%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COM124+1 : TPTP v9.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.oUucCoUuOf true
% Computer : n017.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 04:30:42 PM UTC 2025
% Result : Theorem 6.48s 1.48s
% Output : Refutation 6.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : COM124+1 : TPTP v9.2.0. Released v6.4.0.
% 0.06/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.oUucCoUuOf true
% 0.10/0.31 % Computer : n017.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 13:49:23 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.15/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.45/0.56 % Total configuration time : 435
% 0.45/0.56 % Estimated wc time : 1092
% 0.45/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 6.48/1.48 % Solved by fo/fo5.sh.
% 6.48/1.48 % done 577 iterations in 0.769s
% 6.48/1.48 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.48/1.48 % SZS output start Refutation
% 6.48/1.48 thf(vabs_type, type, vabs: $i > $i > $i > $i).
% 6.48/1.48 thf(vsubst_type, type, vsubst: $i > $i > $i > $i).
% 6.48/1.48 thf(veabs_type, type, veabs: $i).
% 6.48/1.48 thf(valphaEquivalent_type, type, valphaEquivalent: $i > $i > $o).
% 6.48/1.48 thf(vbind_type, type, vbind: $i > $i > $i > $i).
% 6.48/1.48 thf(vvar_type, type, vvar: $i > $i).
% 6.48/1.48 thf(vtcheck_type, type, vtcheck: $i > $i > $i > $o).
% 6.48/1.48 thf(sk__79_type, type, sk__79: $i).
% 6.48/1.48 thf(visFreeVar_type, type, visFreeVar: $i > $i > $o).
% 6.48/1.48 thf(sk__74_type, type, sk__74: $i).
% 6.48/1.48 thf(sk__77_type, type, sk__77: $i).
% 6.48/1.48 thf(vgensym_type, type, vgensym: $i > $i).
% 6.48/1.48 thf(sk__78_type, type, sk__78: $i).
% 6.48/1.48 thf(sk__75_type, type, sk__75: $i).
% 6.48/1.48 thf(vapp_type, type, vapp: $i > $i > $i).
% 6.48/1.48 thf(sk__76_type, type, sk__76: $i).
% 6.48/1.48 thf(isFreeVar0, axiom,
% 6.48/1.48 (![VVar0:$i,VExp0:$i,Vx:$i,Vv:$i]:
% 6.48/1.48 ( ( ( ( VVar0 ) = ( Vv ) ) & ( ( VExp0 ) = ( vvar @ Vx ) ) ) =>
% 6.48/1.48 ( ( ( ( Vx ) = ( Vv ) ) => ( visFreeVar @ VVar0 @ VExp0 ) ) &
% 6.48/1.48 ( ( visFreeVar @ VVar0 @ VExp0 ) => ( ( Vx ) = ( Vv ) ) ) ) ))).
% 6.48/1.48 thf(zip_derived_cl16, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 (((X1) != (vvar @ X0))
% 6.48/1.48 | ((X3) != (X2))
% 6.48/1.48 | (visFreeVar @ X3 @ X1)
% 6.48/1.48 | ((X0) != (X2)))),
% 6.48/1.48 inference('cnf', [status(esa)], [isFreeVar0])).
% 6.48/1.48 thf(zip_derived_cl232, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 (((X0) != (X1)) | (visFreeVar @ X2 @ (vvar @ X0)) | ((X2) != (X1)))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl16])).
% 6.48/1.48 thf(zip_derived_cl235, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i]: (((X0) != (X1)) | (visFreeVar @ X0 @ (vvar @ X1)))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl232])).
% 6.48/1.48 thf(zip_derived_cl236, plain, (![X0 : $i]: (visFreeVar @ X0 @ (vvar @ X0))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl235])).
% 6.48/1.48 thf(isFreeVar2, axiom,
% 6.48/1.48 (![VVar0:$i,VExp0:$i,Ve1:$i,Vv:$i,Ve2:$i]:
% 6.48/1.48 ( ( ( ( VVar0 ) = ( Vv ) ) & ( ( VExp0 ) = ( vapp @ Ve1 @ Ve2 ) ) ) =>
% 6.48/1.48 ( ( ( ( visFreeVar @ Vv @ Ve1 ) | ( visFreeVar @ Vv @ Ve2 ) ) =>
% 6.48/1.48 ( visFreeVar @ VVar0 @ VExp0 ) ) &
% 6.48/1.48 ( ( visFreeVar @ VVar0 @ VExp0 ) =>
% 6.48/1.48 ( ( visFreeVar @ Vv @ Ve1 ) | ( visFreeVar @ Vv @ Ve2 ) ) ) ) ))).
% 6.48/1.48 thf(zip_derived_cl22, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.48/1.48 (((X1) != (X0))
% 6.48/1.48 | ((X4) != (vapp @ X2 @ X3))
% 6.48/1.48 | (visFreeVar @ X1 @ X4)
% 6.48/1.48 | ~ (visFreeVar @ X0 @ X3))),
% 6.48/1.48 inference('cnf', [status(esa)], [isFreeVar2])).
% 6.48/1.48 thf(zip_derived_cl293, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 (~ (visFreeVar @ X1 @ X0)
% 6.48/1.48 | (visFreeVar @ X3 @ (vapp @ X2 @ X0))
% 6.48/1.48 | ((X3) != (X1)))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl22])).
% 6.48/1.48 thf(zip_derived_cl299, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X2 @ (vapp @ X1 @ X0)) | ~ (visFreeVar @ X2 @ X0))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl293])).
% 6.48/1.48 thf(zip_derived_cl300, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i]: (visFreeVar @ X0 @ (vapp @ X1 @ (vvar @ X0)))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl236, zip_derived_cl299])).
% 6.48/1.48 thf('alpha-equiv-subst-abs', axiom,
% 6.48/1.48 (![VS:$i,Vx:$i,Vy:$i,Ve:$i]:
% 6.48/1.48 ( ( ~( visFreeVar @ Vy @ Ve ) ) =>
% 6.48/1.48 ( valphaEquivalent @
% 6.48/1.48 ( vabs @ Vx @ VS @ Ve ) @
% 6.48/1.48 ( vabs @ Vy @ VS @ ( vsubst @ Vx @ ( vvar @ Vy ) @ Ve ) ) ) ))).
% 6.48/1.48 thf(zip_derived_cl154, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 ( (valphaEquivalent @ (vabs @ X0 @ X1 @ X2) @
% 6.48/1.48 (vabs @ X3 @ X1 @ (vsubst @ X0 @ (vvar @ X3) @ X2)))
% 6.48/1.48 | (visFreeVar @ X3 @ X2))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-subst-abs])).
% 6.48/1.48 thf('alpha-equiv-sym', axiom,
% 6.48/1.48 (![Ve2:$i,Ve1:$i]:
% 6.48/1.48 ( ( valphaEquivalent @ Ve1 @ Ve2 ) => ( valphaEquivalent @ Ve2 @ Ve1 ) ))).
% 6.48/1.48 thf(zip_derived_cl152, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i]:
% 6.48/1.48 ( (valphaEquivalent @ X0 @ X1) | ~ (valphaEquivalent @ X1 @ X0))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-sym])).
% 6.48/1.48 thf(zip_derived_cl199, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 ( (visFreeVar @ X1 @ X0)
% 6.48/1.48 | (valphaEquivalent @
% 6.48/1.48 (vabs @ X1 @ X3 @ (vsubst @ X2 @ (vvar @ X1) @ X0)) @
% 6.48/1.48 (vabs @ X2 @ X3 @ X0)))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl152])).
% 6.48/1.48 thf(zip_derived_cl154, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 ( (valphaEquivalent @ (vabs @ X0 @ X1 @ X2) @
% 6.48/1.48 (vabs @ X3 @ X1 @ (vsubst @ X0 @ (vvar @ X3) @ X2)))
% 6.48/1.48 | (visFreeVar @ X3 @ X2))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-subst-abs])).
% 6.48/1.48 thf('T-Weak-FreeVar-abs-2', conjecture,
% 6.48/1.48 (![Vx:$i,VS:$i,VC:$i,Vy:$i,VS1:$i,VT:$i]:
% 6.48/1.48 ( ( ( ( Vx ) = ( Vy ) ) &
% 6.48/1.48 ( ~( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) ) ) &
% 6.48/1.48 ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) =>
% 6.48/1.48 ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ))).
% 6.48/1.48 thf(zf_stmt_0, negated_conjecture,
% 6.48/1.48 (~( ![Vx:$i,VS:$i,VC:$i,Vy:$i,VS1:$i,VT:$i]:
% 6.48/1.48 ( ( ( ( Vx ) = ( Vy ) ) &
% 6.48/1.48 ( ~( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) ) ) &
% 6.48/1.48 ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) =>
% 6.48/1.48 ( vtcheck @
% 6.48/1.48 ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )),
% 6.48/1.48 inference('cnf.neg', [status(esa)], [T-Weak-FreeVar-abs-2])).
% 6.48/1.48 thf(zip_derived_cl161, plain,
% 6.48/1.48 ( (vtcheck @ sk__76 @ (vabs @ sk__77 @ sk__78 @ veabs) @ sk__79)),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl162, plain, (((sk__74) = (sk__77))),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl164, plain,
% 6.48/1.48 ( (vtcheck @ sk__76 @ (vabs @ sk__74 @ sk__78 @ veabs) @ sk__79)),
% 6.48/1.48 inference('demod', [status(thm)], [zip_derived_cl161, zip_derived_cl162])).
% 6.48/1.48 thf('alpha-equiv-typing', axiom,
% 6.48/1.48 (![Ve:$i,VC:$i,Ve1:$i,VT:$i]:
% 6.48/1.48 ( ( ( vtcheck @ VC @ Ve @ VT ) & ( valphaEquivalent @ Ve @ Ve1 ) ) =>
% 6.48/1.48 ( vtcheck @ VC @ Ve1 @ VT ) ))).
% 6.48/1.48 thf(zip_derived_cl155, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 (~ (valphaEquivalent @ X0 @ X1)
% 6.48/1.48 | ~ (vtcheck @ X2 @ X0 @ X3)
% 6.48/1.48 | (vtcheck @ X2 @ X1 @ X3))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-typing])).
% 6.48/1.48 thf(zip_derived_cl247, plain,
% 6.48/1.48 (![X0 : $i]:
% 6.48/1.48 ( (vtcheck @ sk__76 @ X0 @ sk__79)
% 6.48/1.48 | ~ (valphaEquivalent @ (vabs @ sk__74 @ sk__78 @ veabs) @ X0))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl155])).
% 6.48/1.48 thf(zip_derived_cl250, plain,
% 6.48/1.48 (![X0 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | (vtcheck @ sk__76 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs)) @
% 6.48/1.48 sk__79))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl247])).
% 6.48/1.48 thf('T-Weak-FreeVar-abs-1-gen', axiom,
% 6.48/1.48 (![Vx:$i,VS:$i,VC:$i,Vy:$i,VS1:$i,Ve1:$i,VT:$i]:
% 6.48/1.48 ( ( ( ( Vx ) != ( Vy ) ) &
% 6.48/1.48 ( ~( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ Ve1 ) ) ) &
% 6.48/1.48 ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ Ve1 ) @ VT ) ) =>
% 6.48/1.48 ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ Ve1 ) @ VT ) ))).
% 6.48/1.48 thf(zip_derived_cl159, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ (vabs @ X1 @ X2 @ X3))
% 6.48/1.48 | ((X0) = (X1))
% 6.48/1.48 | ~ (vtcheck @ X4 @ (vabs @ X1 @ X2 @ X3) @ X5)
% 6.48/1.48 | (vtcheck @ (vbind @ X0 @ X6 @ X4) @ (vabs @ X1 @ X2 @ X3) @ X5))),
% 6.48/1.48 inference('cnf', [status(esa)], [T-Weak-FreeVar-abs-1-gen])).
% 6.48/1.48 thf(zip_derived_cl685, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | (vtcheck @ (vbind @ X2 @ X1 @ sk__76) @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs)) @
% 6.48/1.48 sk__79)
% 6.48/1.48 | ((X2) = (X0))
% 6.48/1.48 | (visFreeVar @ X2 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs))))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl159])).
% 6.48/1.48 thf(zip_derived_cl155, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 (~ (valphaEquivalent @ X0 @ X1)
% 6.48/1.48 | ~ (vtcheck @ X2 @ X0 @ X3)
% 6.48/1.48 | (vtcheck @ X2 @ X1 @ X3))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-typing])).
% 6.48/1.48 thf(zip_derived_cl1272, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 ( (visFreeVar @ X2 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs)))
% 6.48/1.48 | ((X2) = (X0))
% 6.48/1.48 | (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | (vtcheck @ (vbind @ X2 @ X1 @ sk__76) @ X3 @ sk__79)
% 6.48/1.48 | ~ (valphaEquivalent @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs)) @
% 6.48/1.48 X3))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl685, zip_derived_cl155])).
% 6.48/1.48 thf(zip_derived_cl1282, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | (vtcheck @ (vbind @ X2 @ X1 @ sk__76) @
% 6.48/1.48 (vabs @ sk__74 @ sk__78 @ veabs) @ sk__79)
% 6.48/1.48 | (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | ((X2) = (X0))
% 6.48/1.48 | (visFreeVar @ X2 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs))))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl1272])).
% 6.48/1.48 thf(zip_derived_cl1287, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X2 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs)))
% 6.48/1.48 | ((X2) = (X0))
% 6.48/1.48 | (vtcheck @ (vbind @ X2 @ X1 @ sk__76) @
% 6.48/1.48 (vabs @ sk__74 @ sk__78 @ veabs) @ sk__79)
% 6.48/1.48 | (visFreeVar @ X0 @ veabs))),
% 6.48/1.48 inference('simplify', [status(thm)], [zip_derived_cl1282])).
% 6.48/1.48 thf(zip_derived_cl160, plain,
% 6.48/1.48 (~ (vtcheck @ (vbind @ sk__74 @ sk__75 @ sk__76) @
% 6.48/1.48 (vabs @ sk__77 @ sk__78 @ veabs) @ sk__79)),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl162, plain, (((sk__74) = (sk__77))),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl196, plain,
% 6.48/1.48 (~ (vtcheck @ (vbind @ sk__74 @ sk__75 @ sk__76) @
% 6.48/1.48 (vabs @ sk__74 @ sk__78 @ veabs) @ sk__79)),
% 6.48/1.48 inference('demod', [status(thm)], [zip_derived_cl160, zip_derived_cl162])).
% 6.48/1.48 thf(zip_derived_cl1307, plain,
% 6.48/1.48 (![X0 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | ((sk__74) = (X0))
% 6.48/1.48 | (visFreeVar @ sk__74 @
% 6.48/1.48 (vabs @ X0 @ sk__78 @ (vsubst @ sk__74 @ (vvar @ X0) @ veabs))))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl1287, zip_derived_cl196])).
% 6.48/1.48 thf(zip_derived_cl154, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 ( (valphaEquivalent @ (vabs @ X0 @ X1 @ X2) @
% 6.48/1.48 (vabs @ X3 @ X1 @ (vsubst @ X0 @ (vvar @ X3) @ X2)))
% 6.48/1.48 | (visFreeVar @ X3 @ X2))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-subst-abs])).
% 6.48/1.48 thf('alpha-equiv-FreeVar', axiom,
% 6.48/1.48 (![Ve:$i,Vx:$i,Ve1:$i]:
% 6.48/1.48 ( ( ( ~( visFreeVar @ Vx @ Ve ) ) & ( valphaEquivalent @ Ve @ Ve1 ) ) =>
% 6.48/1.48 ( ~( visFreeVar @ Vx @ Ve1 ) ) ))).
% 6.48/1.48 thf(zip_derived_cl156, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X0 @ X1)
% 6.48/1.48 | ~ (valphaEquivalent @ X1 @ X2)
% 6.48/1.48 | ~ (visFreeVar @ X0 @ X2))),
% 6.48/1.48 inference('cnf', [status(esa)], [alpha-equiv-FreeVar])).
% 6.48/1.48 thf(zip_derived_cl200, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.48/1.48 ( (visFreeVar @ X1 @ X0)
% 6.48/1.48 | ~ (visFreeVar @ X4 @
% 6.48/1.48 (vabs @ X1 @ X3 @ (vsubst @ X2 @ (vvar @ X1) @ X0)))
% 6.48/1.48 | (visFreeVar @ X4 @ (vabs @ X2 @ X3 @ X0)))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl156])).
% 6.48/1.48 thf(zip_derived_cl1313, plain,
% 6.48/1.48 (![X0 : $i]:
% 6.48/1.48 (((sk__74) = (X0))
% 6.48/1.48 | (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | (visFreeVar @ sk__74 @ (vabs @ sk__74 @ sk__78 @ veabs))
% 6.48/1.48 | (visFreeVar @ X0 @ veabs))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl1307, zip_derived_cl200])).
% 6.48/1.48 thf(zip_derived_cl1318, plain,
% 6.48/1.48 (![X0 : $i]:
% 6.48/1.48 ( (visFreeVar @ sk__74 @ (vabs @ sk__74 @ sk__78 @ veabs))
% 6.48/1.48 | (visFreeVar @ X0 @ veabs)
% 6.48/1.48 | ((sk__74) = (X0)))),
% 6.48/1.48 inference('simplify', [status(thm)], [zip_derived_cl1313])).
% 6.48/1.48 thf(zip_derived_cl163, plain,
% 6.48/1.48 (~ (visFreeVar @ sk__74 @ (vabs @ sk__77 @ sk__78 @ veabs))),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl162, plain, (((sk__74) = (sk__77))),
% 6.48/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.48/1.48 thf(zip_derived_cl171, plain,
% 6.48/1.48 (~ (visFreeVar @ sk__74 @ (vabs @ sk__74 @ sk__78 @ veabs))),
% 6.48/1.48 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl162])).
% 6.48/1.48 thf(zip_derived_cl1320, plain,
% 6.48/1.48 (![X0 : $i]: (((sk__74) = (X0)) | (visFreeVar @ X0 @ veabs))),
% 6.48/1.48 inference('clc', [status(thm)], [zip_derived_cl1318, zip_derived_cl171])).
% 6.48/1.48 thf(zip_derived_cl21, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.48/1.48 (((X1) != (X0))
% 6.48/1.48 | ((X4) != (vapp @ X2 @ X3))
% 6.48/1.48 | (visFreeVar @ X1 @ X4)
% 6.48/1.48 | ~ (visFreeVar @ X0 @ X2))),
% 6.48/1.48 inference('cnf', [status(esa)], [isFreeVar2])).
% 6.48/1.48 thf(zip_derived_cl292, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.48/1.48 (~ (visFreeVar @ X1 @ X0)
% 6.48/1.48 | (visFreeVar @ X3 @ (vapp @ X0 @ X2))
% 6.48/1.48 | ((X3) != (X1)))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl21])).
% 6.48/1.48 thf(zip_derived_cl294, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.48/1.48 ( (visFreeVar @ X2 @ (vapp @ X1 @ X0)) | ~ (visFreeVar @ X2 @ X1))),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl292])).
% 6.48/1.48 thf(zip_derived_cl1322, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i]:
% 6.48/1.48 (((sk__74) = (X0)) | (visFreeVar @ X0 @ (vapp @ veabs @ X1)))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl1320, zip_derived_cl294])).
% 6.48/1.48 thf('gensym-is-fresh', axiom,
% 6.48/1.48 (![Vv:$i,Ve:$i]:
% 6.48/1.48 ( ( ( vgensym @ Ve ) = ( Vv ) ) => ( ~( visFreeVar @ Vv @ Ve ) ) ))).
% 6.48/1.48 thf(zip_derived_cl53, plain,
% 6.48/1.48 (![X0 : $i, X1 : $i]:
% 6.48/1.48 (~ (visFreeVar @ X0 @ X1) | ((vgensym @ X1) != (X0)))),
% 6.48/1.48 inference('cnf', [status(esa)], [gensym-is-fresh])).
% 6.48/1.48 thf(zip_derived_cl170, plain,
% 6.48/1.48 (![X0 : $i]: ~ (visFreeVar @ (vgensym @ X0) @ X0)),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl53])).
% 6.48/1.48 thf(zip_derived_cl1331, plain,
% 6.48/1.48 (![X0 : $i]: ((sk__74) = (vgensym @ (vapp @ veabs @ X0)))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl1322, zip_derived_cl170])).
% 6.48/1.48 thf(zip_derived_cl170, plain,
% 6.48/1.48 (![X0 : $i]: ~ (visFreeVar @ (vgensym @ X0) @ X0)),
% 6.48/1.48 inference('eq_res', [status(thm)], [zip_derived_cl53])).
% 6.48/1.48 thf(zip_derived_cl1333, plain,
% 6.48/1.48 (![X0 : $i]: ~ (visFreeVar @ sk__74 @ (vapp @ veabs @ X0))),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl1331, zip_derived_cl170])).
% 6.48/1.48 thf(zip_derived_cl1402, plain, ($false),
% 6.48/1.48 inference('sup-', [status(thm)], [zip_derived_cl300, zip_derived_cl1333])).
% 6.48/1.48
% 6.48/1.48 % SZS output end Refutation
% 6.48/1.48
% 6.48/1.48
% 6.48/1.48 % Terminating...
% 7.10/1.60 % Runner terminated.
% 7.10/1.60 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------