77/39.99 (in( 269.77/39.99 X146,X142) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X144, 269.77/39.99 setadjoin( 269.77/39.99 X146, 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X140,X142))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X148, 269.77/39.99 X150,X152]: 269.77/39.99 (in( 269.77/39.99 X152,X148) => 269.77/39.99 (![X154]: 269.77/39.99 (in( 269.77/39.99 X154,X150) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 setadjoin( 269.77/39.99 X154, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X148,X150))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X156, 269.77/39.99 X158,X160]: 269.77/39.99 (in( 269.77/39.99 X160,X156) => 269.77/39.99 (![X162]: 269.77/39.99 (in( 269.77/39.99 X162,X158) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 setadjoin( 269.77/39.99 X162, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X156,X158)))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X164, 269.77/39.99 X166,X168]: 269.77/39.99 (in( 269.77/39.99 X168,X164) => 269.77/39.99 (![X170]: 269.77/39.99 (in( 269.77/39.99 X170,X166) => 269.77/39.99 in( 269.77/39.99 kpair( 269.77/39.99 X168,X170), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X164,X166)))))))) => 269.77/39.99 ( 269.77/39.99 cartprodpairin => 269.77/39.99 ( 269.77/39.99 cartprodmempair1 => 269.77/39.99 ( 269.77/39.99 cartprodmempair => 269.77/39.99 ( 269.77/39.99 setunionE2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton1 => 269.77/39.99 ( 269.77/39.99 setunionsingleton2 => 269.77/39.99 ( 269.77/39.99 setunionsingleton => 269.77/39.99 ( 269.77/39.99 singletonprop => 269.77/39.99 ( 269.77/39.99 ex1E1 => 269.77/39.99 ( 269.77/39.99 ex1I => 269.77/39.99 ( 269.77/39.99 ex1I2 => 269.77/39.99 ( 269.77/39.99 singletonsuniq => 269.77/39.99 ( 269.77/39.99 setukpairinjL1 => 269.77/39.99 ( 269.77/39.99 kfstsingleton => 269.77/39.99 ( 269.77/39.99 theprop => 269.77/39.99 ( 269.77/39.99 kfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodfstin => 269.77/39.99 ( 269.77/39.99 setukpairinjL2 => 269.77/39.99 ( 269.77/39.99 setukpairinjL => 269.77/39.99 ( 269.77/39.99 setukpairinjR11 => 269.77/39.99 ( 269.77/39.99 setukpairinjR12 => 269.77/39.99 ( 269.77/39.99 setukpairinjR1 => 269.77/39.99 ( 269.77/39.99 upairequniteq => 269.77/39.99 ( 269.77/39.99 setukpairinjR2 => 269.77/39.99 ( 269.77/39.99 setukpairinjR => 269.77/39.99 ( 269.77/39.99 ksndsingleton => 269.77/39.99 ( 269.77/39.99 ksndpairEq => 269.77/39.99 ( 269.77/39.99 kpairsurjEq => 269.77/39.99 ( 269.77/39.99 cartprodsndin => 269.77/39.99 ( 269.77/39.99 cartprodpairmemEL => 269.77/39.99 ( 269.77/39.99 cartprodpairmemER => 269.77/39.99 ( 269.77/39.99 cartprodmempaircEq => 269.77/39.99 ( 269.77/39.99 cartprodfstpairEq => 269.77/39.99 ( 269.77/39.99 cartprodsndpairEq => 269.77/39.99 ( 269.77/39.99 cartprodpairsurjEq => 269.77/39.99 ( 269.77/39.99 dpsetconstrI => 269.77/39.99 ( 269.77/39.99 dpsetconstrSub => 269.77/39.99 ( 269.77/39.99 setOfPairsIsBReln => 269.77/39.99 ( 269.77/39.99 dpsetconstrERa => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL1 => 269.77/39.99 ( 269.77/39.99 dpsetconstrEL2 => 269.77/39.99 ( 269.77/39.99 dpsetconstrER => 269.77/39.99 ( 269.77/39.99 funcImageSingleton => 269.77/39.99 ( 269.77/39.99 apProp => 269.77/39.99 ( 269.77/39.99 app => 269.77/39.99 ( 269.77/39.99 infuncsetfunc => 269.77/39.99 ( 269.77/39.99 ap2p => 269.77/39.99 ( 269.77/39.99 funcinfuncset => 269.77/39.99 ( 269.77/39.99 lamProp => 269.77/39.99 ( 269.77/39.99 lamp => 269.77/39.99 ( 269.77/39.99 lam2p => 269.77/39.99 ( 269.77/39.99 brelnall1 => 269.77/39.99 ( 269.77/39.99 brelnall2 => 269.77/39.99 ( 269.77/39.99 ex1E2 => 269.77/39.99 ( 269.77/39.99 funcGraphProp1 => 269.77/39.99 ( 269.77/39.99 funcGraphProp3 => 269.77/39.99 ( 269.77/39.99 funcGraphProp2 => 269.77/39.99 ( 269.77/39.99 funcextLem => 269.77/39.99 ( 269.77/39.99 funcGraphProp4 => 269.77/39.99 ( 269.77/39.99 subbreln => 269.77/39.99 ( 269.77/39.99 eqbreln => 269.77/39.99 ( 269.77/39.99 funcext => 269.77/39.99 ( 269.77/39.99 funcext2 => 269.77/39.99 ( 269.77/39.99 ap2apEq1 => 269.77/39.99 ( 269.77/39.99 ap2apEq2 => 269.77/39.99 ( 269.77/39.99 beta1 => 269.77/39.99 ( 269.77/39.99 eta1 => 269.77/39.99 ( 269.77/39.99 lam2lamEq => 269.77/39.99 ( 269.77/39.99 beta2 => 269.77/39.99 ( 269.77/39.99 eta2 => 269.77/39.99 ( 269.77/39.99 iffalseProp1 => 269.77/39.99 ( 269.77/39.99 iffalseProp2 => 269.77/39.99 ( 269.77/39.99 iftrueProp1 => 269.77/39.99 ( 269.77/39.99 iftrueProp2 => 269.77/39.99 ( 269.77/39.99 ifSingleton => 269.77/39.99 ( 269.77/39.99 ifp => 269.77/39.99 ( 269.77/39.99 theeq => 269.77/39.99 ( 269.77/39.99 iftrue => 269.77/39.99 ( 269.77/39.99 iffalse => 269.77/39.99 ( 269.77/39.99 iftrueorfalse => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X172, 269.77/39.99 X174]: 269.77/39.99 (in( 269.77/39.99 X174, 269.77/39.99 powerset( 269.77/39.99 X172)) => 269.77/39.99 (![X176]: 269.77/39.99 (in( 269.77/39.99 X176, 269.77/39.99 powerset( 269.77/39.99 X172)) => 269.77/39.99 in( 269.77/39.99 binintersect( 269.77/39.99 X174,X176), 269.77/39.99 powerset( 269.77/39.99 X172)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X178, 269.77/39.99 X180]: 269.77/39.99 (in( 269.77/39.99 X180, 269.77/39.99 powerset( 269.77/39.99 X178)) => 269.77/39.99 (![X182]: 269.77/39.99 (in( 269.77/39.99 X182, 269.77/39.99 powerset( 269.77/39.99 X178)) => 269.77/39.99 in( 269.77/39.99 binunion( 269.77/39.99 X180,X182), 269.77/39.99 powerset( 269.77/39.99 X178)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X184, 269.77/39.99 X186]: 269.77/39.99 (in( 269.77/39.99 X186, 269.77/39.99 powerset( 269.77/39.99 X184)) => 269.77/39.99 in( 269.77/39.99 powerset( 269.77/39.99 X186), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 X184))))) => 269.77/39.99 ( 269.77/39.99 setminusT_lem => 269.77/39.99 ( 269.77/39.99 complementT_lem => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X188, 269.77/39.99 X190]: 269.77/39.99 (in( 269.77/39.99 X190, 269.77/39.99 powerset( 269.77/39.99 X188)) => 269.77/39.99 (![X192]: 269.77/39.99 (in( 269.77/39.99 X192, 269.77/39.99 powerset( 269.77/39.99 X188)) => 269.77/39.99 (( 269.77/39.99 ![X194]: 269.77/39.99 (in( 269.77/39.99 X194,X188) => 269.77/39.99 (in( 269.77/39.99 X194,X190) => 269.77/39.99 in( 269.77/39.99 X194,X192)))) => 269.77/39.99 (( 269.77/39.99 ![X196]: 269.77/39.99 (in( 269.77/39.99 X196,X188) => 269.77/39.99 (in( 269.77/39.99 X196,X192) => 269.77/39.99 in( 269.77/39.99 X196,X190)))) => 269.77/39.99 (X190 = 269.77/39.99 X192))))))) => 269.77/39.99 ( 269.77/39.99 subsetTI => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X198, 269.77/39.99 X200]: 269.77/39.99 (in( 269.77/39.99 X200, 269.77/39.99 powerset( 269.77/39.99 X198)) => 269.77/39.99 (![X202]: 269.77/39.99 (in( 269.77/39.99 X202, 269.77/39.99 powerset( 269.77/39.99 X198)) => 269.77/39.99 (( 269.77/39.99 ![X204]: 269.77/39.99 (in( 269.77/39.99 X204,X198) => 269.77/39.99 (in( 269.77/39.99 X204,X200) => 269.77/39.99 in( 269.77/39.99 X204,X202)))) => 269.77/39.99 in( 269.77/39.99 X200, 269.77/39.99 powerset( 269.77/39.99 X202))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X206, 269.77/39.99 X208]: 269.77/39.99 (in( 269.77/39.99 X208, 269.77/39.99 powerset( 269.77/39.99 X206)) => 269.77/39.99 (![X210]: 269.77/39.99 (in( 269.77/39.99 X210, 269.77/39.99 powerset( 269.77/39.99 X206)) => 269.77/39.99 (![X212]: 269.77/39.99 (in( 269.77/39.99 X212,X206) => 269.77/39.99 (in( 269.77/39.99 X208, 269.77/39.99 powerset( 269.77/39.99 X210)) => 269.77/39.99 (in( 269.77/39.99 X212,X208) => 269.77/39.99 in( 269.77/39.99 X212,X210))))))))) => 269.77/39.99 ( 269.77/39.99 complementTI1 => 269.77/39.99 ( 269.77/39.99 complementTE1 => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X214, 269.77/39.99 X216]: 269.77/39.99 (in( 269.77/39.99 X216, 269.77/39.99 powerset( 269.77/39.99 X214)) => 269.77/39.99 (![X218]: 269.77/39.99 (in( 269.77/39.99 X218, 269.77/39.99 powerset( 269.77/39.99 X214)) => 269.77/39.99 (![X220]: 269.77/39.99 (in( 269.77/39.99 X220,X214) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X220,X216)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X220, 269.77/39.99 binintersect( 269.77/39.99 X216,X218)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X222, 269.77/39.99 X224]: 269.77/39.99 (in( 269.77/39.99 X224, 269.77/39.99 powerset( 269.77/39.99 X222)) => 269.77/39.99 (![X226]: 269.77/39.99 (in( 269.77/39.99 X226, 269.77/39.99 powerset( 269.77/39.99 X222)) => 269.77/39.99 (![X228]: 269.77/39.99 (in( 269.77/39.99 X228,X222) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X228,X226)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X228, 269.77/39.99 binintersect( 269.77/39.99 X224,X226)))))))))) => 269.77/39.99 ( 269.77/39.99 contrasubsetT => 269.77/39.99 ( 269.77/39.99 contrasubsetT1 => 269.77/39.99 ( 269.77/39.99 contrasubsetT2 => 269.77/39.99 ( 269.77/39.99 contrasubsetT3 => 269.77/39.99 ( 269.77/39.99 doubleComplementI1 => 269.77/39.99 ( 269.77/39.99 doubleComplementE1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub1 => 269.77/39.99 ( 269.77/39.99 doubleComplementSub2 => 269.77/39.99 ( 269.77/39.99 doubleComplementEq => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X230, 269.77/39.99 X232]: 269.77/39.99 (in( 269.77/39.99 X232, 269.77/39.99 powerset( 269.77/39.99 X230)) => 269.77/39.99 (![X234]: 269.77/39.99 (in( 269.77/39.99 X234, 269.77/39.99 powerset( 269.77/39.99 X230)) => 269.77/39.99 (![X236]: 269.77/39.99 (in( 269.77/39.99 X236,X230) => 269.77/39.99 (in( 269.77/39.99 X236, 269.77/39.99 setminus( 269.77/39.99 X230,X232)) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X236, 269.77/39.99 binintersect( 269.77/39.99 X232,X234)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X238, 269.77/39.99 X240]: 269.77/39.99 (in( 269.77/39.99 X240, 269.77/39.99 powerset( 269.77/39.99 X238)) => 269.77/39.99 (![X242]: 269.77/39.99 (in( 269.77/39.99 X242, 269.77/39.99 powerset( 269.77/39.99 X238)) => 269.77/39.99 (![X244]: 269.77/39.99 (in( 269.77/39.99 X244,X238) => 269.77/39.99 (in( 269.77/39.99 X244, 269.77/39.99 setminus( 269.77/39.99 X238,X240)) => 269.77/39.99 in( 269.77/39.99 X244, 269.77/39.99 setminus( 269.77/39.99 X238, 269.77/39.99 binintersect( 269.77/39.99 X240,X242)))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X246, 269.77/39.99 X248]: 269.77/39.99 (in( 269.77/39.99 X248, 269.77/39.99 powerset( 269.77/39.99 X246)) => 269.77/39.99 (![X250]: 269.77/39.99 (in( 269.77/39.99 X250, 269.77/39.99 powerset( 269.77/39.99 X246)) => 269.77/39.99 subset( 269.77/39.99 setminus( 269.77/39.99 X246,X248), 269.77/39.99 setminus( 269.77/39.99 X246, 269.77/39.99 binintersect( 269.77/39.99 X248,X250))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X252, 269.77/39.99 X254]: 269.77/39.99 (in( 269.77/39.99 X254, 269.77/39.99 powerset( 269.77/39.99 X252)) => 269.77/39.99 (![X256]: 269.77/39.99 (in( 269.77/39.99 X256, 269.77/39.99 powerset( 269.77/39.99 X252)) => 269.77/39.99 in( 269.77/39.99 setminus( 269.77/39.99 X252,X254), 269.77/39.99 powerset( 269.77/39.99 setminus( 269.77/39.99 X252, 269.77/39.99 binintersect( 269.77/39.99 X254,X256)))))))) => 269.77/39.99 ( 269.77/39.99 contraSubsetComplement => 269.77/39.99 ( 269.77/39.99 complementTcontraSubset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X258, 269.77/39.99 X260]: 269.77/39.99 (in( 269.77/39.99 X260, 269.77/39.99 powerset( 269.77/39.99 X258)) => 269.77/39.99 (![X262]: 269.77/39.99 (in( 269.77/39.99 X262, 269.77/39.99 powerset( 269.77/39.99 X258)) => 269.77/39.99 (![X264]: 269.77/39.99 (in( 269.77/39.99 X264,X258) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X264, 269.77/39.99 binunion( 269.77/39.99 X260,X262))) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X264,X260))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X266, 269.77/39.99 X268]: 269.77/39.99 (in( 269.77/39.99 X268, 269.77/39.99 powerset( 269.77/39.99 X266)) => 269.77/39.99 (![X270]: 269.77/39.99 (in( 269.77/39.99 X270, 269.77/39.99 powerset( 269.77/39.99 X266)) => 269.77/39.99 (![X272]: 269.77/39.99 (in( 269.77/39.99 X272,X266) => 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 in( 269.77/39.99 X272, 269.77/39.99 binunion( 269.77/39.99 X268,X270))) => 269.77/39.99 (~ 269.77/39.99 in( 269.77/39.99 X272,X270))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X274, 269.77/39.99 X276]: 269.77/39.99 (in( 269.77/39.99 X276, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X278]: 269.77/39.99 (in( 269.77/39.99 X278, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X280]: 269.77/39.99 (in( 269.77/39.99 X280, 269.77/39.99 powerset( 269.77/39.99 X274)) => 269.77/39.99 (![X282]: 269.77/39.99 (in( 269.77/39.99 X282,X274) => 269.77/39.99 (in( 269.77/39.99 X282, 269.77/39.99 binintersect( 269.77/39.99 X276,X278)) => 269.77/39.99 in( 269.77/39.99 X282, 269.77/39.99 binunion( 269.77/39.99 X276,X280))))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X284, 269.77/39.99 X286]: 269.77/39.99 (in( 269.77/39.99 X286, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X288]: 269.77/39.99 (in( 269.77/39.99 X288, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X290]: 269.77/39.99 (in( 269.77/39.99 X290, 269.77/39.99 powerset( 269.77/39.99 X284)) => 269.77/39.99 (![X292]: 269.77/39.99 (in( 269.77/39.99 X292,X284) => 269.77/39.99 (in( 269.77/39.99 X292, 269.77/39.99 binintersect( 269.77/39.99 X286,X288)) => 269.77/39.99 in( 269.77/39.99 X292, 269.77/39.99 binunion( 269.77/39.99 X288,X290))))))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X294, 269.77/39.99 X296]: 269.77/39.99 (in( 269.77/39.99 X296, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X298]: 269.77/39.99 (in( 269.77/39.99 X298, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X300]: 269.77/39.99 (in( 269.77/39.99 X300, 269.77/39.99 powerset( 269.77/39.99 X294)) => 269.77/39.99 (![X302]: 269.77/39.99 (in( 269.77/39.99 X302,X294) => 269.77/39.99 (in( 269.77/39.99 X302, 269.77/39.99 binintersect( 269.77/39.99 X296,X298)) => 269.77/39.99 in( 269.77/39.99 X302, 269.77/39.99 binintersect( 269.77/39.99 binunion( 269.77/39.99 X296,X300), 269.77/39.99 binunion( 269.77/39.99 X298,X300)))))))))))) => 269.77/39.99 ( 269.77/39.99 ![X304, 269.77/39.99 X306]: 269.77/39.99 (in( 269.77/39.99 X306, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 (![X308]: 269.77/39.99 (in( 269.77/39.99 X308, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 (![X310]: 269.77/39.99 (in( 269.77/39.99 X310, 269.77/39.99 powerset( 269.77/39.99 X304)) => 269.77/39.99 in( 269.77/39.99 binintersect( 269.77/39.99 X306,X308), 269.77/39.99 powerset( 269.77/39.99 binintersect( 269.77/39.99 binunion( 269.77/39.99 X306,X310), 269.77/39.99 binunion( 269.77/39.99 X308,X310)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 269.77/39.99 tff(zf_stmt_4, negated_conjecture, 269.77/39.99 (~ 269.77/39.99 (setextAx => 269.77/39.99 (emptysetAx => 269.77/39.99 (setadjoinAx => 269.77/39.99 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 269.77/39.99 (setunionAx => 269.77/39.99 (omega0Ax => 269.77/39.99 (omegaSAx => 269.77/39.99 (omegaIndAx => 269.77/39.99 (replAx => 269.77/39.99 (foundationAx => 269.77/39.99 (wellorderingAx => 269.77/39.99 (descrp => 269.77/39.99 (dsetconstrI => 269.77/39.99 (dsetconstrEL => 269.77/39.99 (dsetconstrER => 269.77/39.99 (exuE1 => 269.77/39.99 (prop2setE => 269.77/39.99 (emptysetE => 269.77/39.99 (emptysetimpfalse => 269.77/39.99 (notinemptyset => 269.77/39.99 (exuE3e => 269.77/39.99 (setext => 269.77/39.99 (emptyI => 269.77/39.99 (noeltsimpempty => 269.77/39.99 (setbeta => 269.77/39.99 (nonemptyE1 => 269.77/39.99 (nonemptyI => 269.77/39.99 (nonemptyI1 => 269.77/39.99 (setadjoinIL => 269.77/39.99 (emptyinunitempty => 269.77/39.99 (setadjoinIR => 269.77/39.99 (setadjoinE => 269.77/39.99 (setadjoinOr => 269.77/39.99 (setoftrueEq => 269.77/39.99 ((![X10,X12]: 269.77/39.99 ((![X14]: 269.77/39.99 (in(X14,X12) => in(X14,X10))) => 269.77/39.99 in(X12,powerset(X10)))) => 269.77/39.99 ((![X16]: in(emptyset,powerset(X16))) => 269.77/39.99 ((![X18]: in(emptyset,powerset(X18))) => 269.77/39.99 ((![X20,X22,X24]: 269.77/39.99 (in(X22,powerset(X20)) => 269.77/39.99 (in(X24,X22) => in(X24,X20)))) => 269.77/39.99 (setunionI => 269.77/39.99 (setunionE => 269.77/39.99 (subPowSU => 269.77/39.99 (exuE2 => 269.77/39.99 (nonemptyImpWitness => 269.77/39.99 (uniqinunit => 269.77/39.99 (notinsingleton => 269.77/39.99 (eqinunit => 269.77/39.99 (singletonsswitch => 269.77/39.99 (upairsetE => 269.77/39.99 (upairsetIL => 269.77/39.99 (upairsetIR => 269.77/39.99 (emptyE1 => 269.77/39.99 (vacuousDall => 269.77/39.99 (quantDeMorgan1 => 269.77/39.99 (quantDeMorgan2 => 269.77/39.99 (quantDeMorgan3 => 269.77/39.99 (quantDeMorgan4 => 269.77/39.99 (prop2setI => 269.77/39.99 (prop2set2propI => 269.77/39.99 (notdexE => 269.77/39.99 (notdallE => 269.77/39.99 (exuI1 => 269.77/39.99 (exuI3 => 269.77/39.99 (exuI2 => 269.77/39.99 (inCongP => 269.77/39.99 ( 269.77/39.99 in__Cong => 269.77/39.99 ( 269.77/39.99 exuE3u => 269.77/39.99 ( 269.77/39.99 exu__Cong => 269.77/39.99 ( 269.77/39.99 emptyset__Cong => 269.77/39.99 ( 269.77/39.99 setadjoin__Cong => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X26,X28]: 269.77/39.99 (( 269.77/39.99 X26 = X28) => 269.77/39.99 (powerset( 269.77/39.99 X26) = 269.77/39.99 powerset( 269.77/39.99 X28)))) => 269.77/39.99 ( 269.77/39.99 setunion__Cong => 269.77/39.99 ( 269.77/39.99 omega__Cong => 269.77/39.99 ( 269.77/39.99 exuEu => 269.77/39.99 ( 269.77/39.99 descr__Cong => 269.77/39.99 ( 269.77/39.99 dsetconstr__Cong => 269.77/39.99 ( 269.77/39.99 subsetI1 => 269.77/39.99 ( 269.77/39.99 eqimpsubset2 => 269.77/39.99 ( 269.77/39.99 eqimpsubset1 => 269.77/39.99 ( 269.77/39.99 subsetI2 => 269.77/39.99 ( 269.77/39.99 emptysetsubset => 269.77/39.99 ( 269.77/39.99 subsetE => 269.77/39.99 ( 269.77/39.99 subsetE2 => 269.77/39.99 ( 269.77/39.99 notsubsetI => 269.77/39.99 ( 269.77/39.99 notequalI1 => 269.77/39.99 ( 269.77/39.99 notequalI2 => 269.77/39.99 ( 269.77/39.99 subsetRefl => 269.77/39.99 ( 269.77/39.99 subsetTrans => 269.77/39.99 ( 269.77/39.99 setadjoinSub => 269.77/39.99 ( 269.77/39.99 setadjoinSub2 => 269.77/39.99 ( 269.77/39.99 subset2powerset => 269.77/39.99 ( 269.77/39.99 setextsub => 269.77/39.99 ( 269.77/39.99 subsetemptysetimpeq => 269.77/39.99 ( 269.77/39.99 powersetI1 => 269.77/39.99 ( 269.77/39.99 powersetE1 => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X30]: 269.77/39.99 in( 269.77/39.99 X30, 269.77/39.99 powerset( 269.77/39.99 X30))) => 269.77/39.99 ( 269.77/39.99 powersetsubset => 269.77/39.99 ( 269.77/39.99 sepInPowerset => 269.77/39.99 ( 269.77/39.99 sepSubset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X32, 269.77/39.99 X34,X36]: 269.77/39.99 (in( 269.77/39.99 X36,X32) => 269.77/39.99 in( 269.77/39.99 X36, 269.77/39.99 binunion( 269.77/39.99 X32,X34)))) => 269.77/39.99 ( 269.77/39.99 upairset2IR => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X38, 269.77/39.99 X40,X42]: 269.77/39.99 (in( 269.77/39.99 X42,X40) => 269.77/39.99 in( 269.77/39.99 X42, 269.77/39.99 binunion( 269.77/39.99 X38,X40)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X44, 269.77/39.99 X46,X48, 269.77/39.99 X50:$o]: 269.77/39.99 (in( 269.77/39.99 X48, 269.77/39.99 binunion( 269.77/39.99 X44,X46)) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X44) => 269.77/39.99 X50) => 269.77/39.99 (( 269.77/39.99 in( 269.77/39.99 X48,X46) => 269.77/39.99 X50) => 269.77/39.99 X50)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X52, 269.77/39.99 X54,X56]: 269.77/39.99 (in( 269.77/39.99 X56, 269.77/39.99 binunion( 269.77/39.99 X52,X54)) => 269.77/39.99 (in( 269.77/39.99 X56,X52) | 269.77/39.99 in( 269.77/39.99 X56,X54)))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X58,X60]: 269.77/39.99 subset( 269.77/39.99 X58, 269.77/39.99 binunion( 269.77/39.99 X58,X60))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X62,X64]: 269.77/39.99 subset( 269.77/39.99 X64, 269.77/39.99 binunion( 269.77/39.99 X62,X64))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X66, 269.77/39.99 X68,X70]: 269.77/39.99 (in( 269.77/39.99 X70,X66) => 269.77/39.99 (in( 269.77/39.99 X70,X68) => 269.77/39.99 in( 269.77/39.99 X70, 269.77/39.99 binintersect( 269.77/39.99 X66,X68))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X72, 269.77/39.99 X74,X76]: 269.77/39.99 (subset( 269.77/39.99 X76,X72) => 269.77/39.99 (subset( 269.77/39.99 X76,X74) => 269.77/39.99 subset( 269.77/39.99 X76, 269.77/39.99 binintersect( 269.77/39.99 X72,X74))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X78, 269.77/39.99 X80,X82]: 269.77/39.99 (in( 269.77/39.99 X82, 269.77/39.99 binintersect( 269.77/39.99 X78,X80)) => 269.77/39.99 in( 269.77/39.99 X82,X78))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X84,X86]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X84,X86), 269.77/39.99 X84)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X88,X90]: 269.77/39.99 (subset( 269.77/39.99 X88,X90) => 269.77/39.99 (binintersect( 269.77/39.99 X88,X90) = 269.77/39.99 X88))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X92,X94]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X92,X94) = 269.77/39.99 X94) => 269.77/39.99 subset( 269.77/39.99 X94,X92))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X96, 269.77/39.99 X98,X100]: 269.77/39.99 (in( 269.77/39.99 X100, 269.77/39.99 binintersect( 269.77/39.99 X96,X98)) => 269.77/39.99 in( 269.77/39.99 X100,X98))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X102, 269.77/39.99 X104]: 269.77/39.99 (( 269.77/39.99 ~ 269.77/39.99 ( 269.77/39.99 ?[X106]: 269.77/39.99 (in( 269.77/39.99 X106,X104) & 269.77/39.99 in( 269.77/39.99 X106,X102)))) => 269.77/39.99 (binintersect( 269.77/39.99 X102,X104) = 269.77/39.99 emptyset))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X108, 269.77/39.99 X110]: 269.77/39.99 subset( 269.77/39.99 binintersect( 269.77/39.99 X108,X110), 269.77/39.99 X110)) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X112, 269.77/39.99 X114]: 269.77/39.99 (subset( 269.77/39.99 X114,X112) => 269.77/39.99 (binintersect( 269.77/39.99 X112,X114) = 269.77/39.99 X114))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X116, 269.77/39.99 X118]: 269.77/39.99 (( 269.77/39.99 binintersect( 269.77/39.99 X116,X118) = 269.77/39.99 X116) => 269.77/39.99 subset( 269.77/39.99 X116,X118))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X120, 269.77/39.99 X122,X124]: 269.77/39.99 (binintersect( 269.77/39.99 X120, 269.77/39.99 binunion( 269.77/39.99 X122,X124)) = 269.77/39.99 binunion( 269.77/39.99 binintersect( 269.77/39.99 X120,X122), 269.77/39.99 binintersect( 269.77/39.99 X120,X124)))) => 269.77/39.99 ( 269.77/39.99 setminusI => 269.77/39.99 ( 269.77/39.99 setminusEL => 269.77/39.99 ( 269.77/39.99 setminusER => 269.77/39.99 ( 269.77/39.99 setminusSubset2 => 269.77/39.99 ( 269.77/39.99 setminusERneg => 269.77/39.99 ( 269.77/39.99 setminusELneg => 269.77/39.99 ( 269.77/39.99 setminusILneg => 269.77/39.99 ( 269.77/39.99 setminusIRneg => 269.77/39.99 ( 269.77/39.99 setminusLsub => 269.77/39.99 ( 269.77/39.99 setminusSubset1 => 269.77/39.99 ( 269.77/39.99 symdiffE => 269.77/39.99 ( 269.77/39.99 symdiffI1 => 269.77/39.99 ( 269.77/39.99 symdiffI2 => 269.77/39.99 ( 269.77/39.99 symdiffIneg1 => 269.77/39.99 ( 269.77/39.99 symdiffIneg2 => 269.77/39.99 ( 269.77/39.99 secondinupair => 269.77/39.99 ( 269.77/39.99 setukpairIL => 269.77/39.99 ( 269.77/39.99 setukpairIR => 269.77/39.99 ( 269.77/39.99 kpairiskpair => 269.77/39.99 ( 269.77/39.99 kpairp => 269.77/39.99 ( 269.77/39.99 singletonsubset => 269.77/39.99 ( 269.77/39.99 singletoninpowerset => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X126, 269.77/39.99 X128,X130]: 269.77/39.99 (in( 269.77/39.99 X130,X126) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X130, 269.77/39.99 emptyset), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X126,X128))))) => 269.77/39.99 ( 269.77/39.99 upairset2E => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X132, 269.77/39.99 X134,X136]: 269.77/39.99 (in( 269.77/39.99 X136,X132) => 269.77/39.99 (![X138]: 269.77/39.99 (in( 269.77/39.99 X138,X134) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 X136, 269.77/39.99 setadjoin( 269.77/39.99 X138, 269.77/39.99 emptyset)), 269.77/39.99 binunion( 269.77/39.99 X132,X134)))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X140, 269.77/39.99 X142,X144]: 269.77/39.99 (in( 269.77/39.99 X144,X140) => 269.77/39.99 (![X146]: 269.77/39.99 (in( 269.77/39.99 X146,X142) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 X144, 269.77/39.99 setadjoin( 269.77/39.99 X146, 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X140,X142))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X148, 269.77/39.99 X150,X152]: 269.77/39.99 (in( 269.77/39.99 X152,X148) => 269.77/39.99 (![X154]: 269.77/39.99 (in( 269.77/39.99 X154,X150) => 269.77/39.99 subset( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X152, 269.77/39.99 setadjoin( 269.77/39.99 X154, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X148,X150))))))) => 269.77/39.99 ( 269.77/39.99 ( 269.77/39.99 ![X156, 269.77/39.99 X158,X160]: 269.77/39.99 (in( 269.77/39.99 X160,X156) => 269.77/39.99 (![X162]: 269.77/39.99 (in( 269.77/39.99 X162,X158) => 269.77/39.99 in( 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 emptyset), 269.77/39.99 setadjoin( 269.77/39.99 setadjoin( 269.77/39.99 X160, 269.77/39.99 setadjoin( 269.77/39.99 X162, 269.77/39.99 emptyset)), 269.77/39.99 emptyset)), 269.77/39.99 powerset( 269.77/39.99 powerset( 269.77/39.99 binunion( 269.77/39.99 X156,X158)))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X164, 269.77/40.00 X166,X168]: 269.77/40.00 (in( 269.77/40.00 X168,X164) => 269.77/40.00 (![X170]: 269.77/40.00 (in( 269.77/40.00 X170,X166) => 269.77/40.00 in( 269.77/40.00 kpair( 269.77/40.00 X168,X170), 269.77/40.00 powerset( 269.77/40.00 powerset( 269.77/40.00 binunion( 269.77/40.00 X164,X166)))))))) => 269.77/40.00 ( 269.77/40.00 cartprodpairin => 269.77/40.00 ( 269.77/40.00 cartprodmempair1 => 269.77/40.00 ( 269.77/40.00 cartprodmempair => 269.77/40.00 ( 269.77/40.00 setunionE2 => 269.77/40.00 ( 269.77/40.00 setunionsingleton1 => 269.77/40.00 ( 269.77/40.00 setunionsingleton2 => 269.77/40.00 ( 269.77/40.00 setunionsingleton => 269.77/40.00 ( 269.77/40.00 singletonprop => 269.77/40.00 ( 269.77/40.00 ex1E1 => 269.77/40.00 ( 269.77/40.00 ex1I => 269.77/40.00 ( 269.77/40.00 ex1I2 => 269.77/40.00 ( 269.77/40.00 singletonsuniq => 269.77/40.00 ( 269.77/40.00 setukpairinjL1 => 269.77/40.00 ( 269.77/40.00 kfstsingleton => 269.77/40.00 ( 269.77/40.00 theprop => 269.77/40.00 ( 269.77/40.00 kfstpairEq => 269.77/40.00 ( 269.77/40.00 cartprodfstin => 269.77/40.00 ( 269.77/40.00 setukpairinjL2 => 269.77/40.00 ( 269.77/40.00 setukpairinjL => 269.77/40.00 ( 269.77/40.00 setukpairinjR11 => 269.77/40.00 ( 269.77/40.00 setukpairinjR12 => 269.77/40.00 ( 269.77/40.00 setukpairinjR1 => 269.77/40.00 ( 269.77/40.00 upairequniteq => 269.77/40.00 ( 269.77/40.00 setukpairinjR2 => 269.77/40.00 ( 269.77/40.00 setukpairinjR => 269.77/40.00 ( 269.77/40.00 ksndsingleton => 269.77/40.00 ( 269.77/40.00 ksndpairEq => 269.77/40.00 ( 269.77/40.00 kpairsurjEq => 269.77/40.00 ( 269.77/40.00 cartprodsndin => 269.77/40.00 ( 269.77/40.00 cartprodpairmemEL => 269.77/40.00 ( 269.77/40.00 cartprodpairmemER => 269.77/40.00 ( 269.77/40.00 cartprodmempaircEq => 269.77/40.00 ( 269.77/40.00 cartprodfstpairEq => 269.77/40.00 ( 269.77/40.00 cartprodsndpairEq => 269.77/40.00 ( 269.77/40.00 cartprodpairsurjEq => 269.77/40.00 ( 269.77/40.00 dpsetconstrI => 269.77/40.00 ( 269.77/40.00 dpsetconstrSub => 269.77/40.00 ( 269.77/40.00 setOfPairsIsBReln => 269.77/40.00 ( 269.77/40.00 dpsetconstrERa => 269.77/40.00 ( 269.77/40.00 dpsetconstrEL1 => 269.77/40.00 ( 269.77/40.00 dpsetconstrEL2 => 269.77/40.00 ( 269.77/40.00 dpsetconstrER => 269.77/40.00 ( 269.77/40.00 funcImageSingleton => 269.77/40.00 ( 269.77/40.00 apProp => 269.77/40.00 ( 269.77/40.00 app => 269.77/40.00 ( 269.77/40.00 infuncsetfunc => 269.77/40.00 ( 269.77/40.00 ap2p => 269.77/40.00 ( 269.77/40.00 funcinfuncset => 269.77/40.00 ( 269.77/40.00 lamProp => 269.77/40.00 ( 269.77/40.00 lamp => 269.77/40.00 ( 269.77/40.00 lam2p => 269.77/40.00 ( 269.77/40.00 brelnall1 => 269.77/40.00 ( 269.77/40.00 brelnall2 => 269.77/40.00 ( 269.77/40.00 ex1E2 => 269.77/40.00 ( 269.77/40.00 funcGraphProp1 => 269.77/40.00 ( 269.77/40.00 funcGraphProp3 => 269.77/40.00 ( 269.77/40.00 funcGraphProp2 => 269.77/40.00 ( 269.77/40.00 funcextLem => 269.77/40.00 ( 269.77/40.00 funcGraphProp4 => 269.77/40.00 ( 269.77/40.00 subbreln => 269.77/40.00 ( 269.77/40.00 eqbreln => 269.77/40.00 ( 269.77/40.00 funcext => 269.77/40.00 ( 269.77/40.00 funcext2 => 269.77/40.00 ( 269.77/40.00 ap2apEq1 => 269.77/40.00 ( 269.77/40.00 ap2apEq2 => 269.77/40.00 ( 269.77/40.00 beta1 => 269.77/40.00 ( 269.77/40.00 eta1 => 269.77/40.00 ( 269.77/40.00 lam2lamEq => 269.77/40.00 ( 269.77/40.00 beta2 => 269.77/40.00 ( 269.77/40.00 eta2 => 269.77/40.00 ( 269.77/40.00 iffalseProp1 => 269.77/40.00 ( 269.77/40.00 iffalseProp2 => 269.77/40.00 ( 269.77/40.00 iftrueProp1 => 269.77/40.00 ( 269.77/40.00 iftrueProp2 => 269.77/40.00 ( 269.77/40.00 ifSingleton => 269.77/40.00 ( 269.77/40.00 ifp => 269.77/40.00 ( 269.77/40.00 theeq => 269.77/40.00 ( 269.77/40.00 iftrue => 269.77/40.00 ( 269.77/40.00 iffalse => 269.77/40.00 ( 269.77/40.00 iftrueorfalse => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X172, 269.77/40.00 X174]: 269.77/40.00 (in( 269.77/40.00 X174, 269.77/40.00 powerset( 269.77/40.00 X172)) => 269.77/40.00 (![X176]: 269.77/40.00 (in( 269.77/40.00 X176, 269.77/40.00 powerset( 269.77/40.00 X172)) => 269.77/40.00 in( 269.77/40.00 binintersect( 269.77/40.00 X174,X176), 269.77/40.00 powerset( 269.77/40.00 X172)))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X178, 269.77/40.00 X180]: 269.77/40.00 (in( 269.77/40.00 X180, 269.77/40.00 powerset( 269.77/40.00 X178)) => 269.77/40.00 (![X182]: 269.77/40.00 (in( 269.77/40.00 X182, 269.77/40.00 powerset( 269.77/40.00 X178)) => 269.77/40.00 in( 269.77/40.00 binunion( 269.77/40.00 X180,X182), 269.77/40.00 powerset( 269.77/40.00 X178)))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X184, 269.77/40.00 X186]: 269.77/40.00 (in( 269.77/40.00 X186, 269.77/40.00 powerset( 269.77/40.00 X184)) => 269.77/40.00 in( 269.77/40.00 powerset( 269.77/40.00 X186), 269.77/40.00 powerset( 269.77/40.00 powerset( 269.77/40.00 X184))))) => 269.77/40.00 ( 269.77/40.00 setminusT_lem => 269.77/40.00 ( 269.77/40.00 complementT_lem => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X188, 269.77/40.00 X190]: 269.77/40.00 (in( 269.77/40.00 X190, 269.77/40.00 powerset( 269.77/40.00 X188)) => 269.77/40.00 (![X192]: 269.77/40.00 (in( 269.77/40.00 X192, 269.77/40.00 powerset( 269.77/40.00 X188)) => 269.77/40.00 (( 269.77/40.00 ![X194]: 269.77/40.00 (in( 269.77/40.00 X194,X188) => 269.77/40.00 (in( 269.77/40.00 X194,X190) => 269.77/40.00 in( 269.77/40.00 X194,X192)))) => 269.77/40.00 (( 269.77/40.00 ![X196]: 269.77/40.00 (in( 269.77/40.00 X196,X188) => 269.77/40.00 (in( 269.77/40.00 X196,X192) => 269.77/40.00 in( 269.77/40.00 X196,X190)))) => 269.77/40.00 (X190 = 269.77/40.00 X192))))))) => 269.77/40.00 ( 269.77/40.00 subsetTI => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X198, 269.77/40.00 X200]: 269.77/40.00 (in( 269.77/40.00 X200, 269.77/40.00 powerset( 269.77/40.00 X198)) => 269.77/40.00 (![X202]: 269.77/40.00 (in( 269.77/40.00 X202, 269.77/40.00 powerset( 269.77/40.00 X198)) => 269.77/40.00 (( 269.77/40.00 ![X204]: 269.77/40.00 (in( 269.77/40.00 X204,X198) => 269.77/40.00 (in( 269.77/40.00 X204,X200) => 269.77/40.00 in( 269.77/40.00 X204,X202)))) => 269.77/40.00 in( 269.77/40.00 X200, 269.77/40.00 powerset( 269.77/40.00 X202))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X206, 269.77/40.00 X208]: 269.77/40.00 (in( 269.77/40.00 X208, 269.77/40.00 powerset( 269.77/40.00 X206)) => 269.77/40.00 (![X210]: 269.77/40.00 (in( 269.77/40.00 X210, 269.77/40.00 powerset( 269.77/40.00 X206)) => 269.77/40.00 (![X212]: 269.77/40.00 (in( 269.77/40.00 X212,X206) => 269.77/40.00 (in( 269.77/40.00 X208, 269.77/40.00 powerset( 269.77/40.00 X210)) => 269.77/40.00 (in( 269.77/40.00 X212,X208) => 269.77/40.00 in( 269.77/40.00 X212,X210))))))))) => 269.77/40.00 ( 269.77/40.00 complementTI1 => 269.77/40.00 ( 269.77/40.00 complementTE1 => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X214, 269.77/40.00 X216]: 269.77/40.00 (in( 269.77/40.00 X216, 269.77/40.00 powerset( 269.77/40.00 X214)) => 269.77/40.00 (![X218]: 269.77/40.00 (in( 269.77/40.00 X218, 269.77/40.00 powerset( 269.77/40.00 X214)) => 269.77/40.00 (![X220]: 269.77/40.00 (in( 269.77/40.00 X220,X214) => 269.77/40.00 (( 269.77/40.00 ~ 269.77/40.00 in( 269.77/40.00 X220,X216)) => 269.77/40.00 (~ 269.77/40.00 in( 269.77/40.00 X220, 269.77/40.00 binintersect( 269.77/40.00 X216,X218)))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X222, 269.77/40.00 X224]: 269.77/40.00 (in( 269.77/40.00 X224, 269.77/40.00 powerset( 269.77/40.00 X222)) => 269.77/40.00 (![X226]: 269.77/40.00 (in( 269.77/40.00 X226, 269.77/40.00 powerset( 269.77/40.00 X222)) => 269.77/40.00 (![X228]: 269.77/40.00 (in( 269.77/40.00 X228,X222) => 269.77/40.00 (( 269.77/40.00 ~ 269.77/40.00 in( 269.77/40.00 X228,X226)) => 269.77/40.00 (~ 269.77/40.00 in( 269.77/40.00 X228, 269.77/40.00 binintersect( 269.77/40.00 X224,X226)))))))))) => 269.77/40.00 ( 269.77/40.00 contrasubsetT => 269.77/40.00 ( 269.77/40.00 contrasubsetT1 => 269.77/40.00 ( 269.77/40.00 contrasubsetT2 => 269.77/40.00 ( 269.77/40.00 contrasubsetT3 => 269.77/40.00 ( 269.77/40.00 doubleComplementI1 => 269.77/40.00 ( 269.77/40.00 doubleComplementE1 => 269.77/40.00 ( 269.77/40.00 doubleComplementSub1 => 269.77/40.00 ( 269.77/40.00 doubleComplementSub2 => 269.77/40.00 ( 269.77/40.00 doubleComplementEq => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X230, 269.77/40.00 X232]: 269.77/40.00 (in( 269.77/40.00 X232, 269.77/40.00 powerset( 269.77/40.00 X230)) => 269.77/40.00 (![X234]: 269.77/40.00 (in( 269.77/40.00 X234, 269.77/40.00 powerset( 269.77/40.00 X230)) => 269.77/40.00 (![X236]: 269.77/40.00 (in( 269.77/40.00 X236,X230) => 269.77/40.00 (in( 269.77/40.00 X236, 269.77/40.00 setminus( 269.77/40.00 X230,X232)) => 269.77/40.00 (~ 269.77/40.00 in( 269.77/40.00 X236, 269.77/40.00 binintersect( 269.77/40.00 X232,X234)))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X238, 269.77/40.00 X240]: 269.77/40.00 (in( 269.77/40.00 X240, 269.77/40.00 powerset( 269.77/40.00 X238)) => 269.77/40.00 (![X242]: 269.77/40.00 (in( 269.77/40.00 X242, 269.77/40.00 powerset( 269.77/40.00 X238)) => 269.77/40.00 (![X244]: 269.77/40.00 (in( 269.77/40.00 X244,X238) => 269.77/40.00 (in( 269.77/40.00 X244, 269.77/40.00 setminus( 269.77/40.00 X238,X240)) => 269.77/40.00 in( 269.77/40.00 X244, 269.77/40.00 setminus( 269.77/40.00 X238, 269.77/40.00 binintersect( 269.77/40.00 X240,X242)))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X246, 269.77/40.00 X248]: 269.77/40.00 (in( 269.77/40.00 X248, 269.77/40.00 powerset( 269.77/40.00 X246)) => 269.77/40.00 (![X250]: 269.77/40.00 (in( 269.77/40.00 X250, 269.77/40.00 powerset( 269.77/40.00 X246)) => 269.77/40.00 subset( 269.77/40.00 setminus( 269.77/40.00 X246,X248), 269.77/40.00 setminus( 269.77/40.00 X246, 269.77/40.00 binintersect( 269.77/40.00 X248,X250))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X252, 269.77/40.00 X254]: 269.77/40.00 (in( 269.77/40.00 X254, 269.77/40.00 powerset( 269.77/40.00 X252)) => 269.77/40.00 (![X256]: 269.77/40.00 (in( 269.77/40.00 X256, 269.77/40.00 powerset( 269.77/40.00 X252)) => 269.77/40.00 in( 269.77/40.00 setminus( 269.77/40.00 X252,X254), 269.77/40.00 powerset( 269.77/40.00 setminus( 269.77/40.00 X252, 269.77/40.00 binintersect( 269.77/40.00 X254,X256)))))))) => 269.77/40.00 ( 269.77/40.00 contraSubsetComplement => 269.77/40.00 ( 269.77/40.00 complementTcontraSubset => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X258, 269.77/40.00 X260]: 269.77/40.00 (in( 269.77/40.00 X260, 269.77/40.00 powerset( 269.77/40.00 X258)) => 269.77/40.00 (![X262]: 269.77/40.00 (in( 269.77/40.00 X262, 269.77/40.00 powerset( 269.77/40.00 X258)) => 269.77/40.00 (![X264]: 269.77/40.00 (in( 269.77/40.00 X264,X258) => 269.77/40.00 (( 269.77/40.00 ~ 269.77/40.00 in( 269.77/40.00 X264, 269.77/40.00 binunion( 269.77/40.00 X260,X262))) => 269.77/40.00 (~ 269.77/40.00 in( 269.77/40.00 X264,X260))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X266, 269.77/40.00 X268]: 269.77/40.00 (in( 269.77/40.00 X268, 269.77/40.00 powerset( 269.77/40.00 X266)) => 269.77/40.00 (![X270]: 269.77/40.00 (in( 269.77/40.00 X270, 269.77/40.00 powerset( 269.77/40.00 X266)) => 269.77/40.00 (![X272]: 269.77/40.00 (in( 269.77/40.00 X272,X266) => 269.77/40.00 (( 269.77/40.00 ~ 269.77/40.00 in( 269.77/40.00 X272, 269.77/40.00 binunion( 269.77/40.00 X268,X270))) => 269.77/40.00 (~ 269.77/40.00 in( 269.77/40.00 X272,X270))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X274, 269.77/40.00 X276]: 269.77/40.00 (in( 269.77/40.00 X276, 269.77/40.00 powerset( 269.77/40.00 X274)) => 269.77/40.00 (![X278]: 269.77/40.00 (in( 269.77/40.00 X278, 269.77/40.00 powerset( 269.77/40.00 X274)) => 269.77/40.00 (![X280]: 269.77/40.00 (in( 269.77/40.00 X280, 269.77/40.00 powerset( 269.77/40.00 X274)) => 269.77/40.00 (![X282]: 269.77/40.00 (in( 269.77/40.00 X282,X274) => 269.77/40.00 (in( 269.77/40.00 X282, 269.77/40.00 binintersect( 269.77/40.00 X276,X278)) => 269.77/40.00 in( 269.77/40.00 X282, 269.77/40.00 binunion( 269.77/40.00 X276,X280))))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X284, 269.77/40.00 X286]: 269.77/40.00 (in( 269.77/40.00 X286, 269.77/40.00 powerset( 269.77/40.00 X284)) => 269.77/40.00 (![X288]: 269.77/40.00 (in( 269.77/40.00 X288, 269.77/40.00 powerset( 269.77/40.00 X284)) => 269.77/40.00 (![X290]: 269.77/40.00 (in( 269.77/40.00 X290, 269.77/40.00 powerset( 269.77/40.00 X284)) => 269.77/40.00 (![X292]: 269.77/40.00 (in( 269.77/40.00 X292,X284) => 269.77/40.00 (in( 269.77/40.00 X292, 269.77/40.00 binintersect( 269.77/40.00 X286,X288)) => 269.77/40.00 in( 269.77/40.00 X292, 269.77/40.00 binunion( 269.77/40.00 X288,X290))))))))))) => 269.77/40.00 ( 269.77/40.00 ( 269.77/40.00 ![X294, 269.77/40.00 X296]: 269.77/40.00 (in( 269.77/40.00 X296, 269.77/40.00 powerset( 269.77/40.00 X294)) => 269.77/40.00 (![X298]: 269.77/40.00 (in( 269.77/40.00 X298, 269.77/40.00 powerset( 269.77/40.00 X294)) => 269.77/40.00 (![X300]: 269.77/40.00 (in( 269.77/40.00 X300, 269.77/40.00 powerset( 269.77/40.00 X294)) => 269.77/40.00 (![X302]: 269.77/40.00 (in( 269.77/40.00 X302,X294) => 269.77/40.00 (in( 269.77/40.00 X302, 269.77/40.00 binintersect( 269.77/40.00 X296,X298)) => 269.77/40.00 in( 269.77/40.00 X302, 269.77/40.00 binintersect( 269.77/40.00 binunion( 269.77/40.00 X296,X300), 269.77/40.00 binunion( 269.77/40.00 X298,X300)))))))))))) => 269.77/40.00 ( 269.77/40.00 ![X304, 269.77/40.00 X306]: 269.77/40.00 (in( 269.77/40.00 X306, 269.77/40.00 powerset( 269.77/40.00 X304)) => 269.77/40.00 (![X308]: 269.77/40.00 (in( 269.77/40.00 X308, 269.77/40.00 powerset( 269.77/40.00 X304)) => 269.77/40.00 (![X310]: 269.77/40.00 (in( 269.77/40.00 X310, 269.77/40.00 powerset( 269.77/40.00 X304)) => 269.77/40.00 in( 269.77/40.00 binintersect( 269.77/40.00 X306,X308), 269.77/40.00 powerset( 269.77/40.00 binintersect( 269.77/40.00 binunion( 269.77/40.00 X306,X310), 269.77/40.00 binunion( 269.77/40.00 X308,X310))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 269.77/40.00 tff('48', plain, 269.77/40.00 ~ in(binintersect(sk_X306, sk_X308), 269.77/40.00 powerset( 269.77/40.00 binintersect(binunion(sk_X306, sk_X310), 269.77/40.00 binunion(sk_X308, sk_X310)))), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('49', plain, 269.77/40.00 ![X170, X171, X172]: 269.77/40.00 (~ subset(X170, X171) 269.77/40.00 | subset(X170, binintersect(X172, X171)) 269.77/40.00 | ~ subset(X170, X172)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('50', plain, ![X272, X273]: subset(binintersect(X272, X273), X273), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('51', plain, 269.77/40.00 ![X155, X156]: 269.77/40.00 ( in(X155, powerset(X156)) | in(sk_X14(X155, X156), X155)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('52', plain, 269.77/40.00 ![X162, X163, X164]: ( in(X162, binunion(X163, X164)) | ~ in(X162, X164)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('53', plain, 269.77/40.00 ![X155, X156]: 269.77/40.00 ( in(X155, powerset(X156)) | ~ in(sk_X14(X155, X156), X156)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('54', plain, ![X285, X286]: subset(X285, binunion(X285, X286)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('55', plain, 269.77/40.00 ![X179, X180]: (binintersect(X180, X179) = X179 | ~ subset(X179, X180)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('56', plain, 269.77/40.00 ![X181, X182, X183]: 269.77/40.00 binintersect(X181, binunion(X182, X183)) 269.77/40.00 = binunion(binintersect(X181, X182), binintersect(X181, X183)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('57', plain, ![X173, X174]: subset(binintersect(X173, X174), X173), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('58', plain, ![X168, X169]: subset(X168, binunion(X169, X168)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('59', plain, 269.77/40.00 ![X277, X278]: (binintersect(X277, X278) = X277 | ~ subset(X277, X278)), 269.77/40.00 inference('cnf', [status(esa)], [zf_stmt_4])). 269.77/40.00 tff('60', plain, $false, 269.77/40.00 inference('eprover', [status(thm)], 269.77/40.00 ['48', '49', '50', '51', '52', '53', '54', '55', '56', '57', 269.77/40.00 '58', '59'])). 269.77/40.00 269.77/40.00 % SZS output end Refutation 269.77/40.00 269.77/40.00 269.77/40.00 % Terminating... 269.77/40.00 % /export/starexec/sandbox/solver/bin/lams/c.preprocess2.sh running for 21s 270.14/40.08 % Runner terminated. 270.14/40.09 % Zipperpin 1.5 exiting 270.14/40.09 EOF