%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT411^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.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 : Wed Feb 25 08:45:41 AM UTC 2026
% Result : Theorem 2.17s 1.81s
% Output : Refutation 2.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : DAT411^1 : TPTP v9.2.1. Released v9.2.0.
% 0.08/0.15 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.36 % Computer : n022.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Tue Feb 24 06:17:21 EST 2026
% 0.18/0.37 % CPUTime :
% 0.18/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.23/0.48 ---- Original DTF file ---
% 0.23/0.49 thf(spec,logic,$$dhol).
% 0.23/0.49 %------------------------------------------------------------------------------
% 0.23/0.49 % File : DAT411^1 : TPTP v9.2.1. Released v9.2.0.
% 0.23/0.49 % Domain : Data Structures
% 0.23/0.49 % Problem : List reversal involution polymorphic, step 5a type instantiated
% 0.23/0.49 % Version : Especial.
% 0.23/0.49 % English : List reversal involution for polymorphic fixed-length lists. The
% 0.23/0.49 % proof is split into smaller steps. To simplify proof search, the
% 0.23/0.49 % axioms in each problem file have been preselected.
% 0.23/0.49
% 0.23/0.49 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.23/0.49 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.23/0.49 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.23/0.49 % Source : [Rot25]
% 0.23/0.49 % Names : ListReversalInvolution/list-rev-invol-step5-typeInstantiated_alt.p [Rot25]
% 0.23/0.49
% 0.23/0.49 % Status : Theorem
% 0.23/0.49 % Rating : ? v9.2.0
% 0.23/0.49 % Syntax : Number of formulae : 26 ( 12 unt; 9 typ; 0 def)
% 0.23/0.49 % Number of atoms : 20 ( 20 equ; 0 cnn)
% 0.23/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.23/0.49 % Number of connectives : 473 ( 3 ~; 0 |; 0 &; 463 @)
% 0.23/0.49 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.23/0.49 % Maximal formula depth : 8 ( 4 avg)
% 0.23/0.49 % Number of types : 2 ( 1 usr)
% 0.23/0.49 % Number of type decls : 9 ( 4 !>P; 3 !>D)
% 0.23/0.49 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.23/0.49 % Number of symbols : 9 ( 8 usr; 1 con; 0-5 aty)
% 0.23/0.49 % Number of variables : 47 ( 0 ^; 39 !; 0 ?; 47 :)
% 0.23/0.49 % ( 8 !>; 0 ?*; 0 @-; 0 @+)
% 0.23/0.49 % SPC : DH1_THM_EQU_NAR
% 0.23/0.49
% 0.23/0.49 % Comments :
% 0.23/0.49 %------------------------------------------------------------------------------
% 0.23/0.49 thf(nat_type,type,
% 0.23/0.49 nat: $tType ).
% 0.23/0.49
% 0.23/0.49 thf(zero_type,type,
% 0.23/0.49 zero: nat ).
% 0.23/0.49
% 0.23/0.49 thf(suc_type,type,
% 0.23/0.49 suc: nat > nat ).
% 0.23/0.49
% 0.23/0.49 thf(plus_type,type,
% 0.23/0.49 plus: nat > nat > nat ).
% 0.23/0.49
% 0.23/0.49 thf(list_type,type,
% 0.23/0.49 list: $tType > nat > $tType ).
% 0.23/0.49
% 0.23/0.49 thf(nil_type,type,
% 0.23/0.49 nil:
% 0.23/0.49 !>[A: $tType] : ( list @ A @ zero ) ).
% 0.23/0.49
% 0.23/0.49 thf(cons_type,type,
% 0.23/0.49 cons:
% 0.23/0.49 !>[A: $tType,N: nat] : ( A > ( list @ A @ N ) > ( list @ A @ ( suc @ N ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(app_type,type,
% 0.23/0.49 app:
% 0.23/0.49 !>[A: $tType,N: nat,M: nat] : ( ( list @ A @ N ) > ( list @ A @ M ) > ( list @ A @ ( plus @ N @ M ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(rev_type,type,
% 0.23/0.49 rev:
% 0.23/0.49 !>[A: $tType,N: nat] : ( ( list @ A @ N ) > ( list @ A @ N ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(peano1,axiom,
% 0.23/0.49 ! [N: nat] :
% 0.23/0.49 ( ( suc @ N )
% 0.23/0.49 != zero ) ).
% 0.23/0.49
% 0.23/0.49 thf(peano2,axiom,
% 0.23/0.49 ! [N: nat,M: nat] :
% 0.23/0.49 ( ( N != M )
% 0.23/0.49 => ( ( suc @ N )
% 0.23/0.49 != ( suc @ M ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(peano3,axiom,
% 0.23/0.49 ! [P: nat > $o] :
% 0.23/0.49 ( ( P @ zero )
% 0.23/0.49 => ( ! [M: nat] :
% 0.23/0.49 ( ( P @ M )
% 0.23/0.49 => ( P @ ( suc @ M ) ) )
% 0.23/0.49 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax1,axiom,
% 0.23/0.49 ! [N: nat] :
% 0.23/0.49 ( ( plus @ zero @ N )
% 0.23/0.49 = N ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax2,axiom,
% 0.23/0.49 ! [N: nat,M: nat] :
% 0.23/0.49 ( ( plus @ ( suc @ N ) @ M )
% 0.23/0.49 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax3,axiom,
% 0.23/0.49 ! [A: $tType,N: nat,X: list @ A @ N] :
% 0.23/0.49 ( ( app @ A @ zero @ N @ ( nil @ A ) @ X )
% 0.23/0.49 = X ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax4,axiom,
% 0.23/0.49 ! [A: $tType,N: nat,M: nat,X: A,Y: list @ A @ N,Z: list @ A @ M] :
% 0.23/0.49 ( ( app @ A @ ( suc @ N ) @ M @ ( cons @ A @ N @ X @ Y ) @ Z )
% 0.23/0.49 = ( cons @ A @ ( plus @ N @ M ) @ X @ ( app @ A @ N @ M @ Y @ Z ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax5,axiom,
% 0.23/0.49 ! [A: $tType] :
% 0.23/0.49 ( ( rev @ A @ zero @ ( nil @ A ) )
% 0.23/0.49 = ( nil @ A ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(ax6,axiom,
% 0.23/0.49 ! [A: $tType,N: nat,X: A,Y: list @ A @ N] :
% 0.23/0.49 ( ( rev @ A @ ( suc @ N ) @ ( cons @ A @ N @ X @ Y ) )
% 0.23/0.49 = ( app @ A @ N @ ( suc @ zero ) @ ( rev @ A @ N @ Y ) @ ( cons @ A @ zero @ X @ ( nil @ A ) ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(plus_com,axiom,
% 0.23/0.49 ! [N: nat,M: nat] :
% 0.23/0.49 ( ( plus @ N @ M )
% 0.23/0.49 = ( plus @ M @ N ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(plus1r,axiom,
% 0.23/0.49 ! [N: nat] :
% 0.23/0.49 ( ( suc @ N )
% 0.23/0.49 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_app_nil,axiom,
% 0.23/0.49 ! [A: $tType,N: nat,L: list @ A @ N] :
% 0.23/0.49 ( ( app @ A @ N @ zero @ L @ ( nil @ A ) )
% 0.23/0.49 = L ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_rev_invol_step1,axiom,
% 0.23/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.23/0.49 ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ ( plus @ N @ zero ) @ ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ zero @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_rev_invol_step2,axiom,
% 0.23/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.23/0.49 ( ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ ( plus @ N @ zero ) @ ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ zero @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) ) ) )
% 0.23/0.49 => ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) ) @ L ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_rev_invol_step3,axiom,
% 0.23/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.23/0.49 ( ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) ) @ L ) )
% 0.23/0.49 => ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ N @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) @ L ) ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_rev_invol_step4,axiom,
% 0.23/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.23/0.49 ( ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ N @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) @ L ) )
% 0.23/0.49 => ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = L ) ) ).
% 0.23/0.49
% 0.23/0.49 thf(list_rev_invol,conjecture,
% 0.23/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.23/0.49 ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.23/0.49 = L ) ).
% 0.23/0.49
% 0.23/0.49 %------------------------------------------------------------------------------
% 0.23/0.49 ------------------------
% 2.11/1.43 ---- Embedded in THF ---
% 2.11/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.11/1.43 %%% Generated on Tue Feb 24 06:17:22 EST 2026
% 2.11/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.11/1.43 %%% Logic specification used:
% 2.11/1.43 %%% thf(spec, logic, $$dhol).
% 2.11/1.43
% 2.11/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2DTF21362.p
% 2.11/1.43 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 2.11/1.43 thf(is_per, definition, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) <=> ((! [X:A,Y:A]: ((((AStar @ X) @ Y) => ((AStar @ Y) @ X)))) & (! [X:A,Y:A,Z:A]: ((((AStar @ X) @ Y) => (((AStar @ Y) @ Z) => ((AStar @ X) @ Z)))))))))).
% 2.11/1.43 thf(nat_type, type, nat: $tType).
% 2.11/1.43 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 2.11/1.43 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 2.11/1.43 thf(zero_type, type, zero: nat).
% 2.11/1.43 thf(suc_type, type, suc: (nat > nat)).
% 2.11/1.43 thf(plus_type, type, plus: (nat > (nat > nat))).
% 2.11/1.43 thf(list_type, type, list: ($tType > $tType)).
% 2.11/1.43 thf(listStar, type, 'listStar': (!> [A:$tType]: (((A > (A > $o)) > (nat > ((list @ A) > ((list @ A) > $o))))))).
% 2.11/1.43 thf('\'listStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:nat]: (((isPer @ (list @ B)) @ (((listStar @ B) @ BStar) @ C)))))))).
% 2.11/1.43 thf(nil_type, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.11/1.43 thf(nil_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (nil @ A)) @ (nil @ A)))))).
% 2.11/1.43 thf(cons_type, type, cons: (!> [A:$tType]: ((nat > (A > ((list @ A) > (list @ A))))))).
% 2.11/1.43 thf(cons_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:A,D_prime:A]: (((D = D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ ((((cons @ A) @ N) @ D) @ D0)) @ ((((cons @ A) @ N) @ D_prime) @ D0_prime)))))))))))))).
% 2.11/1.43 thf(app_type, type, app: (!> [A:$tType]: ((nat > (nat > ((list @ A) > ((list @ A) > (list @ A)))))))).
% 2.11/1.43 thf(app_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ M) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ M)) @ (((((app @ A) @ N) @ M) @ D) @ D0)) @ (((((app @ A) @ N) @ M) @ D_prime) @ D0_prime)))))))))))))))).
% 2.11/1.43 thf(rev_type, type, rev: (!> [A:$tType]: ((nat > ((list @ A) > (list @ A)))))).
% 2.11/1.43 thf(rev_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (((((listStar @ A) @ AStar) @ N) @ (((rev @ A) @ N) @ D)) @ (((rev @ A) @ N) @ D_prime))))))))))).
% 2.11/1.43 thf(peano1, axiom, (! [N:nat]: (((suc @ N) != zero)))).
% 2.11/1.43 thf(peano2, axiom, (! [N:nat]: ((! [M:nat]: (((N != M) => ((suc @ N) != (suc @ M)))))))).
% 2.11/1.43 thf(peano3, axiom, (! [P:(nat > $o)]: (((P @ zero) => ((! [M:nat]: (((P @ M) => (P @ (suc @ M))))) => (! [N:nat]: ((P @ N)))))))).
% 2.11/1.43 thf(ax1, axiom, (! [N:nat]: ((((plus @ zero) @ N) = N)))).
% 2.11/1.43 thf(ax2, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ (suc @ N)) @ M) = (suc @ ((plus @ N) @ M)))))))).
% 2.11/1.43 thf(ax3, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [X:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ X) @ X) => (((((listStar @ A) @ AStar) @ ((plus @ zero) @ N)) @ (((((app @ A) @ zero) @ N) @ (nil @ A)) @ X)) @ X)))))))))).
% 2.11/1.43 thf(ax4, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [X:A]: ((! [Y:(list @ A),Z:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ Y) @ Y) => ((((((listStar @ A) @ AStar) @ M) @ Z) @ Z) => (((((listStar @ A) @ AStar) @ ((plus @ (suc @ N)) @ M)) @ (((((app @ A) @ (suc @ N)) @ M) @ ((((cons @ A) @ N) @ X) @ Y)) @ Z)) @ ((((cons @ A) @ ((plus @ N) @ M)) @ X) @ (((((app @ A) @ N) @ M) @ Y) @ Z))))))))))))))))).
% 2.11/1.43 thf(ax5, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (((rev @ A) @ zero) @ (nil @ A))) @ (nil @ A)))))).
% 2.11/1.43 thf(ax6, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [X:A]: ((! [Y:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ Y) @ Y) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ (((rev @ A) @ (suc @ N)) @ ((((cons @ A) @ N) @ X) @ Y))) @ (((((app @ A) @ N) @ (suc @ zero)) @ (((rev @ A) @ N) @ Y)) @ ((((cons @ A) @ zero) @ X) @ (nil @ A))))))))))))))).
% 2.11/1.43 thf(plus_com, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ N) @ M) = ((plus @ M) @ N))))))).
% 2.11/1.43 thf(plus1r, axiom, (! [N:nat]: (((suc @ N) = ((plus @ N) @ (suc @ zero)))))).
% 2.11/1.43 thf(list_app_nil, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [L:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ L) @ L) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ zero)) @ (((((app @ A) @ N) @ zero) @ L) @ (nil @ A))) @ L)))))))))).
% 2.11/1.43 thf(list_rev_invol_step1, axiom, (! [N:nat]: ((! [L:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ L) @ L) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((rev @ (list @ (list @ nat))) @ ((plus @ N) @ zero)) @ (((((app @ (list @ (list @ nat))) @ N) @ zero) @ (((rev @ (list @ (list @ nat))) @ N) @ L)) @ (nil @ (list @ (list @ nat)))))))))))).
% 2.11/1.43 thf(list_rev_invol_step2, axiom, (! [N:nat]: ((! [L:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ L) @ L) => ((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((rev @ (list @ (list @ nat))) @ ((plus @ N) @ zero)) @ (((((app @ (list @ (list @ nat))) @ N) @ zero) @ (((rev @ (list @ (list @ nat))) @ N) @ L)) @ (nil @ (list @ (list @ nat)))))) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((((app @ (list @ (list @ nat))) @ zero) @ N) @ (((rev @ (list @ (list @ nat))) @ zero) @ (nil @ (list @ (list @ nat))))) @ L))))))))).
% 2.11/1.43 thf(list_rev_invol_step3, axiom, (! [N:nat]: ((! [L:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ L) @ L) => ((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((((app @ (list @ (list @ nat))) @ zero) @ N) @ (((rev @ (list @ (list @ nat))) @ zero) @ (nil @ (list @ (list @ nat))))) @ L)) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((((app @ (list @ (list @ nat))) @ zero) @ N) @ (nil @ (list @ (list @ nat)))) @ L))))))))).
% 2.11/1.43 thf(list_rev_invol_step4, axiom, (! [N:nat]: ((! [L:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ L) @ L) => ((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ (((((app @ (list @ (list @ nat))) @ zero) @ N) @ (nil @ (list @ (list @ nat)))) @ L)) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ L)))))))).
% 2.11/1.43 thf(list_rev_invol, conjecture, (! [N:nat]: ((! [L:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ L) @ L) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ (((rev @ (list @ (list @ nat))) @ N) @ L))) @ L))))))).
% 2.11/1.43 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2DTF21362.p
% 2.11/1.43 ------------------------
% 2.11/1.44 ---- Cleaned THF ---
% 2.11/1.45 thf(is_per_type,type,
% 2.11/1.45 isPer:
% 2.11/1.45 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 2.11/1.45
% 2.11/1.45 thf(is_per,definition,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 <=> ( ! [X: A,Y: A] :
% 2.11/1.45 ( ( AStar @ X @ Y )
% 2.11/1.45 => ( AStar @ Y @ X ) )
% 2.11/1.45 & ! [X: A,Y: A,Z: A] :
% 2.11/1.45 ( ( AStar @ X @ Y )
% 2.11/1.45 => ( ( AStar @ Y @ Z )
% 2.11/1.45 => ( AStar @ X @ Z ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(nat_type,type,
% 2.11/1.45 nat: $tType ).
% 2.11/1.45
% 2.11/1.45 thf(natStar,type,
% 2.11/1.45 natStar: nat > nat > $o ).
% 2.11/1.45
% 2.11/1.45 thf(natStar_is_eq,axiom,
% 2.11/1.45 ! [X: nat,Y: nat] :
% 2.11/1.45 ( ( natStar @ X @ Y )
% 2.11/1.45 <=> ( X = Y ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(zero_type,type,
% 2.11/1.45 zero: nat ).
% 2.11/1.45
% 2.11/1.45 thf(suc_type,type,
% 2.11/1.45 suc: nat > nat ).
% 2.11/1.45
% 2.11/1.45 thf(plus_type,type,
% 2.11/1.45 plus: nat > nat > nat ).
% 2.11/1.45
% 2.11/1.45 thf(list_type,type,
% 2.11/1.45 list: $tType > $tType ).
% 2.11/1.45
% 2.11/1.45 thf(listStar,type,
% 2.11/1.45 listStar:
% 2.11/1.45 !>[A: $tType] : ( ( A > A > $o ) > nat > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.11/1.45
% 2.11/1.45 thf('\'listStar\'_is_per',axiom,
% 2.11/1.45 ! [B: $tType,BStar: B > B > $o] :
% 2.11/1.45 ( ( isPer @ B @ BStar )
% 2.11/1.45 => ! [C: nat] : ( isPer @ ( list @ B ) @ ( listStar @ B @ BStar @ C ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(nil_type,type,
% 2.11/1.45 nil:
% 2.11/1.45 !>[A: $tType] : ( list @ A ) ).
% 2.11/1.45
% 2.11/1.45 thf(nil_tp_ax,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ( listStar @ A @ AStar @ zero @ ( nil @ A ) @ ( nil @ A ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(cons_type,type,
% 2.11/1.45 cons:
% 2.11/1.45 !>[A: $tType] : ( nat > A > ( list @ A ) > ( list @ A ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(cons_tp_ax,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,D: A,D_prime: A] :
% 2.11/1.45 ( ( D = D_prime )
% 2.11/1.45 => ! [D0: list @ A,D0_prime: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ D0 @ D0_prime )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( cons @ A @ N @ D @ D0 ) @ ( cons @ A @ N @ D_prime @ D0_prime ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(app_type,type,
% 2.11/1.45 app:
% 2.11/1.45 !>[A: $tType] : ( nat > nat > ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(app_tp_ax,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,M: nat,D: list @ A,D_prime: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 2.11/1.45 => ! [D0: list @ A,D0_prime: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ M @ D0 @ D0_prime )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( plus @ N @ M ) @ ( app @ A @ N @ M @ D @ D0 ) @ ( app @ A @ N @ M @ D_prime @ D0_prime ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(rev_type,type,
% 2.11/1.45 rev:
% 2.11/1.45 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ A ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(rev_tp_ax,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,D: list @ A,D_prime: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 2.11/1.45 => ( listStar @ A @ AStar @ N @ ( rev @ A @ N @ D ) @ ( rev @ A @ N @ D_prime ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(peano1,axiom,
% 2.11/1.45 ! [N: nat] :
% 2.11/1.45 ( ( suc @ N )
% 2.11/1.45 != zero ) ).
% 2.11/1.45
% 2.11/1.45 thf(peano2,axiom,
% 2.11/1.45 ! [N: nat,M: nat] :
% 2.11/1.45 ( ( N != M )
% 2.11/1.45 => ( ( suc @ N )
% 2.11/1.45 != ( suc @ M ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(peano3,axiom,
% 2.11/1.45 ! [P: nat > $o] :
% 2.11/1.45 ( ( P @ zero )
% 2.11/1.45 => ( ! [M: nat] :
% 2.11/1.45 ( ( P @ M )
% 2.11/1.45 => ( P @ ( suc @ M ) ) )
% 2.11/1.45 => ! [N: nat] : ( P @ N ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax1,axiom,
% 2.11/1.45 ! [N: nat] :
% 2.11/1.45 ( ( plus @ zero @ N )
% 2.11/1.45 = N ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax2,axiom,
% 2.11/1.45 ! [N: nat,M: nat] :
% 2.11/1.45 ( ( plus @ ( suc @ N ) @ M )
% 2.11/1.45 = ( suc @ ( plus @ N @ M ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax3,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,X: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ X @ X )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( plus @ zero @ N ) @ ( app @ A @ zero @ N @ ( nil @ A ) @ X ) @ X ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax4,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,M: nat,X: A,Y: list @ A,Z: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ Y @ Y )
% 2.11/1.45 => ( ( listStar @ A @ AStar @ M @ Z @ Z )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ A @ ( suc @ N ) @ M @ ( cons @ A @ N @ X @ Y ) @ Z ) @ ( cons @ A @ ( plus @ N @ M ) @ X @ ( app @ A @ N @ M @ Y @ Z ) ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax5,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ( listStar @ A @ AStar @ zero @ ( rev @ A @ zero @ ( nil @ A ) ) @ ( nil @ A ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(ax6,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,X: A,Y: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ Y @ Y )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( rev @ A @ ( suc @ N ) @ ( cons @ A @ N @ X @ Y ) ) @ ( app @ A @ N @ ( suc @ zero ) @ ( rev @ A @ N @ Y ) @ ( cons @ A @ zero @ X @ ( nil @ A ) ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(plus_com,axiom,
% 2.11/1.45 ! [N: nat,M: nat] :
% 2.11/1.45 ( ( plus @ N @ M )
% 2.11/1.45 = ( plus @ M @ N ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(plus1r,axiom,
% 2.11/1.45 ! [N: nat] :
% 2.11/1.45 ( ( suc @ N )
% 2.11/1.45 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_app_nil,axiom,
% 2.11/1.45 ! [A: $tType,AStar: A > A > $o] :
% 2.11/1.45 ( ( isPer @ A @ AStar )
% 2.11/1.45 => ! [N: nat,L: list @ A] :
% 2.11/1.45 ( ( listStar @ A @ AStar @ N @ L @ L )
% 2.11/1.45 => ( listStar @ A @ AStar @ ( plus @ N @ zero ) @ ( app @ A @ N @ zero @ L @ ( nil @ A ) ) @ L ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_rev_invol_step1,axiom,
% 2.11/1.45 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 2.11/1.45 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 2.11/1.45 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( rev @ ( list @ ( list @ nat ) ) @ ( plus @ N @ zero ) @ ( app @ ( list @ ( list @ nat ) ) @ N @ zero @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) @ ( nil @ ( list @ ( list @ nat ) ) ) ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_rev_invol_step2,axiom,
% 2.11/1.45 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 2.11/1.45 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 2.11/1.45 => ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( rev @ ( list @ ( list @ nat ) ) @ ( plus @ N @ zero ) @ ( app @ ( list @ ( list @ nat ) ) @ N @ zero @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) @ ( nil @ ( list @ ( list @ nat ) ) ) ) ) )
% 2.11/1.45 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( app @ ( list @ ( list @ nat ) ) @ zero @ N @ ( rev @ ( list @ ( list @ nat ) ) @ zero @ ( nil @ ( list @ ( list @ nat ) ) ) ) @ L ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_rev_invol_step3,axiom,
% 2.11/1.45 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 2.11/1.45 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 2.11/1.45 => ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( app @ ( list @ ( list @ nat ) ) @ zero @ N @ ( rev @ ( list @ ( list @ nat ) ) @ zero @ ( nil @ ( list @ ( list @ nat ) ) ) ) @ L ) )
% 2.11/1.45 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( app @ ( list @ ( list @ nat ) ) @ zero @ N @ ( nil @ ( list @ ( list @ nat ) ) ) @ L ) ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_rev_invol_step4,axiom,
% 2.11/1.45 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 2.11/1.45 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 2.11/1.45 => ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ ( app @ ( list @ ( list @ nat ) ) @ zero @ N @ ( nil @ ( list @ ( list @ nat ) ) ) @ L ) )
% 2.11/1.45 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ L ) ) ) ).
% 2.11/1.45
% 2.11/1.45 thf(list_rev_invol,conjecture,
% 2.11/1.45 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 2.11/1.45 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 2.11/1.45 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ ( rev @ ( list @ ( list @ nat ) ) @ N @ L ) ) @ L ) ) ).
% 2.11/1.45 ------------------------
% 2.11/1.46 % (21648)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/183Mi)
% 2.11/1.46 % (21654)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/18Mi)
% 2.11/1.47 % (21654)Instruction limit reached!
% 2.11/1.47 % (21654)------------------------------
% 2.11/1.47 % (21654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (21654)Termination reason: Unknown
% 2.11/1.47 % (21654)Termination phase: Saturation
% 2.11/1.47
% 2.11/1.47 % (21654)Memory used [KB]: 5628
% 2.11/1.47 % (21654)Time elapsed: 0.008 s
% 2.11/1.47 % (21654)Instructions burned: 19 (million)
% 2.11/1.47 % (21654)------------------------------
% 2.11/1.47 % (21654)------------------------------
% 2.11/1.47 % (21649)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/4Mi)
% 2.11/1.47 % (21650)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/27Mi)
% 2.11/1.47 % (21651)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/2Mi)
% 2.11/1.47 % (21652)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/2Mi)
% 2.11/1.47 % (21653)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/275Mi)
% 2.11/1.47 % (21651)Instruction limit reached!
% 2.11/1.47 % (21651)------------------------------
% 2.11/1.47 % (21651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (21651)Termination reason: Unknown
% 2.11/1.47 % (21651)Termination phase: shuffling
% 2.11/1.47
% 2.11/1.47 % (21651)Memory used [KB]: 1023
% 2.11/1.47 % (21651)Time elapsed: 0.003 s
% 2.11/1.47 % (21651)Instructions burned: 2 (million)
% 2.11/1.47 % (21651)------------------------------
% 2.11/1.47 % (21651)------------------------------
% 2.11/1.47 % (21652)Instruction limit reached!
% 2.11/1.47 % (21652)------------------------------
% 2.11/1.47 % (21652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (21652)Termination reason: Unknown
% 2.11/1.47 % (21652)Termination phase: shuffling
% 2.11/1.47
% 2.11/1.47 % (21652)Memory used [KB]: 1023
% 2.11/1.47 % (21652)Time elapsed: 0.003 s
% 2.11/1.47 % (21652)Instructions burned: 2 (million)
% 2.11/1.47 % (21652)------------------------------
% 2.11/1.47 % (21652)------------------------------
% 2.11/1.47 % (21649)Instruction limit reached!
% 2.11/1.47 % (21649)------------------------------
% 2.11/1.47 % (21649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (21649)Termination reason: Unknown
% 2.11/1.47 % (21649)Termination phase: shuffling
% 2.11/1.47
% 2.11/1.47 % (21649)Memory used [KB]: 1023
% 2.11/1.47 % (21649)Time elapsed: 0.004 s
% 2.11/1.47 % (21649)Instructions burned: 4 (million)
% 2.11/1.47 % (21649)------------------------------
% 2.11/1.47 % (21649)------------------------------
% 2.11/1.48 % (21655)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.11/1.48 % (21655)Instruction limit reached!
% 2.11/1.48 % (21655)------------------------------
% 2.11/1.48 % (21655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (21655)Termination reason: Unknown
% 2.11/1.48 % (21655)Termination phase: shuffling
% 2.11/1.48
% 2.11/1.48 % (21655)Memory used [KB]: 1023
% 2.11/1.48 % (21655)Time elapsed: 0.003 s
% 2.11/1.48 % (21655)Instructions burned: 4 (million)
% 2.11/1.48 % (21655)------------------------------
% 2.11/1.48 % (21655)------------------------------
% 2.11/1.48 % (21650)Instruction limit reached!
% 2.11/1.48 % (21650)------------------------------
% 2.11/1.48 % (21650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (21650)Termination reason: Unknown
% 2.11/1.48 % (21650)Termination phase: Saturation
% 2.11/1.48
% 2.11/1.48 % (21650)Memory used [KB]: 5628
% 2.11/1.48 % (21650)Time elapsed: 0.018 s
% 2.11/1.48 % (21650)Instructions burned: 27 (million)
% 2.11/1.48 % (21650)------------------------------
% 2.11/1.48 % (21650)------------------------------
% 2.11/1.48 % (21653)Refutation not found, incomplete strategy
% 2.11/1.48 % (21653)------------------------------
% 2.11/1.48 % (21653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (21653)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.48
% 2.11/1.48
% 2.11/1.48 % (21653)Memory used [KB]: 5756
% 2.11/1.48 % (21653)Time elapsed: 0.018 s
% 2.11/1.48 % (21653)Instructions burned: 29 (million)
% 2.11/1.48 % (21653)------------------------------
% 2.11/1.48 % (21653)------------------------------
% 2.11/1.49 % (21656)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/37Mi)
% 2.11/1.49 % (21657)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/15Mi)
% 2.11/1.49 % (21658)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.11/1.49 % (21659)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/1041Mi)
% 2.11/1.49 % (21658)Instruction limit reached!
% 2.11/1.49 % (21658)------------------------------
% 2.11/1.49 % (21658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (21658)Termination reason: Unknown
% 2.11/1.49 % (21658)Termination phase: shuffling
% 2.11/1.49
% 2.11/1.49 % (21658)Memory used [KB]: 1023
% 2.11/1.49 % (21658)Time elapsed: 0.004 s
% 2.11/1.49 % (21658)Instructions burned: 4 (million)
% 2.11/1.49 % (21658)------------------------------
% 2.11/1.49 % (21658)------------------------------
% 2.11/1.49 % (21660)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/7Mi)
% 2.11/1.49 % (21657)Instruction limit reached!
% 2.11/1.49 % (21657)------------------------------
% 2.11/1.49 % (21657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (21657)Termination reason: Unknown
% 2.11/1.49 % (21657)Termination phase: Property scanning
% 2.11/1.49
% 2.11/1.49 % (21657)Memory used [KB]: 1023
% 2.11/1.49 % (21657)Time elapsed: 0.010 s
% 2.11/1.49 % (21657)Instructions burned: 15 (million)
% 2.11/1.49 % (21657)------------------------------
% 2.11/1.49 % (21657)------------------------------
% 2.11/1.50 % (21660)Instruction limit reached!
% 2.11/1.50 % (21660)------------------------------
% 2.11/1.50 % (21660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.50 % (21660)Termination reason: Unknown
% 2.11/1.50 % (21660)Termination phase: shuffling
% 2.11/1.50
% 2.11/1.50 % (21660)Memory used [KB]: 1023
% 2.11/1.50 % (21660)Time elapsed: 0.004 s
% 2.11/1.50 % (21660)Instructions burned: 7 (million)
% 2.11/1.50 % (21660)------------------------------
% 2.11/1.50 % (21660)------------------------------
% 2.17/1.50 % (21661)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/16Mi)
% 2.17/1.50 % (21661)Instruction limit reached!
% 2.17/1.50 % (21661)------------------------------
% 2.17/1.50 % (21661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.50 % (21661)Termination reason: Unknown
% 2.17/1.50 % (21661)Termination phase: Property scanning
% 2.17/1.50
% 2.17/1.50 % (21661)Memory used [KB]: 1023
% 2.17/1.50 % (21661)Time elapsed: 0.007 s
% 2.17/1.50 % (21661)Instructions burned: 16 (million)
% 2.17/1.50 % (21661)------------------------------
% 2.17/1.50 % (21661)------------------------------
% 2.17/1.51 % (21656)Instruction limit reached!
% 2.17/1.51 % (21656)------------------------------
% 2.17/1.51 % (21656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (21656)Termination reason: Unknown
% 2.17/1.51 % (21656)Termination phase: Saturation
% 2.17/1.51
% 2.17/1.51 % (21656)Memory used [KB]: 5756
% 2.17/1.51 % (21656)Time elapsed: 0.022 s
% 2.17/1.51 % (21656)Instructions burned: 38 (million)
% 2.17/1.51 % (21656)------------------------------
% 2.17/1.51 % (21656)------------------------------
% 2.17/1.51 % (21662)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.17/1.51 % (21664)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/7Mi)
% 2.17/1.51 % (21662)Instruction limit reached!
% 2.17/1.51 % (21662)------------------------------
% 2.17/1.51 % (21662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (21662)Termination reason: Unknown
% 2.17/1.51 % (21662)Termination phase: shuffling
% 2.17/1.51
% 2.17/1.51 % (21662)Memory used [KB]: 1023
% 2.17/1.51 % (21662)Time elapsed: 0.004 s
% 2.17/1.51 % (21662)Instructions burned: 4 (million)
% 2.17/1.51 % (21662)------------------------------
% 2.17/1.51 % (21662)------------------------------
% 2.17/1.51 % (21664)Instruction limit reached!
% 2.17/1.51 % (21664)------------------------------
% 2.17/1.51 % (21664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (21664)Termination reason: Unknown
% 2.17/1.51 % (21664)Termination phase: Property scanning
% 2.17/1.51
% 2.17/1.51 % (21664)Memory used [KB]: 1023
% 2.17/1.51 % (21664)Time elapsed: 0.005 s
% 2.17/1.51 % (21664)Instructions burned: 9 (million)
% 2.17/1.51 % (21664)------------------------------
% 2.17/1.51 % (21664)------------------------------
% 2.17/1.51 % (21663)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.17/1.51 % (21665)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.17/1.51 % (21663)Instruction limit reached!
% 2.17/1.51 % (21663)------------------------------
% 2.17/1.51 % (21663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (21663)Termination reason: Unknown
% 2.17/1.51 % (21663)Termination phase: shuffling
% 2.17/1.51
% 2.17/1.51 % (21663)Memory used [KB]: 1023
% 2.17/1.51 % (21663)Time elapsed: 0.004 s
% 2.17/1.51 % (21663)Instructions burned: 4 (million)
% 2.17/1.51 % (21663)------------------------------
% 2.17/1.51 % (21663)------------------------------
% 2.17/1.51 % (21665)Instruction limit reached!
% 2.17/1.51 % (21665)------------------------------
% 2.17/1.51 % (21665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (21665)Termination reason: Unknown
% 2.17/1.51 % (21665)Termination phase: shuffling
% 2.17/1.51
% 2.17/1.51 % (21665)Memory used [KB]: 1023
% 2.17/1.51 % (21665)Time elapsed: 0.003 s
% 2.17/1.51 % (21665)Instructions burned: 5 (million)
% 2.17/1.51 % (21665)------------------------------
% 2.17/1.51 % (21665)------------------------------
% 2.17/1.52 % (21668)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/710Mi)
% 2.17/1.52 % (21648)Instruction limit reached!
% 2.17/1.52 % (21648)------------------------------
% 2.17/1.52 % (21648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52 % (21648)Termination reason: Unknown
% 2.17/1.52 % (21648)Termination phase: Saturation
% 2.17/1.52
% 2.17/1.52 % (21648)Memory used [KB]: 6268
% 2.17/1.52 % (21648)Time elapsed: 0.063 s
% 2.17/1.52 % (21648)Instructions burned: 185 (million)
% 2.17/1.52 % (21648)------------------------------
% 2.17/1.52 % (21648)------------------------------
% 2.17/1.52 % (21666)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/4Mi)
% 2.17/1.52 % (21670)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/902Mi)
% 2.17/1.52 % (21666)Instruction limit reached!
% 2.17/1.52 % (21666)------------------------------
% 2.17/1.52 % (21666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52 % (21666)Termination reason: Unknown
% 2.17/1.52 % (21666)Termination phase: shuffling
% 2.17/1.52
% 2.17/1.52 % (21666)Memory used [KB]: 1023
% 2.17/1.52 % (21666)Time elapsed: 0.004 s
% 2.17/1.52 % (21666)Instructions burned: 4 (million)
% 2.17/1.52 % (21666)------------------------------
% 2.17/1.52 % (21666)------------------------------
% 2.17/1.52 % (21667)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/18Mi)
% 2.17/1.53 % (21669)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/6Mi)
% 2.17/1.53 % (21671)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/21Mi)
% 2.17/1.53 % (21670)Refutation not found, incomplete strategy
% 2.17/1.53 % (21670)------------------------------
% 2.17/1.53 % (21670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.53 % (21670)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.53
% 2.17/1.53
% 2.17/1.53 % (21670)Memory used [KB]: 5756
% 2.17/1.53 % (21670)Time elapsed: 0.011 s
% 2.17/1.53 % (21670)Instructions burned: 29 (million)
% 2.17/1.53 % (21670)------------------------------
% 2.17/1.53 % (21670)------------------------------
% 2.17/1.53 % (21669)Instruction limit reached!
% 2.17/1.53 % (21669)------------------------------
% 2.17/1.53 % (21669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.53 % (21669)Termination reason: Unknown
% 2.17/1.53 % (21669)Termination phase: shuffling
% 2.17/1.53
% 2.17/1.53 % (21669)Memory used [KB]: 1023
% 2.17/1.53 % (21669)Time elapsed: 0.005 s
% 2.17/1.53 % (21669)Instructions burned: 6 (million)
% 2.17/1.53 % (21669)------------------------------
% 2.17/1.53 % (21669)------------------------------
% 2.17/1.54 % (21667)Instruction limit reached!
% 2.17/1.54 % (21667)------------------------------
% 2.17/1.54 % (21667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54 % (21667)Termination reason: Unknown
% 2.17/1.54 % (21667)Termination phase: Saturation
% 2.17/1.54
% 2.17/1.54 % (21667)Memory used [KB]: 5500
% 2.17/1.54 % (21667)Time elapsed: 0.012 s
% 2.17/1.54 % (21667)Instructions burned: 19 (million)
% 2.17/1.54 % (21667)------------------------------
% 2.17/1.54 % (21667)------------------------------
% 2.17/1.54 % (21671)Instruction limit reached!
% 2.17/1.54 % (21671)------------------------------
% 2.17/1.54 % (21671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54 % (21671)Termination reason: Unknown
% 2.17/1.54 % (21671)Termination phase: Saturation
% 2.17/1.54
% 2.17/1.54 % (21671)Memory used [KB]: 5628
% 2.17/1.54 % (21671)Time elapsed: 0.009 s
% 2.17/1.54 % (21671)Instructions burned: 23 (million)
% 2.17/1.54 % (21671)------------------------------
% 2.17/1.54 % (21671)------------------------------
% 2.17/1.54 % (21672)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/5Mi)
% 2.17/1.54 % (21673)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/6Mi)
% 2.17/1.54 % (21672)Instruction limit reached!
% 2.17/1.54 % (21672)------------------------------
% 2.17/1.54 % (21672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54 % (21672)Termination reason: Unknown
% 2.17/1.54 % (21672)Termination phase: shuffling
% 2.17/1.54
% 2.17/1.54 % (21672)Memory used [KB]: 1023
% 2.17/1.54 % (21672)Time elapsed: 0.004 s
% 2.17/1.54 % (21672)Instructions burned: 5 (million)
% 2.17/1.54 % (21672)------------------------------
% 2.17/1.54 % (21672)------------------------------
% 2.17/1.55 % (21673)Instruction limit reached!
% 2.17/1.55 % (21673)------------------------------
% 2.17/1.55 % (21673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.55 % (21673)Termination reason: Unknown
% 2.17/1.55 % (21673)Termination phase: Property scanning
% 2.17/1.55
% 2.17/1.55 % (21673)Memory used [KB]: 1023
% 2.17/1.55 % (21673)Time elapsed: 0.004 s
% 2.17/1.55 % (21673)Instructions burned: 8 (million)
% 2.17/1.55 % (21673)------------------------------
% 2.17/1.55 % (21673)------------------------------
% 2.17/1.55 % (21676)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/19Mi)
% 2.17/1.55 % (21674)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/377Mi)
% 2.17/1.55 % (21675)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/779Mi)
% 2.17/1.56 % (21676)Instruction limit reached!
% 2.17/1.56 % (21676)------------------------------
% 2.17/1.56 % (21676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.56 % (21676)Termination reason: Unknown
% 2.17/1.56 % (21676)Termination phase: Saturation
% 2.17/1.56
% 2.17/1.56 % (21676)Memory used [KB]: 5628
% 2.17/1.56 % (21676)Time elapsed: 0.008 s
% 2.17/1.56 % (21676)Instructions burned: 21 (million)
% 2.17/1.56 % (21676)------------------------------
% 2.17/1.56 % (21676)------------------------------
% 2.17/1.56 % (21678)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/17Mi)
% 2.17/1.56 % (21678)Instruction limit reached!
% 2.17/1.56 % (21678)------------------------------
% 2.17/1.56 % (21678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.56 % (21678)Termination reason: Unknown
% 2.17/1.56 % (21678)Termination phase: Property scanning
% 2.17/1.56
% 2.17/1.56 % (21678)Memory used [KB]: 1023
% 2.17/1.56 % (21678)Time elapsed: 0.007 s
% 2.17/1.56 % (21678)Instructions burned: 17 (million)
% 2.17/1.56 % (21678)------------------------------
% 2.17/1.56 % (21678)------------------------------
% 2.17/1.56 % (21677)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/879Mi)
% 2.17/1.57 % (21679)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/3Mi)
% 2.17/1.57 % (21679)Instruction limit reached!
% 2.17/1.57 % (21679)------------------------------
% 2.17/1.57 % (21679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.57 % (21679)Termination reason: Unknown
% 2.17/1.57 % (21679)Termination phase: shuffling
% 2.17/1.57
% 2.17/1.57 % (21679)Memory used [KB]: 1023
% 2.17/1.57 % (21679)Time elapsed: 0.003 s
% 2.17/1.57 % (21679)Instructions burned: 4 (million)
% 2.17/1.57 % (21679)------------------------------
% 2.17/1.57 % (21679)------------------------------
% 2.17/1.57 % (21680)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21362 for (2999ds/30Mi)
% 2.17/1.58 % (21681)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/127Mi)
% 2.17/1.58 % (21680)Instruction limit reached!
% 2.17/1.58 % (21680)------------------------------
% 2.17/1.58 % (21680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.58 % (21680)Termination reason: Unknown
% 2.17/1.58 % (21680)Termination phase: Saturation
% 2.17/1.58
% 2.17/1.58 % (21680)Memory used [KB]: 5756
% 2.17/1.58 % (21680)Time elapsed: 0.012 s
% 2.17/1.58 % (21680)Instructions burned: 32 (million)
% 2.17/1.58 % (21680)------------------------------
% 2.17/1.58 % (21680)------------------------------
% 2.17/1.59 % (21682)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/100Mi)
% 2.17/1.62 % (21681)Instruction limit reached!
% 2.17/1.62 % (21681)------------------------------
% 2.17/1.62 % (21681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.62 % (21681)Termination reason: Unknown
% 2.17/1.62 % (21681)Termination phase: Saturation
% 2.17/1.62
% 2.17/1.62 % (21681)Memory used [KB]: 6012
% 2.17/1.62 % (21681)Time elapsed: 0.042 s
% 2.17/1.62 % (21681)Instructions burned: 129 (million)
% 2.17/1.62 % (21681)------------------------------
% 2.17/1.62 % (21681)------------------------------
% 2.17/1.62 % (21682)Instruction limit reached!
% 2.17/1.62 % (21682)------------------------------
% 2.17/1.62 % (21682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.62 % (21682)Termination reason: Unknown
% 2.17/1.62 % (21682)Termination phase: Saturation
% 2.17/1.62
% 2.17/1.62 % (21682)Memory used [KB]: 6012
% 2.17/1.62 % (21682)Time elapsed: 0.033 s
% 2.17/1.62 % (21682)Instructions burned: 100 (million)
% 2.17/1.62 % (21682)------------------------------
% 2.17/1.62 % (21682)------------------------------
% 2.17/1.63 % (21683)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/3Mi)
% 2.17/1.63 % (21683)Instruction limit reached!
% 2.17/1.63 % (21683)------------------------------
% 2.17/1.63 % (21683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.63 % (21683)Termination reason: Unknown
% 2.17/1.63 % (21683)Termination phase: shuffling
% 2.17/1.63
% 2.17/1.63 % (21683)Memory used [KB]: 1023
% 2.17/1.63 % (21683)Time elapsed: 0.002 s
% 2.17/1.63 % (21683)Instructions burned: 4 (million)
% 2.17/1.63 % (21683)------------------------------
% 2.17/1.63 % (21683)------------------------------
% 2.17/1.63 % (21684)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/20Mi)
% 2.17/1.64 % (21685)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/86Mi)
% 2.17/1.64 % (21684)Instruction limit reached!
% 2.17/1.64 % (21684)------------------------------
% 2.17/1.64 % (21684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.64 % (21684)Termination reason: Unknown
% 2.17/1.64 % (21684)Termination phase: Saturation
% 2.17/1.64
% 2.17/1.64 % (21684)Memory used [KB]: 5500
% 2.17/1.64 % (21684)Time elapsed: 0.008 s
% 2.17/1.64 % (21684)Instructions burned: 21 (million)
% 2.17/1.64 % (21684)------------------------------
% 2.17/1.64 % (21684)------------------------------
% 2.17/1.65 % (21686)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/107Mi)
% 2.17/1.66 % (21685)Instruction limit reached!
% 2.17/1.66 % (21685)------------------------------
% 2.17/1.66 % (21685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.66 % (21685)Termination reason: Unknown
% 2.17/1.66 % (21685)Termination phase: Saturation
% 2.17/1.66
% 2.17/1.66 % (21685)Memory used [KB]: 6140
% 2.17/1.66 % (21685)Time elapsed: 0.028 s
% 2.17/1.66 % (21685)Instructions burned: 89 (million)
% 2.17/1.66 % (21685)------------------------------
% 2.17/1.66 % (21685)------------------------------
% 2.17/1.67 % (21687)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_21362 for (2998ds/39Mi)
% 2.17/1.68 % (21686)Instruction limit reached!
% 2.17/1.68 % (21686)------------------------------
% 2.17/1.68 % (21686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.68 % (21686)Termination reason: Unknown
% 2.17/1.68 % (21686)Termination phase: Saturation
% 2.17/1.68
% 2.17/1.68 % (21686)Memory used [KB]: 5884
% 2.17/1.68 % (21686)Time elapsed: 0.037 s
% 2.17/1.68 % (21686)Instructions burned: 107 (million)
% 2.17/1.68 % (21686)------------------------------
% 2.17/1.68 % (21686)------------------------------
% 2.17/1.69 % (21687)Instruction limit reached!
% 2.17/1.69 % (21687)------------------------------
% 2.17/1.69 % (21687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.69 % (21687)Termination reason: Unknown
% 2.17/1.69 % (21687)Termination phase: Saturation
% 2.17/1.69
% 2.17/1.69 % (21687)Memory used [KB]: 5756
% 2.17/1.69 % (21687)Time elapsed: 0.013 s
% 2.17/1.69 % (21687)Instructions burned: 41 (million)
% 2.17/1.69 % (21687)------------------------------
% 2.17/1.69 % (21687)------------------------------
% 2.17/1.69 % (21674)Instruction limit reached!
% 2.17/1.69 % (21674)------------------------------
% 2.17/1.69 % (21674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.69 % (21674)Termination reason: Unknown
% 2.17/1.69 % (21674)Termination phase: Saturation
% 2.17/1.69
% 2.17/1.69 % (21674)Memory used [KB]: 6140
% 2.17/1.69 % (21674)Time elapsed: 0.139 s
% 2.17/1.69 % (21674)Instructions burned: 379 (million)
% 2.17/1.69 % (21674)------------------------------
% 2.17/1.69 % (21674)------------------------------
% 2.17/1.69 % (21688)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/448Mi)
% 2.17/1.69 % (21689)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/46Mi)
% 2.17/1.70 % (21690)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/98Mi)
% 2.17/1.71 % (21689)Instruction limit reached!
% 2.17/1.71 % (21689)------------------------------
% 2.17/1.71 % (21689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.71 % (21689)Termination reason: Unknown
% 2.17/1.71 % (21689)Termination phase: Saturation
% 2.17/1.71
% 2.17/1.71 % (21689)Memory used [KB]: 5756
% 2.17/1.71 % (21689)Time elapsed: 0.015 s
% 2.17/1.71 % (21689)Instructions burned: 47 (million)
% 2.17/1.71 % (21689)------------------------------
% 2.17/1.71 % (21689)------------------------------
% 2.17/1.72 % (21691)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/507Mi)
% 2.17/1.73 % (21668)Instruction limit reached!
% 2.17/1.73 % (21668)------------------------------
% 2.17/1.73 % (21668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.73 % (21668)Termination reason: Unknown
% 2.17/1.73 % (21668)Termination phase: Saturation
% 2.17/1.73
% 2.17/1.73 % (21668)Memory used [KB]: 7036
% 2.17/1.73 % (21668)Time elapsed: 0.208 s
% 2.17/1.73 % (21668)Instructions burned: 710 (million)
% 2.17/1.73 % (21668)------------------------------
% 2.17/1.73 % (21668)------------------------------
% 2.17/1.73 % (21691)Refutation not found, incomplete strategy
% 2.17/1.73 % (21691)------------------------------
% 2.17/1.73 % (21691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.73 % (21691)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.73
% 2.17/1.73
% 2.17/1.73 % (21691)Memory used [KB]: 5756
% 2.17/1.73 % (21691)Time elapsed: 0.033 s
% 2.17/1.73 % (21691)Instructions burned: 30 (million)
% 2.17/1.73 % (21691)------------------------------
% 2.17/1.73 % (21691)------------------------------
% 2.17/1.73 % (21690)Instruction limit reached!
% 2.17/1.73 % (21690)------------------------------
% 2.17/1.73 % (21690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.73 % (21690)Termination reason: Unknown
% 2.17/1.73 % (21690)Termination phase: Saturation
% 2.17/1.73
% 2.17/1.73 % (21690)Memory used [KB]: 1407
% 2.17/1.73 % (21690)Time elapsed: 0.055 s
% 2.17/1.73 % (21690)Instructions burned: 98 (million)
% 2.17/1.73 % (21690)------------------------------
% 2.17/1.73 % (21690)------------------------------
% 2.17/1.74 % (21692)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/149Mi)
% 2.17/1.74 % (21693)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/39Mi)
% 2.17/1.74 % (21694)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/6Mi)
% 2.17/1.74 % (21694)Instruction limit reached!
% 2.17/1.74 % (21694)------------------------------
% 2.17/1.74 % (21694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.74 % (21694)Termination reason: Unknown
% 2.17/1.74 % (21694)Termination phase: Property scanning
% 2.17/1.74
% 2.17/1.74 % (21694)Memory used [KB]: 1023
% 2.17/1.74 % (21694)Time elapsed: 0.004 s
% 2.17/1.74 % (21694)Instructions burned: 8 (million)
% 2.17/1.74 % (21694)------------------------------
% 2.17/1.74 % (21694)------------------------------
% 2.17/1.75 % (21693)Instruction limit reached!
% 2.17/1.75 % (21693)------------------------------
% 2.17/1.75 % (21693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.75 % (21693)Termination reason: Unknown
% 2.17/1.75 % (21693)Termination phase: Saturation
% 2.17/1.75
% 2.17/1.75 % (21693)Memory used [KB]: 5628
% 2.17/1.75 % (21693)Time elapsed: 0.013 s
% 2.17/1.75 % (21693)Instructions burned: 39 (million)
% 2.17/1.75 % (21693)------------------------------
% 2.17/1.75 % (21693)------------------------------
% 2.17/1.75 % (21695)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_21362 for (2997ds/1087Mi)
% 2.17/1.76 % (21696)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21362 for (2996ds/47Mi)
% 2.17/1.77 % (21696)Instruction limit reached!
% 2.17/1.77 % (21696)------------------------------
% 2.17/1.77 % (21696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.77 % (21696)Termination reason: Unknown
% 2.17/1.77 % (21696)Termination phase: Saturation
% 2.17/1.77
% 2.17/1.77 % (21696)Memory used [KB]: 5756
% 2.17/1.77 % (21696)Time elapsed: 0.016 s
% 2.17/1.77 % (21696)Instructions burned: 48 (million)
% 2.17/1.77 % (21696)------------------------------
% 2.17/1.77 % (21696)------------------------------
% 2.17/1.78 % (21697)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_21362 for (2996ds/44Mi)
% 2.17/1.78 % (21692)Instruction limit reached!
% 2.17/1.78 % (21692)------------------------------
% 2.17/1.78 % (21692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.78 % (21692)Termination reason: Unknown
% 2.17/1.78 % (21692)Termination phase: Saturation
% 2.17/1.78
% 2.17/1.78 % (21692)Memory used [KB]: 6140
% 2.17/1.78 % (21692)Time elapsed: 0.048 s
% 2.17/1.78 % (21692)Instructions burned: 151 (million)
% 2.17/1.78 % (21692)------------------------------
% 2.17/1.78 % (21692)------------------------------
% 2.17/1.79 % (21698)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_21362 for (2996ds/432Mi)
% 2.17/1.80 % (21697)Instruction limit reached!
% 2.17/1.80 % (21697)------------------------------
% 2.17/1.80 % (21697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.80 % (21697)Termination reason: Unknown
% 2.17/1.80 % (21697)Termination phase: Saturation
% 2.17/1.80
% 2.17/1.80 % (21697)Memory used [KB]: 1279
% 2.17/1.80 % (21697)Time elapsed: 0.014 s
% 2.17/1.80 % (21697)Instructions burned: 45 (million)
% 2.17/1.80 % (21697)------------------------------
% 2.17/1.80 % (21697)------------------------------
% 2.17/1.80 % (21659)First to succeed.
% 2.17/1.80 % (21699)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21362 for (2996ds/62Mi)
% 2.17/1.81 % (21659)Refutation found. Thanks to Tanya!
% 2.17/1.81 % SZS status Theorem for DTF2THF_21362
% 2.17/1.81 % SZS output start Proof for DTF2THF_21362
% 2.17/1.81 thf(type_def_6, type, nat: $tType).
% 2.17/1.81 thf(type_def_7, type, list: ($tType) > $tType).
% 2.17/1.81 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 2.17/1.81 thf(func_def_2, type, nat: $tType).
% 2.17/1.81 thf(func_def_3, type, natStar: nat > nat > $o).
% 2.17/1.81 thf(func_def_4, type, zero: nat).
% 2.17/1.81 thf(func_def_5, type, suc: nat > nat).
% 2.17/1.81 thf(func_def_6, type, plus: nat > nat > nat).
% 2.17/1.81 thf(func_def_7, type, list: ($tType) > $tType).
% 2.17/1.81 thf(func_def_8, type, listStar: !>[X0: $tType]:((X0 > X0 > $o) > nat > list @ X0 > list @ X0 > $o)).
% 2.17/1.81 thf(func_def_9, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.17/1.81 thf(func_def_10, type, cons: !>[X0: $tType]:(nat > X0 > list @ X0 > list @ X0)).
% 2.17/1.81 thf(func_def_11, type, app: !>[X0: $tType]:(nat > nat > list @ X0 > list @ X0 > list @ X0)).
% 2.17/1.81 thf(func_def_12, type, rev: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 2.17/1.81 thf(func_def_30, type, ph1: !>[X0: $tType]:(X0)).
% 2.17/1.81 thf(func_def_31, type, sK2: list @ list @ list @ nat).
% 2.17/1.81 thf(func_def_32, type, sK3: nat).
% 2.17/1.81 thf(f2492,plain,(
% 2.17/1.81 $false),
% 2.17/1.81 inference(trivial_inequality_removal,[status(thm)],[f2491])).
% 2.17/1.81 thf(f2491,plain,(
% 2.17/1.81 ($false = $true)),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2490])).
% 2.17/1.81 thf(f2490,plain,(
% 2.17/1.81 ((~ $true) = $true)),
% 2.17/1.81 inference(backward_demodulation,[status(thm)],[f2020,f2489])).
% 2.17/1.81 thf(f2489,plain,(
% 2.17/1.81 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2)))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2488])).
% 2.17/1.81 thf(f2488,plain,(
% 2.17/1.81 (($true => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2))) = $true)),
% 2.17/1.81 inference(backward_demodulation,[status(thm)],[f2485,f2487])).
% 2.17/1.81 thf(f2487,plain,(
% 2.17/1.81 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2)) = $true)),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2486])).
% 2.17/1.81 thf(f2486,plain,(
% 2.17/1.81 ($true = ($true => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2))))),
% 2.17/1.81 inference(backward_demodulation,[status(thm)],[f2484,f2483])).
% 2.17/1.81 thf(f2483,plain,(
% 2.17/1.81 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (rev @ list @ list @ nat @ sK3 @ (app @ list @ list @ nat @ sK3 @ zero @ (rev @ list @ list @ nat @ sK3 @ sK2) @ nil @ list @ list @ nat))))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2481])).
% 2.17/1.81 thf(f2481,plain,(
% 2.17/1.81 (($true => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (rev @ list @ list @ nat @ sK3 @ (app @ list @ list @ nat @ sK3 @ zero @ (rev @ list @ list @ nat @ sK3 @ sK2) @ nil @ list @ list @ nat)))) = $true)),
% 2.17/1.81 inference(superposition,[status(thm)],[f1495,f1177])).
% 2.17/1.81 thf(f1177,plain,(
% 2.17/1.81 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ sK2 @ sK2) = $true)),
% 2.17/1.81 inference(binary_proxy_clausification,[status(thm)],[f1152])).
% 2.17/1.81 thf(f1152,plain,(
% 2.17/1.81 ($false = ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ sK2 @ sK2) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ sK2)))),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1150])).
% 2.17/1.81 thf(f1150,plain,(
% 2.17/1.81 ($false = ((^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ sK2 @ sK2) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ sK2)) @ sK2))) @ sK3))),
% 2.17/1.81 inference(sigma_clausification,[status(thm)],[f1139])).
% 2.17/1.81 thf(f1139,plain,(
% 2.17/1.81 ($false = (!! @ nat @ (^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ sK2 @ sK2) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ sK2)) @ sK2)))))),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1138])).
% 2.17/1.81 thf(f1138,plain,(
% 2.17/1.81 ($false = ((^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0))))) @ sK2))),
% 2.17/1.81 inference(sigma_clausification,[status(thm)],[f1110])).
% 2.17/1.81 thf(f1110,plain,(
% 2.17/1.81 ($false = (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0)))))))),
% 2.17/1.81 inference(not_proxy_clausification,[status(thm)],[f95])).
% 2.17/1.81 thf(f95,plain,(
% 2.17/1.81 ($true = (~ (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0))))))))),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f64])).
% 2.17/1.81 thf(f64,plain,(
% 2.17/1.81 ($true = (~ (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0))))))))),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f63])).
% 2.17/1.81 thf(f63,plain,(
% 2.17/1.81 ~! [X0 : nat,X1 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ X1))),
% 2.17/1.81 inference(rectify,[status(thm)],[f25])).
% 2.17/1.81 thf(f25,negated_conjecture,(
% 2.17/1.81 ~! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ X15))),
% 2.17/1.81 inference(negated_conjecture,[status(cth)],[f24])).
% 2.17/1.81 thf(f24,conjecture,(
% 2.17/1.81 ! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ X15))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',list_rev_invol)).
% 2.17/1.81 thf(f1495,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (rev @ list @ list @ nat @ X2 @ (app @ list @ list @ nat @ X2 @ zero @ (rev @ list @ list @ nat @ X2 @ X1) @ nil @ list @ list @ nat)))) = $true)) )),
% 2.17/1.81 inference(forward_demodulation,[status(thm)],[f1494,f149])).
% 2.17/1.81 thf(f149,plain,(
% 2.17/1.81 ( ! [X0 : nat] : (((plus @ X0 @ zero) = X0)) )),
% 2.17/1.81 inference(superposition,[status(thm)],[f142,f119])).
% 2.17/1.81 thf(f119,plain,(
% 2.17/1.81 ( ! [X1 : nat] : (((plus @ zero @ X1) = X1)) )),
% 2.17/1.81 inference(equality_proxy_clausification,[status(thm)],[f118])).
% 2.17/1.81 thf(f118,plain,(
% 2.17/1.81 ( ! [X1 : nat] : (($true = ((plus @ zero @ X1) = X1))) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f117])).
% 2.17/1.81 thf(f117,plain,(
% 2.17/1.81 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((plus @ zero @ Y0) = Y0)) @ X1) = $true)) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f96])).
% 2.17/1.81 thf(f96,plain,(
% 2.17/1.81 ((!! @ nat @ (^[Y0 : nat]: ((plus @ zero @ Y0) = Y0))) = $true)),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f28])).
% 2.17/1.81 thf(f28,plain,(
% 2.17/1.81 ((!! @ nat @ (^[Y0 : nat]: ((plus @ zero @ Y0) = Y0))) = $true)),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f27])).
% 2.17/1.81 thf(f27,plain,(
% 2.17/1.81 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 2.17/1.81 inference(rectify,[status(thm)],[f11])).
% 2.17/1.81 thf(f11,axiom,(
% 2.17/1.81 ! [X8 : nat] : ((plus @ zero @ X8) = X8)),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',ax1)).
% 2.17/1.81 thf(f142,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : nat] : (((plus @ X2 @ X1) = (plus @ X1 @ X2))) )),
% 2.17/1.81 inference(equality_proxy_clausification,[status(thm)],[f141])).
% 2.17/1.81 thf(f141,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : nat] : (($true = ((plus @ X2 @ X1) = (plus @ X1 @ X2)))) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f140])).
% 2.17/1.81 thf(f140,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((plus @ Y0 @ X1) = (plus @ X1 @ Y0))) @ X2))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f139])).
% 2.17/1.81 thf(f139,plain,(
% 2.17/1.81 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((plus @ Y0 @ X1) = (plus @ X1 @ Y0)))))) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f138])).
% 2.17/1.81 thf(f138,plain,(
% 2.17/1.81 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((plus @ Y1 @ Y0) = (plus @ Y0 @ Y1))))) @ X1))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f93])).
% 2.17/1.81 thf(f93,plain,(
% 2.17/1.81 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((plus @ Y1 @ Y0) = (plus @ Y0 @ Y1)))))))),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f72])).
% 2.17/1.81 thf(f72,plain,(
% 2.17/1.81 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((plus @ Y1 @ Y0) = (plus @ Y0 @ Y1)))))))),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f71])).
% 2.17/1.81 thf(f71,plain,(
% 2.17/1.81 ! [X0 : nat,X1 : nat] : ((plus @ X0 @ X1) = (plus @ X1 @ X0))),
% 2.17/1.81 inference(rectify,[status(thm)],[f17])).
% 2.17/1.81 thf(f17,axiom,(
% 2.17/1.81 ! [X8 : nat,X13 : nat] : ((plus @ X8 @ X13) = (plus @ X13 @ X8))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',plus_com)).
% 2.17/1.81 thf(f1494,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (rev @ list @ list @ nat @ (plus @ X2 @ zero) @ (app @ list @ list @ nat @ X2 @ zero @ (rev @ list @ list @ nat @ X2 @ X1) @ nil @ list @ list @ nat)))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1489])).
% 2.17/1.81 thf(f1489,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ Y0 @ zero) @ (app @ list @ list @ nat @ Y0 @ zero @ (rev @ list @ list @ nat @ Y0 @ X1) @ nil @ list @ list @ nat))))) @ X2) = $true)) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f1462])).
% 2.17/1.81 thf(f1462,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (((!! @ nat @ (^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ Y0 @ zero) @ (app @ list @ list @ nat @ Y0 @ zero @ (rev @ list @ list @ nat @ Y0 @ X1) @ nil @ list @ list @ nat)))))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1461])).
% 2.17/1.81 thf(f1461,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (($true = ((^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat))))))) @ X1))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f99])).
% 2.17/1.81 thf(f99,plain,(
% 2.17/1.81 ($true = (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat)))))))))),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f32])).
% 2.17/1.81 thf(f32,plain,(
% 2.17/1.81 ($true = (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat)))))))))),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f31])).
% 2.17/1.81 thf(f31,plain,(
% 2.17/1.81 ! [X0 : nat,X1 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ X0 @ zero) @ (app @ list @ list @ nat @ X0 @ zero @ (rev @ list @ list @ nat @ X0 @ X1) @ nil @ list @ list @ nat))))),
% 2.17/1.81 inference(rectify,[status(thm)],[f20])).
% 2.17/1.81 thf(f20,axiom,(
% 2.17/1.81 ! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (rev @ list @ list @ nat @ (plus @ X8 @ zero) @ (app @ list @ list @ nat @ X8 @ zero @ (rev @ list @ list @ nat @ X8 @ X15) @ nil @ list @ list @ nat))))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',list_rev_invol_step1)).
% 2.17/1.81 thf(f2484,plain,(
% 2.17/1.81 ($true = ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (rev @ list @ list @ nat @ sK3 @ (app @ list @ list @ nat @ sK3 @ zero @ (rev @ list @ list @ nat @ sK3 @ sK2) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2))))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2478])).
% 2.17/1.81 thf(f2478,plain,(
% 2.17/1.81 ($true = ($true => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (rev @ list @ list @ nat @ sK3 @ (app @ list @ list @ nat @ sK3 @ zero @ (rev @ list @ list @ nat @ sK3 @ sK2) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2)))))),
% 2.17/1.81 inference(superposition,[status(thm)],[f2413,f1177])).
% 2.17/1.81 thf(f2413,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : (($true = ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (rev @ list @ list @ nat @ X2 @ (app @ list @ list @ nat @ X2 @ zero @ (rev @ list @ list @ nat @ X2 @ X1) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (app @ list @ list @ nat @ zero @ X2 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)))))) )),
% 2.17/1.81 inference(forward_demodulation,[status(thm)],[f2409,f149])).
% 2.17/1.81 thf(f2409,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (rev @ list @ list @ nat @ (plus @ X2 @ zero) @ (app @ list @ list @ nat @ X2 @ zero @ (rev @ list @ list @ nat @ X2 @ X1) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (app @ list @ list @ nat @ zero @ X2 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f2407])).
% 2.17/1.81 thf(f2407,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ Y0 @ zero) @ (app @ list @ list @ nat @ Y0 @ zero @ (rev @ list @ list @ nat @ Y0 @ X1) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1))))) @ X2) = $true)) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f2330])).
% 2.17/1.81 thf(f2330,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (((!! @ nat @ (^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ Y0 @ zero) @ (app @ list @ list @ nat @ Y0 @ zero @ (rev @ list @ list @ nat @ Y0 @ X1) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)))))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f2329])).
% 2.17/1.81 thf(f2329,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : ((((^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0))))))) @ X1) = $true)) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f89])).
% 2.17/1.81 thf(f89,plain,(
% 2.17/1.81 ((!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0)))))))) = $true)),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f52])).
% 2.17/1.81 thf(f52,plain,(
% 2.17/1.81 ((!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (rev @ list @ list @ nat @ (plus @ Y1 @ zero) @ (app @ list @ list @ nat @ Y1 @ zero @ (rev @ list @ list @ nat @ Y1 @ Y0) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0)))))))) = $true)),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f51])).
% 2.17/1.81 thf(f51,plain,(
% 2.17/1.81 ! [X0 : nat,X1 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (rev @ list @ list @ nat @ (plus @ X0 @ zero) @ (app @ list @ list @ nat @ X0 @ zero @ (rev @ list @ list @ nat @ X0 @ X1) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (app @ list @ list @ nat @ zero @ X0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1))))),
% 2.17/1.81 inference(rectify,[status(thm)],[f21])).
% 2.17/1.81 thf(f21,axiom,(
% 2.17/1.81 ! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (rev @ list @ list @ nat @ (plus @ X8 @ zero) @ (app @ list @ list @ nat @ X8 @ zero @ (rev @ list @ list @ nat @ X8 @ X15) @ nil @ list @ list @ nat))) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (app @ list @ list @ nat @ zero @ X8 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X15))))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',list_rev_invol_step2)).
% 2.17/1.81 thf(f2485,plain,(
% 2.17/1.81 ($true = ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2))))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2479])).
% 2.17/1.81 thf(f2479,plain,(
% 2.17/1.81 (($true => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ sK2)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2)))) = $true)),
% 2.17/1.81 inference(superposition,[status(thm)],[f2150,f1177])).
% 2.17/1.81 thf(f2150,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (app @ list @ list @ nat @ zero @ X2 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (app @ list @ list @ nat @ zero @ X2 @ nil @ list @ list @ nat @ X1)))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f2145])).
% 2.17/1.81 thf(f2145,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ nil @ list @ list @ nat @ X1))))) @ X2) = $true)) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f2106])).
% 2.17/1.81 thf(f2106,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ nil @ list @ list @ nat @ X1)))))))) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f2105])).
% 2.17/1.81 thf(f2105,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (($true = ((^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0))))))) @ X1))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f90])).
% 2.17/1.81 thf(f90,plain,(
% 2.17/1.81 ($true = (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0)))))))))),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f54])).
% 2.17/1.81 thf(f54,plain,(
% 2.17/1.81 ($true = (!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0)))))))))),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f53])).
% 2.17/1.81 thf(f53,plain,(
% 2.17/1.81 ! [X0 : nat,X1 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (app @ list @ list @ nat @ zero @ X0 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1))))),
% 2.17/1.81 inference(rectify,[status(thm)],[f22])).
% 2.17/1.81 thf(f22,axiom,(
% 2.17/1.81 ! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (app @ list @ list @ nat @ zero @ X8 @ (rev @ list @ list @ nat @ zero @ nil @ list @ list @ nat) @ X15)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (app @ list @ list @ nat @ zero @ X8 @ nil @ list @ list @ nat @ X15))))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',list_rev_invol_step3)).
% 2.17/1.81 thf(f2020,plain,(
% 2.17/1.81 ($true = (~ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2))))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2019])).
% 2.17/1.81 thf(f2019,plain,(
% 2.17/1.81 ($true = ($true => (~ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2)))))),
% 2.17/1.81 inference(forward_demodulation,[status(thm)],[f2018,f1177])).
% 2.17/1.81 thf(f2018,plain,(
% 2.17/1.81 (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ sK2 @ sK2) => (~ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2)))) = $true)),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f2017])).
% 2.17/1.81 thf(f2017,plain,(
% 2.17/1.81 (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ sK2 @ sK2) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ (app @ list @ list @ nat @ zero @ sK3 @ nil @ list @ list @ nat @ sK2)) => $false)) = $true)),
% 2.17/1.81 inference(superposition,[status(thm)],[f1871,f1179])).
% 2.17/1.81 thf(f1179,plain,(
% 2.17/1.81 ($false = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ sK2))),
% 2.17/1.81 inference(boolean_simplification,[status(thm)],[f1178])).
% 2.17/1.81 thf(f1178,plain,(
% 2.17/1.81 ($false = ($true => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK3 @ (rev @ list @ list @ nat @ sK3 @ (rev @ list @ list @ nat @ sK3 @ sK2)) @ sK2)))),
% 2.17/1.81 inference(backward_demodulation,[status(thm)],[f1152,f1177])).
% 2.17/1.81 thf(f1871,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ (app @ list @ list @ nat @ zero @ X2 @ nil @ list @ list @ nat @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ (rev @ list @ list @ nat @ X2 @ (rev @ list @ list @ nat @ X2 @ X1)) @ X1))) = $true)) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1869])).
% 2.17/1.81 thf(f1869,plain,(
% 2.17/1.81 ( ! [X2 : nat,X1 : list @ list @ list @ nat] : (($true = ((^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ nil @ list @ list @ nat @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ X1)))) @ X2))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f1766])).
% 2.17/1.81 thf(f1766,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ (app @ list @ list @ nat @ zero @ Y0 @ nil @ list @ list @ nat @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y0 @ (rev @ list @ list @ nat @ Y0 @ (rev @ list @ list @ nat @ Y0 @ X1)) @ X1))))))) )),
% 2.17/1.81 inference(beta_eta_normalization,[status(thm)],[f1765])).
% 2.17/1.81 thf(f1765,plain,(
% 2.17/1.81 ( ! [X1 : list @ list @ list @ nat] : (($true = ((^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0)))))) @ X1))) )),
% 2.17/1.81 inference(pi_clausification,[status(thm)],[f105])).
% 2.17/1.81 thf(f105,plain,(
% 2.17/1.81 ((!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0))))))) = $true)),
% 2.17/1.81 inference(cnf_transformation,[status(thm)],[f46])).
% 2.17/1.81 thf(f46,plain,(
% 2.17/1.81 ((!! @ list @ list @ list @ nat @ (^[Y0 : list @ list @ list @ nat]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ Y0 @ Y0) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ (app @ list @ list @ nat @ zero @ Y1 @ nil @ list @ list @ nat @ Y0)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ Y1 @ (rev @ list @ list @ nat @ Y1 @ (rev @ list @ list @ nat @ Y1 @ Y0)) @ Y0))))))) = $true)),
% 2.17/1.81 inference(fool_elimination,[status(thm)],[f45])).
% 2.17/1.81 thf(f45,plain,(
% 2.17/1.81 ! [X0 : nat,X1 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ (rev @ list @ list @ nat @ X0 @ (rev @ list @ list @ nat @ X0 @ X1)) @ X1)))),
% 2.17/1.81 inference(rectify,[status(thm)],[f23])).
% 2.17/1.81 thf(f23,axiom,(
% 2.17/1.81 ! [X8 : nat,X15 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ X15 @ X15) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ (app @ list @ list @ nat @ zero @ X8 @ nil @ list @ list @ nat @ X15)) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X8 @ (rev @ list @ list @ nat @ X8 @ (rev @ list @ list @ nat @ X8 @ X15)) @ X15)))),
% 2.17/1.81 file('/export/starexec/sandbox2/tmp/tmp.7QQELFDdzm/DTF2THF_21362.p',list_rev_invol_step4)).
% 2.17/1.81 % SZS output end Proof for DTF2THF_21362
% 2.17/1.81 % (21659)------------------------------
% 2.17/1.81 % (21659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.81 % (21659)Termination reason: Refutation
% 2.17/1.81
% 2.17/1.81 % (21659)Memory used [KB]: 7291
% 2.17/1.81 % (21659)Time elapsed: 0.321 s
% 2.17/1.81 % (21659)Instructions burned: 982 (million)
% 2.17/1.81 % (21659)------------------------------
% 2.17/1.81 % (21659)------------------------------
% 2.17/1.81 % (21647)Success in time 0.358 s
%------------------------------------------------------------------------------