%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COM142+1 : TPTP v9.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1ZPo3qYdz5 true
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:30:44 PM UTC 2025
% Result : Theorem 68.37s 12.29s
% Output : Refutation 68.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM142+1 : TPTP v9.2.0. Released v6.4.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1ZPo3qYdz5 true
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 13:48:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.54/0.67 % Total configuration time : 435
% 0.54/0.67 % Estimated wc time : 1092
% 0.54/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 68.37/12.29 % Solved by fo/fo3_bce.sh.
% 68.37/12.29 % BCE start: 156
% 68.37/12.29 % BCE eliminated: 0
% 68.37/12.29 % PE start: 156
% 68.37/12.29 logic: eq
% 68.37/12.29 % PE eliminated: -34
% 68.37/12.29 % done 1687 iterations in 11.456s
% 68.37/12.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 68.37/12.29 % SZS output start Refutation
% 68.37/12.29 thf(vabs_type, type, vabs: $i > $i > $i > $i).
% 68.37/12.29 thf(zip_tseitin_18_type, type, zip_tseitin_18: $i > $i > $i > $i > $o).
% 68.37/12.29 thf(sk__71_type, type, sk__71: $i > $i > $i > $i).
% 68.37/12.29 thf(vsubst_type, type, vsubst: $i > $i > $i > $i).
% 68.37/12.29 thf(zip_tseitin_17_type, type, zip_tseitin_17: $i > $i > $i > $i > $i > $i >
% 68.37/12.29 $i > $o).
% 68.37/12.29 thf(sk__73_type, type, sk__73: $i > $i > $i > $i).
% 68.37/12.29 thf(vsomeType_type, type, vsomeType: $i > $i).
% 68.37/12.29 thf(sk__70_type, type, sk__70: $i > $i > $i > $i).
% 68.37/12.29 thf(sk__69_type, type, sk__69: $i > $i > $i > $i).
% 68.37/12.29 thf(vbind_type, type, vbind: $i > $i > $i > $i).
% 68.37/12.29 thf(vvar_type, type, vvar: $i > $i).
% 68.37/12.29 thf(varrow_type, type, varrow: $i > $i > $i).
% 68.37/12.29 thf(vnoType_type, type, vnoType: $i).
% 68.37/12.29 thf(vlookup_type, type, vlookup: $i > $i > $i).
% 68.37/12.29 thf(sk__67_type, type, sk__67: $i > $i > $i > $i).
% 68.37/12.29 thf(sk__76_type, type, sk__76: $i).
% 68.37/12.29 thf(ve2app_type, type, ve2app: $i).
% 68.37/12.29 thf(sk__75_type, type, sk__75: $i).
% 68.37/12.29 thf(vtcheck_type, type, vtcheck: $i > $i > $i > $o).
% 68.37/12.29 thf(sk__66_type, type, sk__66: $i > $i > $i > $i).
% 68.37/12.29 thf(sk__68_type, type, sk__68: $i > $i > $i > $i).
% 68.37/12.29 thf(sk__72_type, type, sk__72: $i > $i > $i > $i).
% 68.37/12.29 thf(zip_tseitin_16_type, type, zip_tseitin_16: $i > $i > $i > $i > $i > $i > $o).
% 68.37/12.29 thf(sk__77_type, type, sk__77: $i).
% 68.37/12.29 thf(sk__74_type, type, sk__74: $i).
% 68.37/12.29 thf(vapp_type, type, vapp: $i > $i > $i).
% 68.37/12.29 thf(ve1app_type, type, ve1app: $i).
% 68.37/12.29 thf('T-Weak-app', conjecture,
% 68.37/12.29 (![Vx:$i,VS:$i,VC:$i,VT:$i]:
% 68.37/12.29 ( ( ( ( vlookup @ Vx @ VC ) = ( vnoType ) ) &
% 68.37/12.29 ( vtcheck @ VC @ ( vapp @ ve1app @ ve2app ) @ VT ) ) =>
% 68.37/12.29 ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vapp @ ve1app @ ve2app ) @ VT ) ))).
% 68.37/12.29 thf(zf_stmt_0, negated_conjecture,
% 68.37/12.29 (~( ![Vx:$i,VS:$i,VC:$i,VT:$i]:
% 68.37/12.29 ( ( ( ( vlookup @ Vx @ VC ) = ( vnoType ) ) &
% 68.37/12.29 ( vtcheck @ VC @ ( vapp @ ve1app @ ve2app ) @ VT ) ) =>
% 68.37/12.29 ( vtcheck @
% 68.37/12.29 ( vbind @ Vx @ VS @ VC ) @ ( vapp @ ve1app @ ve2app ) @ VT ) ) )),
% 68.37/12.29 inference('cnf.neg', [status(esa)], [T-Weak-app])).
% 68.37/12.29 thf(zip_derived_cl153, plain,
% 68.37/12.29 (~ (vtcheck @ (vbind @ sk__74 @ sk__75 @ sk__76) @
% 68.37/12.29 (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf('T-inv', axiom,
% 68.37/12.29 (![Ve:$i,VT:$i,VC:$i]:
% 68.37/12.29 ( ( vtcheck @ VC @ Ve @ VT ) =>
% 68.37/12.29 ( ( ?[Ve1:$i,Ve2:$i,VS:$i]:
% 68.37/12.29 ( ( ( Ve ) = ( vapp @ Ve1 @ Ve2 ) ) &
% 68.37/12.29 ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) ) &
% 68.37/12.29 ( vtcheck @ VC @ Ve2 @ VS ) ) ) |
% 68.37/12.29 ( ?[Vx:$i,Ve2:$i,VT1:$i,VT2:$i]:
% 68.37/12.29 ( ( ( Ve ) = ( vabs @ Vx @ VT1 @ Ve2 ) ) &
% 68.37/12.29 ( ( VT ) = ( varrow @ VT1 @ VT2 ) ) &
% 68.37/12.29 ( vtcheck @ ( vbind @ Vx @ VT1 @ VC ) @ Ve2 @ VT2 ) ) ) |
% 68.37/12.29 ( ?[Vx:$i]:
% 68.37/12.29 ( ( ( Ve ) = ( vvar @ Vx ) ) &
% 68.37/12.29 ( ( vlookup @ Vx @ VC ) = ( vsomeType @ VT ) ) ) ) ) ))).
% 68.37/12.29 thf(zf_stmt_1, type, zip_tseitin_18 : $i > $i > $i > $i > $o).
% 68.37/12.29 thf(zf_stmt_2, axiom,
% 68.37/12.29 (![Vx:$i,VC:$i,VT:$i,Ve:$i]:
% 68.37/12.29 ( ( zip_tseitin_18 @ Vx @ VC @ VT @ Ve ) =>
% 68.37/12.29 ( ( ( vlookup @ Vx @ VC ) = ( vsomeType @ VT ) ) &
% 68.37/12.29 ( ( Ve ) = ( vvar @ Vx ) ) ) ))).
% 68.37/12.29 thf(zf_stmt_3, type, zip_tseitin_17 : $i > $i > $i > $i > $i > $i > $i > $o).
% 68.37/12.29 thf(zf_stmt_4, axiom,
% 68.37/12.29 (![VT2:$i,VT1:$i,Ve2:$i,Vx:$i,VC:$i,VT:$i,Ve:$i]:
% 68.37/12.29 ( ( zip_tseitin_17 @ VT2 @ VT1 @ Ve2 @ Vx @ VC @ VT @ Ve ) =>
% 68.37/12.29 ( ( vtcheck @ ( vbind @ Vx @ VT1 @ VC ) @ Ve2 @ VT2 ) &
% 68.37/12.29 ( ( VT ) = ( varrow @ VT1 @ VT2 ) ) &
% 68.37/12.29 ( ( Ve ) = ( vabs @ Vx @ VT1 @ Ve2 ) ) ) ))).
% 68.37/12.29 thf(zf_stmt_5, type, zip_tseitin_16 : $i > $i > $i > $i > $i > $i > $o).
% 68.37/12.29 thf(zf_stmt_6, axiom,
% 68.37/12.29 (![VS:$i,Ve2:$i,Ve1:$i,VC:$i,VT:$i,Ve:$i]:
% 68.37/12.29 ( ( zip_tseitin_16 @ VS @ Ve2 @ Ve1 @ VC @ VT @ Ve ) =>
% 68.37/12.29 ( ( vtcheck @ VC @ Ve2 @ VS ) &
% 68.37/12.29 ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) ) &
% 68.37/12.29 ( ( Ve ) = ( vapp @ Ve1 @ Ve2 ) ) ) ))).
% 68.37/12.29 thf(zf_stmt_7, axiom,
% 68.37/12.29 (![Ve:$i,VT:$i,VC:$i]:
% 68.37/12.29 ( ( vtcheck @ VC @ Ve @ VT ) =>
% 68.37/12.29 ( ( ?[Vx:$i]: ( zip_tseitin_18 @ Vx @ VC @ VT @ Ve ) ) |
% 68.37/12.29 ( ?[Vx:$i,Ve2:$i,VT1:$i,VT2:$i]:
% 68.37/12.29 ( zip_tseitin_17 @ VT2 @ VT1 @ Ve2 @ Vx @ VC @ VT @ Ve ) ) |
% 68.37/12.29 ( ?[Ve1:$i,Ve2:$i,VS:$i]:
% 68.37/12.29 ( zip_tseitin_16 @ VS @ Ve2 @ Ve1 @ VC @ VT @ Ve ) ) ) ))).
% 68.37/12.29 thf(zip_derived_cl150, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (zip_tseitin_16 @ (sk__68 @ X0 @ X1 @ X2) @
% 68.37/12.29 (sk__67 @ X0 @ X1 @ X2) @ (sk__66 @ X0 @ X1 @ X2) @ X0 @ X1 @ X2)
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X0 @ X1 @ X2) @
% 68.37/12.29 (sk__71 @ X0 @ X1 @ X2) @ (sk__70 @ X0 @ X1 @ X2) @
% 68.37/12.29 (sk__69 @ X0 @ X1 @ X2) @ X0 @ X1 @ X2)
% 68.37/12.29 | (zip_tseitin_18 @ (sk__73 @ X0 @ X1 @ X2) @ X0 @ X1 @ X2)
% 68.37/12.29 | ~ (vtcheck @ X0 @ X2 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_7])).
% 68.37/12.29 thf(zip_derived_cl149, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((X1) = (vvar @ X0)) | ~ (zip_tseitin_18 @ X0 @ X2 @ X3 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_2])).
% 68.37/12.29 thf(zip_derived_cl474, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__71 @ X2 @ X1 @ X0) @ (sk__70 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__69 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | (zip_tseitin_16 @ (sk__68 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__67 @ X2 @ X1 @ X0) @ (sk__66 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl150, zip_derived_cl149])).
% 68.37/12.29 thf(zip_derived_cl143, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 ( (vtcheck @ X0 @ X1 @ (varrow @ X2 @ X3))
% 68.37/12.29 | ~ (zip_tseitin_16 @ X2 @ X4 @ X1 @ X0 @ X3 @ X5))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_6])).
% 68.37/12.29 thf(zip_derived_cl488, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((X1) = (vvar @ (sk__73 @ X2 @ X0 @ X1)))
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__71 @ X2 @ X0 @ X1) @ (sk__70 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__69 @ X2 @ X0 @ X1) @ X2 @ X0 @ X1)
% 68.37/12.29 | ~ (vtcheck @ X2 @ X1 @ X0)
% 68.37/12.29 | (vtcheck @ X2 @ (sk__66 @ X2 @ X0 @ X1) @
% 68.37/12.29 (varrow @ (sk__68 @ X2 @ X0 @ X1) @ X0)))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl474, zip_derived_cl143])).
% 68.37/12.29 thf(zip_derived_cl147, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 68.37/12.29 (((X3) = (vabs @ X0 @ X1 @ X2))
% 68.37/12.29 | ~ (zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 68.37/12.29 thf(zip_derived_cl548, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__66 @ X2 @ X1 @ X0) @
% 68.37/12.29 (varrow @ (sk__68 @ X2 @ X1 @ X0) @ X1))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl488, zip_derived_cl147])).
% 68.37/12.29 thf(subst1, axiom,
% 68.37/12.29 (![Ve:$i,Vx:$i,VVar0:$i,VExp0:$i,VExp1:$i,RESULT:$i,Vy:$i]:
% 68.37/12.29 ( ( ( ( VVar0 ) = ( Vx ) ) & ( ( VExp0 ) = ( Ve ) ) &
% 68.37/12.29 ( ( VExp1 ) = ( vvar @ Vy ) ) ) =>
% 68.37/12.29 ( ( ( Vx ) != ( Vy ) ) =>
% 68.37/12.29 ( ( ( RESULT ) = ( vsubst @ VVar0 @ VExp0 @ VExp1 ) ) =>
% 68.37/12.29 ( ( RESULT ) = ( vvar @ Vy ) ) ) ) ))).
% 68.37/12.29 thf(zip_derived_cl55, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 68.37/12.29 (((X3) != (vsubst @ X0 @ X1 @ X2))
% 68.37/12.29 | ((X1) != (X4))
% 68.37/12.29 | ((X0) != (X5))
% 68.37/12.29 | ((X2) != (vvar @ X6))
% 68.37/12.29 | ((X3) = (vvar @ X6))
% 68.37/12.29 | ((X5) = (X6)))),
% 68.37/12.29 inference('cnf', [status(esa)], [subst1])).
% 68.37/12.29 thf(zip_derived_cl1547, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 (((X0) = (X1))
% 68.37/12.29 | ((X2) = (vvar @ X1))
% 68.37/12.29 | ((X3) != (vvar @ X1))
% 68.37/12.29 | ((X4) != (X0))
% 68.37/12.29 | ((X2) != (vsubst @ X4 @ X5 @ X3)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl55])).
% 68.37/12.29 thf(zip_derived_cl1551, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (((X0) != (vsubst @ X3 @ X2 @ X1))
% 68.37/12.29 | ((X1) != (vvar @ X4))
% 68.37/12.29 | ((X0) = (vvar @ X4))
% 68.37/12.29 | ((X3) = (X4)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1547])).
% 68.37/12.29 thf(zip_derived_cl1558, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((X0) = (X1))
% 68.37/12.29 | ((vsubst @ X0 @ X3 @ X2) = (vvar @ X1))
% 68.37/12.29 | ((X2) != (vvar @ X1)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1551])).
% 68.37/12.29 thf(zip_derived_cl1559, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((vsubst @ X2 @ X1 @ (vvar @ X0)) = (vvar @ X0)) | ((X2) = (X0)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1558])).
% 68.37/12.29 thf(zip_derived_cl1735, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (((vsubst @ X4 @ X3 @ X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | (vtcheck @ X2 @ (sk__66 @ X2 @ X1 @ X0) @
% 68.37/12.29 (varrow @ (sk__68 @ X2 @ X1 @ X0) @ X1))
% 68.37/12.29 | ((X4) = (sk__73 @ X2 @ X1 @ X0)))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl548, zip_derived_cl1559])).
% 68.37/12.29 thf(zip_derived_cl24855, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl1735])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl474, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__71 @ X2 @ X1 @ X0) @ (sk__70 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__69 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | (zip_tseitin_16 @ (sk__68 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__67 @ X2 @ X1 @ X0) @ (sk__66 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl150, zip_derived_cl149])).
% 68.37/12.29 thf(zip_derived_cl144, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 (((X2) = (vapp @ X0 @ X1))
% 68.37/12.29 | ~ (zip_tseitin_16 @ X3 @ X1 @ X0 @ X4 @ X5 @ X2))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_6])).
% 68.37/12.29 thf(zip_derived_cl489, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((X1) = (vvar @ (sk__73 @ X2 @ X0 @ X1)))
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__71 @ X2 @ X0 @ X1) @ (sk__70 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__69 @ X2 @ X0 @ X1) @ X2 @ X0 @ X1)
% 68.37/12.29 | ~ (vtcheck @ X2 @ X1 @ X0)
% 68.37/12.29 | ((X1) = (vapp @ (sk__66 @ X2 @ X0 @ X1) @ (sk__67 @ X2 @ X0 @ X1))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl474, zip_derived_cl144])).
% 68.37/12.29 thf(zip_derived_cl147, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 68.37/12.29 (((X3) = (vabs @ X0 @ X1 @ X2))
% 68.37/12.29 | ~ (zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 68.37/12.29 thf(zip_derived_cl551, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((X0) = (vapp @ (sk__66 @ X2 @ X1 @ X0) @ (sk__67 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl489, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl1559, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((vsubst @ X2 @ X1 @ (vvar @ X0)) = (vvar @ X0)) | ((X2) = (X0)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1558])).
% 68.37/12.29 thf(zip_derived_cl1698, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (((vsubst @ X4 @ X3 @ X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vapp @ (sk__66 @ X2 @ X1 @ X0) @ (sk__67 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X4) = (sk__73 @ X2 @ X1 @ X0)))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl551, zip_derived_cl1559])).
% 68.37/12.29 thf(zip_derived_cl13863, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl1698])).
% 68.37/12.29 thf('DIFF-abs-app', axiom,
% 68.37/12.29 (![VVar0:$i,VTyp0:$i,VExp0:$i,VExp1:$i,VExp2:$i]:
% 68.37/12.29 ( ( vabs @ VVar0 @ VTyp0 @ VExp0 ) != ( vapp @ VExp1 @ VExp2 ) ))).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl13885, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl13863, zip_derived_cl11])).
% 68.37/12.29 thf(subst2, axiom,
% 68.37/12.29 (![VVar0:$i,VExp0:$i,VExp1:$i,RESULT:$i,Ve1:$i,Vx:$i,Ve:$i,Ve2:$i]:
% 68.37/12.29 ( ( ( ( VVar0 ) = ( Vx ) ) & ( ( VExp0 ) = ( Ve ) ) &
% 68.37/12.29 ( ( VExp1 ) = ( vapp @ Ve1 @ Ve2 ) ) ) =>
% 68.37/12.29 ( ( ( RESULT ) = ( vsubst @ VVar0 @ VExp0 @ VExp1 ) ) =>
% 68.37/12.29 ( ( RESULT ) =
% 68.37/12.29 ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ))).
% 68.37/12.29 thf(zip_derived_cl56, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 68.37/12.29 (((X3) != (vsubst @ X0 @ X1 @ X2))
% 68.37/12.29 | ((X1) != (X4))
% 68.37/12.29 | ((X0) != (X5))
% 68.37/12.29 | ((X2) != (vapp @ X6 @ X7))
% 68.37/12.29 | ((X3) = (vapp @ (vsubst @ X5 @ X4 @ X6) @ (vsubst @ X5 @ X4 @ X7))))),
% 68.37/12.29 inference('cnf', [status(esa)], [subst2])).
% 68.37/12.29 thf(zip_derived_cl1567, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 68.37/12.29 (((X0) = (vapp @ (vsubst @ X3 @ X2 @ X4) @ (vsubst @ X3 @ X2 @ X1)))
% 68.37/12.29 | ((X5) != (vapp @ X4 @ X1))
% 68.37/12.29 | ((X6) != (X3))
% 68.37/12.29 | ((X0) != (vsubst @ X6 @ X2 @ X5)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl56])).
% 68.37/12.29 thf(zip_derived_cl2125, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 (((X0) != (vsubst @ X3 @ X2 @ X1))
% 68.37/12.29 | ((X1) != (vapp @ X5 @ X4))
% 68.37/12.29 | ((X0) = (vapp @ (vsubst @ X3 @ X2 @ X5) @ (vsubst @ X3 @ X2 @ X4))))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1567])).
% 68.37/12.29 thf(zip_derived_cl2198, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (((vsubst @ X2 @ X1 @ X0)
% 68.37/12.29 = (vapp @ (vsubst @ X2 @ X1 @ X4) @ (vsubst @ X2 @ X1 @ X3)))
% 68.37/12.29 | ((X0) != (vapp @ X4 @ X3)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl2125])).
% 68.37/12.29 thf(zip_derived_cl2200, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 ((vsubst @ X3 @ X2 @ (vapp @ X1 @ X0))
% 68.37/12.29 = (vapp @ (vsubst @ X3 @ X2 @ X1) @ (vsubst @ X3 @ X2 @ X0)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl2198])).
% 68.37/12.29 thf(zip_derived_cl20385, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 = (vapp @ (vsubst @ X1 @ X0 @ ve1app) @ (vsubst @ X1 @ X0 @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup+', [status(thm)],
% 68.37/12.29 [zip_derived_cl13885, zip_derived_cl2200])).
% 68.37/12.29 thf('DIFF-var-app', axiom,
% 68.37/12.29 (![VVar0:$i,VExp0:$i,VExp1:$i]:
% 68.37/12.29 ( ( vvar @ VVar0 ) != ( vapp @ VExp0 @ VExp1 ) ))).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl20790, plain,
% 68.37/12.29 (![X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @ (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl20385, zip_derived_cl10])).
% 68.37/12.29 thf(zip_derived_cl551, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((X0) = (vapp @ (sk__66 @ X2 @ X1 @ X0) @ (sk__67 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl489, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl20799, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ~ (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl20790, zip_derived_cl551])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl23426, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl20799, zip_derived_cl154])).
% 68.37/12.29 thf(zip_derived_cl23427, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @ (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app) = (vvar @ X0)))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl23426])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl23428, plain,
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @ (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl23427, zip_derived_cl10, zip_derived_cl11])).
% 68.37/12.29 thf('EQ-app', axiom,
% 68.37/12.29 (![VExp0:$i,VExp1:$i,VExp2:$i,VExp3:$i]:
% 68.37/12.29 ( ( ( ( ( VExp0 ) = ( VExp2 ) ) & ( ( VExp1 ) = ( VExp3 ) ) ) =>
% 68.37/12.29 ( ( vapp @ VExp0 @ VExp1 ) = ( vapp @ VExp2 @ VExp3 ) ) ) &
% 68.37/12.29 ( ( ( vapp @ VExp0 @ VExp1 ) = ( vapp @ VExp2 @ VExp3 ) ) =>
% 68.37/12.29 ( ( ( VExp0 ) = ( VExp2 ) ) & ( ( VExp1 ) = ( VExp3 ) ) ) ) ))).
% 68.37/12.29 thf(zip_derived_cl6, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((X1) = (X0)) | ((vapp @ X1 @ X3) != (vapp @ X0 @ X2)))),
% 68.37/12.29 inference('cnf', [status(esa)], [EQ-app])).
% 68.37/12.29 thf(zip_derived_cl23496, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ X1 @ X0) != (vapp @ ve1app @ ve2app))
% 68.37/12.29 | ((X1) = (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl23428, zip_derived_cl6])).
% 68.37/12.29 thf(zip_derived_cl23757, plain,
% 68.37/12.29 (((ve1app) = (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl23496])).
% 68.37/12.29 thf(zip_derived_cl24875, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl24855, zip_derived_cl23757])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl24876, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl24875, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl2200, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 ((vsubst @ X3 @ X2 @ (vapp @ X1 @ X0))
% 68.37/12.29 = (vapp @ (vsubst @ X3 @ X2 @ X1) @ (vsubst @ X3 @ X2 @ X0)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl2198])).
% 68.37/12.29 thf(zip_derived_cl27701, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 = (vapp @ (vsubst @ X1 @ X0 @ ve1app) @ (vsubst @ X1 @ X0 @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup+', [status(thm)],
% 68.37/12.29 [zip_derived_cl24876, zip_derived_cl2200])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl28118, plain,
% 68.37/12.29 (![X1 : $i]:
% 68.37/12.29 ( (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @ (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 sk__77))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl27701, zip_derived_cl10])).
% 68.37/12.29 thf(zip_derived_cl548, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__66 @ X2 @ X1 @ X0) @
% 68.37/12.29 (varrow @ (sk__68 @ X2 @ X1 @ X0) @ X1))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl488, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl28124, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ~ (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77)))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl28118, zip_derived_cl548])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl23757, plain,
% 68.37/12.29 (((ve1app) = (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl23496])).
% 68.37/12.29 thf(zip_derived_cl30822, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77)))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl28124, zip_derived_cl154, zip_derived_cl23757])).
% 68.37/12.29 thf(zip_derived_cl30823, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @ (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @ sk__77))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app) = (vvar @ X0)))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl30822])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl30824, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ ve1app @
% 68.37/12.29 (varrow @ (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 sk__77))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl30823, zip_derived_cl10, zip_derived_cl11])).
% 68.37/12.29 thf('T-Weak-app-IH2', axiom,
% 68.37/12.29 (![Vx:$i,VS:$i,VC:$i,VT:$i]:
% 68.37/12.29 ( ( ( ( vlookup @ Vx @ VC ) = ( vnoType ) ) &
% 68.37/12.29 ( vtcheck @ VC @ ve2app @ VT ) ) =>
% 68.37/12.29 ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ve2app @ VT ) ))).
% 68.37/12.29 thf(zip_derived_cl152, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((vlookup @ X0 @ X1) != (vnoType))
% 68.37/12.29 | ~ (vtcheck @ X1 @ ve2app @ X2)
% 68.37/12.29 | (vtcheck @ (vbind @ X0 @ X3 @ X1) @ ve2app @ X2))),
% 68.37/12.29 inference('cnf', [status(esa)], [T-Weak-app-IH2])).
% 68.37/12.29 thf('T-Weak-app-IH1', axiom,
% 68.37/12.29 (![Vx:$i,VS:$i,VC:$i,VT:$i]:
% 68.37/12.29 ( ( ( ( vlookup @ Vx @ VC ) = ( vnoType ) ) &
% 68.37/12.29 ( vtcheck @ VC @ ve1app @ VT ) ) =>
% 68.37/12.29 ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ve1app @ VT ) ))).
% 68.37/12.29 thf(zip_derived_cl151, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((vlookup @ X0 @ X1) != (vnoType))
% 68.37/12.29 | ~ (vtcheck @ X1 @ ve1app @ X2)
% 68.37/12.29 | (vtcheck @ (vbind @ X0 @ X3 @ X1) @ ve1app @ X2))),
% 68.37/12.29 inference('cnf', [status(esa)], [T-Weak-app-IH1])).
% 68.37/12.29 thf('T-app', axiom,
% 68.37/12.29 (![VS:$i,VC:$i,Ve1:$i,Ve2:$i,VT:$i]:
% 68.37/12.29 ( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) ) &
% 68.37/12.29 ( vtcheck @ VC @ Ve2 @ VS ) ) =>
% 68.37/12.29 ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ))).
% 68.37/12.29 thf(zip_derived_cl141, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (~ (vtcheck @ X0 @ X1 @ X2)
% 68.37/12.29 | ~ (vtcheck @ X0 @ X3 @ (varrow @ X2 @ X4))
% 68.37/12.29 | (vtcheck @ X0 @ (vapp @ X3 @ X1) @ X4))),
% 68.37/12.29 inference('cnf', [status(esa)], [T-app])).
% 68.37/12.29 thf(zip_derived_cl1578, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 (~ (vtcheck @ X2 @ ve1app @ (varrow @ X1 @ X0))
% 68.37/12.29 | ((vlookup @ X4 @ X2) != (vnoType))
% 68.37/12.29 | (vtcheck @ (vbind @ X4 @ X3 @ X2) @ (vapp @ ve1app @ X5) @ X0)
% 68.37/12.29 | ~ (vtcheck @ (vbind @ X4 @ X3 @ X2) @ X5 @ X1))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl141])).
% 68.37/12.29 thf(zip_derived_cl2746, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (~ (vtcheck @ X1 @ ve2app @ X0)
% 68.37/12.29 | ((vlookup @ X3 @ X1) != (vnoType))
% 68.37/12.29 | (vtcheck @ (vbind @ X3 @ X2 @ X1) @ (vapp @ ve1app @ ve2app) @ X4)
% 68.37/12.29 | ((vlookup @ X3 @ X1) != (vnoType))
% 68.37/12.29 | ~ (vtcheck @ X1 @ ve1app @ (varrow @ X0 @ X4)))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl1578])).
% 68.37/12.29 thf(zip_derived_cl2748, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (~ (vtcheck @ X1 @ ve1app @ (varrow @ X0 @ X4))
% 68.37/12.29 | (vtcheck @ (vbind @ X3 @ X2 @ X1) @ (vapp @ ve1app @ ve2app) @ X4)
% 68.37/12.29 | ((vlookup @ X3 @ X1) != (vnoType))
% 68.37/12.29 | ~ (vtcheck @ X1 @ ve2app @ X0))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl2746])).
% 68.37/12.29 thf(zip_derived_cl30912, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (~ (vtcheck @ sk__76 @ ve2app @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vlookup @ X0 @ sk__76) != (vnoType))
% 68.37/12.29 | (vtcheck @ (vbind @ X0 @ X1 @ sk__76) @
% 68.37/12.29 (vapp @ ve1app @ ve2app) @ sk__77))),
% 68.37/12.29 inference('sup-', [status(thm)],
% 68.37/12.29 [zip_derived_cl30824, zip_derived_cl2748])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl474, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__71 @ X2 @ X1 @ X0) @ (sk__70 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__69 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | (zip_tseitin_16 @ (sk__68 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__67 @ X2 @ X1 @ X0) @ (sk__66 @ X2 @ X1 @ X0) @ X2 @ X1 @ X0)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl150, zip_derived_cl149])).
% 68.37/12.29 thf(zip_derived_cl142, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.37/12.29 ( (vtcheck @ X0 @ X1 @ X2)
% 68.37/12.29 | ~ (zip_tseitin_16 @ X2 @ X1 @ X3 @ X0 @ X4 @ X5))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_6])).
% 68.37/12.29 thf(zip_derived_cl487, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((X1) = (vvar @ (sk__73 @ X2 @ X0 @ X1)))
% 68.37/12.29 | (zip_tseitin_17 @ (sk__72 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__71 @ X2 @ X0 @ X1) @ (sk__70 @ X2 @ X0 @ X1) @
% 68.37/12.29 (sk__69 @ X2 @ X0 @ X1) @ X2 @ X0 @ X1)
% 68.37/12.29 | ~ (vtcheck @ X2 @ X1 @ X0)
% 68.37/12.29 | (vtcheck @ X2 @ (sk__67 @ X2 @ X0 @ X1) @ (sk__68 @ X2 @ X0 @ X1)))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl474, zip_derived_cl142])).
% 68.37/12.29 thf(zip_derived_cl147, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 68.37/12.29 (((X3) = (vabs @ X0 @ X1 @ X2))
% 68.37/12.29 | ~ (zip_tseitin_17 @ X4 @ X1 @ X2 @ X0 @ X5 @ X6 @ X3))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_4])).
% 68.37/12.29 thf(zip_derived_cl545, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__67 @ X2 @ X1 @ X0) @ (sk__68 @ X2 @ X1 @ X0))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl487, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl1559, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 (((vsubst @ X2 @ X1 @ (vvar @ X0)) = (vvar @ X0)) | ((X2) = (X0)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl1558])).
% 68.37/12.29 thf(zip_derived_cl1686, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 (((vsubst @ X4 @ X3 @ X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | (vtcheck @ X2 @ (sk__67 @ X2 @ X1 @ X0) @ (sk__68 @ X2 @ X1 @ X0))
% 68.37/12.29 | ((X4) = (sk__73 @ X2 @ X1 @ X0)))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl545, zip_derived_cl1559])).
% 68.37/12.29 thf(zip_derived_cl10092, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl1686])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl10111, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl10092, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl545, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__67 @ X2 @ X1 @ X0) @ (sk__68 @ X2 @ X1 @ X0))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl487, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl12539, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vsubst @ X1 @ X0 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ~ (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl10111, zip_derived_cl545])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl12722, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vsubst @ X1 @ X0 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl12539, zip_derived_cl154])).
% 68.37/12.29 thf(zip_derived_cl12723, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @ (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vsubst @ X1 @ X0 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl12722])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl12724, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vsubst @ X1 @ X0 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl12723, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl10111, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((X0) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl10092, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl545, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__67 @ X2 @ X1 @ X0) @ (sk__68 @ X2 @ X1 @ X0))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl487, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl10173, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ~ (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl10111, zip_derived_cl545])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl12571, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl10173, zip_derived_cl154])).
% 68.37/12.29 thf(zip_derived_cl12572, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @ (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app) = (vvar @ X0)))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl12571])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl12573, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 ( (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vsubst @ X0 @ X1 @ (vapp @ ve1app @ ve2app))
% 68.37/12.29 = (vvar @ (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl12572, zip_derived_cl10, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl12951, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((vsubst @ X1 @ X0 @ (vapp @ ve1app @ ve2app)) != (vapp @ X3 @ X2))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl12573, zip_derived_cl10])).
% 68.37/12.29 thf(zip_derived_cl14230, plain,
% 68.37/12.29 (![X1 : $i]:
% 68.37/12.29 ( (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((X1) = (sk__73 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('clc', [status(thm)],
% 68.37/12.29 [zip_derived_cl12724, zip_derived_cl12951])).
% 68.37/12.29 thf(zip_derived_cl545, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.37/12.29 ( (vtcheck @ X2 @ (sk__67 @ X2 @ X1 @ X0) @ (sk__68 @ X2 @ X1 @ X0))
% 68.37/12.29 | ~ (vtcheck @ X2 @ X0 @ X1)
% 68.37/12.29 | ((X0) = (vvar @ (sk__73 @ X2 @ X1 @ X0)))
% 68.37/12.29 | ((X0)
% 68.37/12.29 = (vabs @ (sk__69 @ X2 @ X1 @ X0) @ (sk__71 @ X2 @ X1 @ X0) @
% 68.37/12.29 (sk__70 @ X2 @ X1 @ X0))))),
% 68.37/12.29 inference('dp-resolution', [status(thm)],
% 68.37/12.29 [zip_derived_cl487, zip_derived_cl147])).
% 68.37/12.29 thf(zip_derived_cl14233, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | ~ (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl14230, zip_derived_cl545])).
% 68.37/12.29 thf(zip_derived_cl154, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ (vapp @ ve1app @ ve2app) @ sk__77)),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl16910, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app) = (vvar @ X0))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @
% 68.37/12.29 (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl14233, zip_derived_cl154])).
% 68.37/12.29 thf(zip_derived_cl16911, plain,
% 68.37/12.29 (![X0 : $i]:
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vabs @ (sk__69 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__71 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__70 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))
% 68.37/12.29 | (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))
% 68.37/12.29 | ((vapp @ ve1app @ ve2app) = (vvar @ X0)))),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl16910])).
% 68.37/12.29 thf(zip_derived_cl10, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i]: ((vvar @ X2) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-var-app])).
% 68.37/12.29 thf(zip_derived_cl11, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.37/12.29 ((vabs @ X2 @ X3 @ X4) != (vapp @ X0 @ X1))),
% 68.37/12.29 inference('cnf', [status(esa)], [DIFF-abs-app])).
% 68.37/12.29 thf(zip_derived_cl16912, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl16911, zip_derived_cl10, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl23428, plain,
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @ (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)) @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('simplify_reflect-', [status(thm)],
% 68.37/12.29 [zip_derived_cl23427, zip_derived_cl10, zip_derived_cl11])).
% 68.37/12.29 thf(zip_derived_cl23757, plain,
% 68.37/12.29 (((ve1app) = (sk__66 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl23496])).
% 68.37/12.29 thf(zip_derived_cl23768, plain,
% 68.37/12.29 (((vapp @ ve1app @ ve2app)
% 68.37/12.29 = (vapp @ ve1app @
% 68.37/12.29 (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl23428, zip_derived_cl23757])).
% 68.37/12.29 thf(zip_derived_cl7, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.37/12.29 (((X1) = (X0)) | ((vapp @ X3 @ X1) != (vapp @ X2 @ X0)))),
% 68.37/12.29 inference('cnf', [status(esa)], [EQ-app])).
% 68.37/12.29 thf(zip_derived_cl23781, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vapp @ X1 @ X0) != (vapp @ ve1app @ ve2app))
% 68.37/12.29 | ((X0) = (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app))))),
% 68.37/12.29 inference('sup-', [status(thm)], [zip_derived_cl23768, zip_derived_cl7])).
% 68.37/12.29 thf(zip_derived_cl24185, plain,
% 68.37/12.29 (((ve2app) = (sk__67 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('eq_res', [status(thm)], [zip_derived_cl23781])).
% 68.37/12.29 thf(zip_derived_cl24256, plain,
% 68.37/12.29 ( (vtcheck @ sk__76 @ ve2app @
% 68.37/12.29 (sk__68 @ sk__76 @ sk__77 @ (vapp @ ve1app @ ve2app)))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl16912, zip_derived_cl24185])).
% 68.37/12.29 thf(zip_derived_cl30919, plain,
% 68.37/12.29 (![X0 : $i, X1 : $i]:
% 68.37/12.29 (((vlookup @ X0 @ sk__76) != (vnoType))
% 68.37/12.29 | (vtcheck @ (vbind @ X0 @ X1 @ sk__76) @
% 68.37/12.29 (vapp @ ve1app @ ve2app) @ sk__77))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl30912, zip_derived_cl24256])).
% 68.37/12.29 thf(zip_derived_cl30932, plain, (((vlookup @ sk__74 @ sk__76) != (vnoType))),
% 68.37/12.29 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl30919])).
% 68.37/12.29 thf(zip_derived_cl155, plain, (((vlookup @ sk__74 @ sk__76) = (vnoType))),
% 68.37/12.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.37/12.29 thf(zip_derived_cl30933, plain, (((vnoType) != (vnoType))),
% 68.37/12.29 inference('demod', [status(thm)],
% 68.37/12.29 [zip_derived_cl30932, zip_derived_cl155])).
% 68.37/12.29 thf(zip_derived_cl30934, plain, ($false),
% 68.37/12.29 inference('simplify', [status(thm)], [zip_derived_cl30933])).
% 68.37/12.29
% 68.37/12.29 % SZS output end Refutation
% 68.37/12.29
% 68.37/12.29
% 68.37/12.29 % Terminating...
% 68.79/12.45 % Runner terminated.
% 68.79/12.46 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------