%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT408^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 1.83s 1.71s
% Output : Refutation 1.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT408^1 : TPTP v9.2.1. Released v9.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:18:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : DAT408^1 : TPTP v9.2.1. Released v9.2.0.
% 0.32/0.49 % Domain : Data Structures
% 0.32/0.49 % Problem : List reversal involution polymorphic, step 4 type instantiated
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English : List reversal involution for polymorphic fixed-length lists. The
% 0.32/0.49 % proof is split into smaller steps. To simplify proof search, the
% 0.32/0.49 % axioms in each problem file have been preselected.
% 0.32/0.49
% 0.32/0.49 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.32/0.49 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.32/0.49 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.32/0.49 % Source : [Rot25]
% 0.32/0.49 % Names : ListReversalInvolution/list-rev-invol-step4-typeInstantiated.p [Rot25]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : ? v9.2.0
% 0.32/0.49 % Syntax : Number of formulae : 18 ( 6 unt; 9 typ; 0 def)
% 0.32/0.49 % Number of atoms : 10 ( 10 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.32/0.49 % Number of connectives : 121 ( 3 ~; 0 |; 0 &; 113 @)
% 0.32/0.49 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 8 ( 4 avg)
% 0.32/0.49 % Number of types : 2 ( 1 usr)
% 0.32/0.49 % Number of type decls : 9 ( 4 !>P; 3 !>D)
% 0.32/0.49 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 9 ( 8 usr; 1 con; 0-5 aty)
% 0.32/0.49 % Number of variables : 25 ( 0 ^; 17 !; 0 ?; 25 :)
% 0.32/0.49 % ( 8 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.49 % SPC : DH1_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments :
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(nat_type,type,
% 0.32/0.49 nat: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(zero_type,type,
% 0.32/0.49 zero: nat ).
% 0.32/0.49
% 0.32/0.49 thf(suc_type,type,
% 0.32/0.49 suc: nat > nat ).
% 0.32/0.49
% 0.32/0.49 thf(plus_type,type,
% 0.32/0.49 plus: nat > nat > nat ).
% 0.32/0.49
% 0.32/0.49 thf(list_type,type,
% 0.32/0.49 list: $tType > nat > $tType ).
% 0.32/0.49
% 0.32/0.49 thf(nil_type,type,
% 0.32/0.49 nil:
% 0.32/0.49 !>[A: $tType] : ( list @ A @ zero ) ).
% 0.32/0.49
% 0.32/0.49 thf(cons_type,type,
% 0.32/0.49 cons:
% 0.32/0.49 !>[A: $tType,N: nat] : ( A > ( list @ A @ N ) > ( list @ A @ ( suc @ N ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(app_type,type,
% 0.32/0.49 app:
% 0.32/0.49 !>[A: $tType,N: nat,M: nat] : ( ( list @ A @ N ) > ( list @ A @ M ) > ( list @ A @ ( plus @ N @ M ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(rev_type,type,
% 0.32/0.49 rev:
% 0.32/0.49 !>[A: $tType,N: nat] : ( ( list @ A @ N ) > ( list @ A @ N ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(peano1,axiom,
% 0.32/0.49 ! [N: nat] :
% 0.32/0.49 ( ( suc @ N )
% 0.32/0.49 != zero ) ).
% 0.32/0.49
% 0.32/0.49 thf(peano2,axiom,
% 0.32/0.49 ! [N: nat,M: nat] :
% 0.32/0.49 ( ( N != M )
% 0.32/0.49 => ( ( suc @ N )
% 0.32/0.49 != ( suc @ M ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(peano3,axiom,
% 0.32/0.49 ! [P: nat > $o] :
% 0.32/0.49 ( ( P @ zero )
% 0.32/0.49 => ( ! [M: nat] :
% 0.32/0.49 ( ( P @ M )
% 0.32/0.49 => ( P @ ( suc @ M ) ) )
% 0.32/0.49 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax1,axiom,
% 0.32/0.49 ! [N: nat] :
% 0.32/0.49 ( ( plus @ zero @ N )
% 0.32/0.49 = N ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax2,axiom,
% 0.32/0.49 ! [N: nat,M: nat] :
% 0.32/0.49 ( ( plus @ ( suc @ N ) @ M )
% 0.32/0.49 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax3,axiom,
% 0.32/0.49 ! [A: $tType,N: nat,X: list @ A @ N] :
% 0.32/0.49 ( ( app @ A @ zero @ N @ ( nil @ A ) @ X )
% 0.32/0.49 = X ) ).
% 0.32/0.49
% 0.32/0.49 thf(plus_com,axiom,
% 0.32/0.49 ! [N: nat,M: nat] :
% 0.32/0.49 ( ( plus @ N @ M )
% 0.32/0.49 = ( plus @ M @ N ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(plus1r,axiom,
% 0.32/0.49 ! [N: nat] :
% 0.32/0.49 ( ( suc @ N )
% 0.32/0.49 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(list_rev_invol_step4,conjecture,
% 0.32/0.49 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.32/0.49 ( ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.32/0.49 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ N @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) @ L ) )
% 0.32/0.49 => ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.32/0.49 = L ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.79/1.31 ---- Embedded in THF ---
% 1.79/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.31 %%% Generated on Tue Feb 24 06:18:10 EST 2026
% 1.79/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.31 %%% Logic specification used:
% 1.79/1.31 %%% thf(spec, logic, $$dhol).
% 1.79/1.31
% 1.79/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2DTF923.p
% 1.79/1.31 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.79/1.31 thf(is_per, definition, (! [A:$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)))))))))).
% 1.79/1.31 thf(nat_type, type, nat: $tType).
% 1.79/1.31 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.79/1.31 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.79/1.31 thf(zero_type, type, zero: nat).
% 1.79/1.31 thf(suc_type, type, suc: (nat > nat)).
% 1.79/1.31 thf(plus_type, type, plus: (nat > (nat > nat))).
% 1.79/1.31 thf(list_type, type, list: ($tType > $tType)).
% 1.79/1.31 thf(listStar, type, 'listStar': (!> [A:$tType]: (((A > (A > $o)) > (nat > ((list @ A) > ((list @ A) > $o))))))).
% 1.79/1.31 thf('\'listStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:nat]: (((isPer @ (list @ B)) @ (((listStar @ B) @ BStar) @ C)))))))).
% 1.79/1.31 thf(nil_type, type, nil: (!> [A:$tType]: ((list @ A)))).
% 1.79/1.31 thf(nil_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (nil @ A)) @ (nil @ A)))))).
% 1.79/1.31 thf(cons_type, type, cons: (!> [A:$tType]: ((nat > (A > ((list @ A) > (list @ A))))))).
% 1.79/1.31 thf(cons_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:A,D_prime:A]: (((D = D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ ((((cons @ A) @ N) @ D) @ D0)) @ ((((cons @ A) @ N) @ D_prime) @ D0_prime)))))))))))))).
% 1.79/1.31 thf(app_type, type, app: (!> [A:$tType]: ((nat > (nat > ((list @ A) > ((list @ A) > (list @ A)))))))).
% 1.79/1.31 thf(app_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ M) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ M)) @ (((((app @ A) @ N) @ M) @ D) @ D0)) @ (((((app @ A) @ N) @ M) @ D_prime) @ D0_prime)))))))))))))))).
% 1.79/1.31 thf(rev_type, type, rev: (!> [A:$tType]: ((nat > ((list @ A) > (list @ A)))))).
% 1.79/1.31 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))))))))))).
% 1.79/1.31 thf(peano1, axiom, (! [N:nat]: (((suc @ N) != zero)))).
% 1.79/1.31 thf(peano2, axiom, (! [N:nat]: ((! [M:nat]: (((N != M) => ((suc @ N) != (suc @ M)))))))).
% 1.79/1.31 thf(peano3, axiom, (! [P:(nat > $o)]: (((P @ zero) => ((! [M:nat]: (((P @ M) => (P @ (suc @ M))))) => (! [N:nat]: ((P @ N)))))))).
% 1.79/1.31 thf(ax1, axiom, (! [N:nat]: ((((plus @ zero) @ N) = N)))).
% 1.79/1.31 thf(ax2, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ (suc @ N)) @ M) = (suc @ ((plus @ N) @ M)))))))).
% 1.79/1.31 thf(ax3, axiom, (! [A:$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)))))))))).
% 1.79/1.31 thf(plus_com, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ N) @ M) = ((plus @ M) @ N))))))).
% 1.79/1.31 thf(plus1r, axiom, (! [N:nat]: (((suc @ N) = ((plus @ N) @ (suc @ zero)))))).
% 1.79/1.31 thf(list_rev_invol_step4, 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))) @ (((((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)))))))).
% 1.79/1.31 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2DTF923.p
% 1.79/1.31 ------------------------
% 1.79/1.32 ---- Cleaned THF ---
% 1.79/1.33 thf(is_per_type,type,
% 1.79/1.33 isPer:
% 1.79/1.33 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.79/1.33
% 1.79/1.33 thf(is_per,definition,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 <=> ( ! [X: A,Y: A] :
% 1.79/1.33 ( ( AStar @ X @ Y )
% 1.79/1.33 => ( AStar @ Y @ X ) )
% 1.79/1.33 & ! [X: A,Y: A,Z: A] :
% 1.79/1.33 ( ( AStar @ X @ Y )
% 1.79/1.33 => ( ( AStar @ Y @ Z )
% 1.79/1.33 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(nat_type,type,
% 1.79/1.33 nat: $tType ).
% 1.79/1.33
% 1.79/1.33 thf(natStar,type,
% 1.79/1.33 natStar: nat > nat > $o ).
% 1.79/1.33
% 1.79/1.33 thf(natStar_is_eq,axiom,
% 1.79/1.33 ! [X: nat,Y: nat] :
% 1.79/1.33 ( ( natStar @ X @ Y )
% 1.79/1.33 <=> ( X = Y ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(zero_type,type,
% 1.79/1.33 zero: nat ).
% 1.79/1.33
% 1.79/1.33 thf(suc_type,type,
% 1.79/1.33 suc: nat > nat ).
% 1.79/1.33
% 1.79/1.33 thf(plus_type,type,
% 1.79/1.33 plus: nat > nat > nat ).
% 1.79/1.33
% 1.79/1.33 thf(list_type,type,
% 1.79/1.33 list: $tType > $tType ).
% 1.79/1.33
% 1.79/1.33 thf(listStar,type,
% 1.79/1.33 listStar:
% 1.79/1.33 !>[A: $tType] : ( ( A > A > $o ) > nat > ( list @ A ) > ( list @ A ) > $o ) ).
% 1.79/1.33
% 1.79/1.33 thf('\'listStar\'_is_per',axiom,
% 1.79/1.33 ! [B: $tType,BStar: B > B > $o] :
% 1.79/1.33 ( ( isPer @ B @ BStar )
% 1.79/1.33 => ! [C: nat] : ( isPer @ ( list @ B ) @ ( listStar @ B @ BStar @ C ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(nil_type,type,
% 1.79/1.33 nil:
% 1.79/1.33 !>[A: $tType] : ( list @ A ) ).
% 1.79/1.33
% 1.79/1.33 thf(nil_tp_ax,axiom,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 => ( listStar @ A @ AStar @ zero @ ( nil @ A ) @ ( nil @ A ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(cons_type,type,
% 1.79/1.33 cons:
% 1.79/1.33 !>[A: $tType] : ( nat > A > ( list @ A ) > ( list @ A ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(cons_tp_ax,axiom,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 => ! [N: nat,D: A,D_prime: A] :
% 1.79/1.33 ( ( D = D_prime )
% 1.79/1.33 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.79/1.33 ( ( listStar @ A @ AStar @ N @ D0 @ D0_prime )
% 1.79/1.33 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( cons @ A @ N @ D @ D0 ) @ ( cons @ A @ N @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(app_type,type,
% 1.79/1.33 app:
% 1.79/1.33 !>[A: $tType] : ( nat > nat > ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(app_tp_ax,axiom,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 => ! [N: nat,M: nat,D: list @ A,D_prime: list @ A] :
% 1.79/1.33 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.79/1.33 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.79/1.33 ( ( listStar @ A @ AStar @ M @ D0 @ D0_prime )
% 1.79/1.33 => ( listStar @ A @ AStar @ ( plus @ N @ M ) @ ( app @ A @ N @ M @ D @ D0 ) @ ( app @ A @ N @ M @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(rev_type,type,
% 1.79/1.33 rev:
% 1.79/1.33 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ A ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(rev_tp_ax,axiom,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 => ! [N: nat,D: list @ A,D_prime: list @ A] :
% 1.79/1.33 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.79/1.33 => ( listStar @ A @ AStar @ N @ ( rev @ A @ N @ D ) @ ( rev @ A @ N @ D_prime ) ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(peano1,axiom,
% 1.79/1.33 ! [N: nat] :
% 1.79/1.33 ( ( suc @ N )
% 1.79/1.33 != zero ) ).
% 1.79/1.33
% 1.79/1.33 thf(peano2,axiom,
% 1.79/1.33 ! [N: nat,M: nat] :
% 1.79/1.33 ( ( N != M )
% 1.79/1.33 => ( ( suc @ N )
% 1.79/1.33 != ( suc @ M ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(peano3,axiom,
% 1.79/1.33 ! [P: nat > $o] :
% 1.79/1.33 ( ( P @ zero )
% 1.79/1.33 => ( ! [M: nat] :
% 1.79/1.33 ( ( P @ M )
% 1.79/1.33 => ( P @ ( suc @ M ) ) )
% 1.79/1.33 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(ax1,axiom,
% 1.79/1.33 ! [N: nat] :
% 1.79/1.33 ( ( plus @ zero @ N )
% 1.79/1.33 = N ) ).
% 1.79/1.33
% 1.79/1.33 thf(ax2,axiom,
% 1.79/1.33 ! [N: nat,M: nat] :
% 1.79/1.33 ( ( plus @ ( suc @ N ) @ M )
% 1.79/1.33 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(ax3,axiom,
% 1.79/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.79/1.33 ( ( isPer @ A @ AStar )
% 1.79/1.33 => ! [N: nat,X: list @ A] :
% 1.79/1.33 ( ( listStar @ A @ AStar @ N @ X @ X )
% 1.79/1.33 => ( listStar @ A @ AStar @ ( plus @ zero @ N ) @ ( app @ A @ zero @ N @ ( nil @ A ) @ X ) @ X ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(plus_com,axiom,
% 1.79/1.33 ! [N: nat,M: nat] :
% 1.79/1.33 ( ( plus @ N @ M )
% 1.79/1.33 = ( plus @ M @ N ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(plus1r,axiom,
% 1.79/1.33 ! [N: nat] :
% 1.79/1.33 ( ( suc @ N )
% 1.79/1.33 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.79/1.33
% 1.79/1.33 thf(list_rev_invol_step4,conjecture,
% 1.79/1.33 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 1.79/1.33 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 1.79/1.33 => ( ( 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 ) )
% 1.79/1.33 => ( 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 ) ) ) ).
% 1.79/1.33 ------------------------
% 1.79/1.34 % (1314)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/18Mi)
% 1.79/1.35 % (1308)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/183Mi)
% 1.79/1.35 % (1309)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_923 for (2999ds/4Mi)
% 1.79/1.35 % (1314)Instruction limit reached!
% 1.79/1.35 % (1314)------------------------------
% 1.79/1.35 % (1314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (1314)Termination reason: Unknown
% 1.79/1.35 % (1314)Termination phase: Saturation
% 1.79/1.35
% 1.79/1.35 % (1314)Memory used [KB]: 5628
% 1.79/1.35 % (1314)Time elapsed: 0.008 s
% 1.79/1.35 % (1314)Instructions burned: 20 (million)
% 1.79/1.35 % (1314)------------------------------
% 1.79/1.35 % (1314)------------------------------
% 1.79/1.35 % (1310)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_923 for (2999ds/27Mi)
% 1.79/1.35 % (1311)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/2Mi)
% 1.79/1.35 % (1312)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_923 for (2999ds/2Mi)
% 1.79/1.35 % (1313)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_923 for (2999ds/275Mi)
% 1.79/1.35 % (1311)Instruction limit reached!
% 1.79/1.35 % (1311)------------------------------
% 1.79/1.35 % (1311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (1311)Termination reason: Unknown
% 1.79/1.35 % (1311)Termination phase: shuffling
% 1.79/1.35
% 1.79/1.35 % (1311)Memory used [KB]: 1023
% 1.79/1.35 % (1311)Time elapsed: 0.003 s
% 1.79/1.35 % (1311)Instructions burned: 2 (million)
% 1.79/1.35 % (1311)------------------------------
% 1.79/1.35 % (1311)------------------------------
% 1.79/1.35 % (1312)Instruction limit reached!
% 1.79/1.35 % (1312)------------------------------
% 1.79/1.35 % (1312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (1312)Termination reason: Unknown
% 1.79/1.35 % (1312)Termination phase: shuffling
% 1.79/1.35
% 1.79/1.35 % (1312)Memory used [KB]: 1023
% 1.79/1.35 % (1312)Time elapsed: 0.003 s
% 1.79/1.35 % (1312)Instructions burned: 2 (million)
% 1.79/1.35 % (1312)------------------------------
% 1.79/1.35 % (1312)------------------------------
% 1.79/1.35 % (1309)Instruction limit reached!
% 1.79/1.35 % (1309)------------------------------
% 1.79/1.35 % (1309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (1309)Termination reason: Unknown
% 1.79/1.35 % (1309)Termination phase: shuffling
% 1.79/1.35
% 1.79/1.35 % (1309)Memory used [KB]: 1023
% 1.79/1.35 % (1309)Time elapsed: 0.004 s
% 1.79/1.35 % (1309)Instructions burned: 4 (million)
% 1.79/1.35 % (1309)------------------------------
% 1.79/1.35 % (1309)------------------------------
% 1.79/1.36 % (1315)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/3Mi)
% 1.79/1.36 % (1315)Instruction limit reached!
% 1.79/1.36 % (1315)------------------------------
% 1.79/1.36 % (1315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.36 % (1315)Termination reason: Unknown
% 1.79/1.36 % (1315)Termination phase: Property scanning
% 1.79/1.36
% 1.79/1.36 % (1315)Memory used [KB]: 1023
% 1.79/1.36 % (1315)Time elapsed: 0.003 s
% 1.79/1.36 % (1315)Instructions burned: 4 (million)
% 1.79/1.36 % (1315)------------------------------
% 1.79/1.36 % (1315)------------------------------
% 1.79/1.36 % (1313)Refutation not found, incomplete strategy
% 1.79/1.36 % (1313)------------------------------
% 1.79/1.36 % (1313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.36 % (1313)Termination reason: Refutation not found, incomplete strategy
% 1.79/1.36
% 1.79/1.36
% 1.79/1.36 % (1313)Memory used [KB]: 5628
% 1.79/1.36 % (1313)Time elapsed: 0.014 s
% 1.79/1.36 % (1313)Instructions burned: 20 (million)
% 1.79/1.36 % (1313)------------------------------
% 1.79/1.36 % (1313)------------------------------
% 1.79/1.37 % (1310)Instruction limit reached!
% 1.79/1.37 % (1310)------------------------------
% 1.79/1.37 % (1310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.37 % (1310)Termination reason: Unknown
% 1.79/1.37 % (1310)Termination phase: Saturation
% 1.79/1.37
% 1.79/1.37 % (1310)Memory used [KB]: 5756
% 1.79/1.37 % (1310)Time elapsed: 0.019 s
% 1.79/1.37 % (1310)Instructions burned: 28 (million)
% 1.79/1.37 % (1310)------------------------------
% 1.79/1.37 % (1310)------------------------------
% 1.79/1.37 % (1316)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_923 for (2999ds/37Mi)
% 1.79/1.37 % (1317)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_923 for (2999ds/15Mi)
% 1.79/1.37 % (1318)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_923 for (2999ds/3Mi)
% 1.79/1.37 % (1318)Instruction limit reached!
% 1.79/1.37 % (1318)------------------------------
% 1.79/1.37 % (1318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.37 % (1318)Termination reason: Unknown
% 1.79/1.37 % (1318)Termination phase: Property scanning
% 1.79/1.37
% 1.79/1.37 % (1318)Memory used [KB]: 1023
% 1.79/1.37 % (1318)Time elapsed: 0.004 s
% 1.79/1.37 % (1318)Instructions burned: 4 (million)
% 1.79/1.37 % (1318)------------------------------
% 1.79/1.37 % (1318)------------------------------
% 1.79/1.37 % (1319)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_923 for (2999ds/1041Mi)
% 1.79/1.38 % (1317)Instruction limit reached!
% 1.79/1.38 % (1317)------------------------------
% 1.79/1.38 % (1317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (1317)Termination reason: Unknown
% 1.79/1.38 % (1317)Termination phase: Saturation
% 1.79/1.38
% 1.79/1.38 % (1317)Memory used [KB]: 5756
% 1.79/1.38 % (1317)Time elapsed: 0.011 s
% 1.79/1.38 % (1317)Instructions burned: 15 (million)
% 1.79/1.38 % (1317)------------------------------
% 1.79/1.38 % (1317)------------------------------
% 1.79/1.38 % (1321)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/16Mi)
% 1.79/1.38 % (1320)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/7Mi)
% 1.79/1.38 % (1321)Instruction limit reached!
% 1.79/1.38 % (1321)------------------------------
% 1.79/1.38 % (1321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (1321)Termination reason: Unknown
% 1.79/1.38 % (1321)Termination phase: Saturation
% 1.79/1.38
% 1.79/1.38 % (1321)Memory used [KB]: 5628
% 1.79/1.38 % (1321)Time elapsed: 0.007 s
% 1.79/1.38 % (1321)Instructions burned: 16 (million)
% 1.79/1.38 % (1321)------------------------------
% 1.79/1.38 % (1321)------------------------------
% 1.79/1.38 % (1320)Instruction limit reached!
% 1.79/1.38 % (1320)------------------------------
% 1.79/1.38 % (1320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (1320)Termination reason: Unknown
% 1.79/1.38 % (1320)Termination phase: Property scanning
% 1.79/1.38
% 1.79/1.38 % (1320)Memory used [KB]: 1023
% 1.79/1.38 % (1320)Time elapsed: 0.006 s
% 1.79/1.38 % (1320)Instructions burned: 8 (million)
% 1.79/1.38 % (1320)------------------------------
% 1.79/1.38 % (1320)------------------------------
% 1.79/1.39 % (1316)Instruction limit reached!
% 1.79/1.39 % (1316)------------------------------
% 1.79/1.39 % (1316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.39 % (1316)Termination reason: Unknown
% 1.79/1.39 % (1316)Termination phase: Saturation
% 1.79/1.39
% 1.79/1.39 % (1316)Memory used [KB]: 5756
% 1.79/1.39 % (1316)Time elapsed: 0.022 s
% 1.79/1.39 % (1316)Instructions burned: 37 (million)
% 1.79/1.39 % (1316)------------------------------
% 1.79/1.39 % (1316)------------------------------
% 1.79/1.39 % (1322)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_923 for (2999ds/3Mi)
% 1.79/1.39 % (1322)Instruction limit reached!
% 1.79/1.39 % (1322)------------------------------
% 1.79/1.39 % (1322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.39 % (1322)Termination reason: Unknown
% 1.79/1.39 % (1322)Termination phase: Property scanning
% 1.79/1.39
% 1.79/1.39 % (1322)Memory used [KB]: 1023
% 1.79/1.39 % (1322)Time elapsed: 0.004 s
% 1.79/1.39 % (1322)Instructions burned: 4 (million)
% 1.79/1.39 % (1322)------------------------------
% 1.79/1.39 % (1322)------------------------------
% 1.79/1.39 % (1324)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/7Mi)
% 1.79/1.39 % (1323)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_923 for (2999ds/3Mi)
% 1.79/1.39 % (1325)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/3Mi)
% 1.79/1.39 % (1324)Instruction limit reached!
% 1.79/1.39 % (1324)------------------------------
% 1.79/1.39 % (1324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.39 % (1324)Termination reason: Unknown
% 1.79/1.39 % (1324)Termination phase: Property scanning
% 1.79/1.39
% 1.79/1.39 % (1324)Memory used [KB]: 1023
% 1.79/1.39 % (1324)Time elapsed: 0.004 s
% 1.79/1.39 % (1324)Instructions burned: 7 (million)
% 1.79/1.39 % (1324)------------------------------
% 1.79/1.39 % (1324)------------------------------
% 1.79/1.40 % (1325)Instruction limit reached!
% 1.79/1.40 % (1325)------------------------------
% 1.79/1.40 % (1325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.40 % (1325)Termination reason: Unknown
% 1.79/1.40 % (1325)Termination phase: Property scanning
% 1.79/1.40
% 1.79/1.40 % (1325)Memory used [KB]: 1023
% 1.79/1.40 % (1325)Time elapsed: 0.003 s
% 1.79/1.40 % (1325)Instructions burned: 5 (million)
% 1.79/1.40 % (1325)------------------------------
% 1.79/1.40 % (1325)------------------------------
% 1.79/1.40 % (1323)Instruction limit reached!
% 1.79/1.40 % (1323)------------------------------
% 1.79/1.40 % (1323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.40 % (1323)Termination reason: Unknown
% 1.79/1.40 % (1323)Termination phase: Property scanning
% 1.79/1.40
% 1.79/1.40 % (1323)Memory used [KB]: 1023
% 1.79/1.40 % (1323)Time elapsed: 0.004 s
% 1.79/1.40 % (1323)Instructions burned: 4 (million)
% 1.79/1.40 % (1323)------------------------------
% 1.79/1.40 % (1323)------------------------------
% 1.83/1.40 % (1326)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/4Mi)
% 1.83/1.40 % (1326)Instruction limit reached!
% 1.83/1.40 % (1326)------------------------------
% 1.83/1.40 % (1326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.40 % (1326)Termination reason: Unknown
% 1.83/1.40 % (1326)Termination phase: Preprocessing 3
% 1.83/1.40
% 1.83/1.40 % (1326)Memory used [KB]: 1023
% 1.83/1.40 % (1326)Time elapsed: 0.004 s
% 1.83/1.40 % (1326)Instructions burned: 5 (million)
% 1.83/1.40 % (1326)------------------------------
% 1.83/1.40 % (1326)------------------------------
% 1.83/1.40 % (1328)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/710Mi)
% 1.83/1.41 % (1329)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/6Mi)
% 1.83/1.41 % (1327)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/18Mi)
% 1.83/1.41 % (1329)Instruction limit reached!
% 1.83/1.41 % (1329)------------------------------
% 1.83/1.41 % (1329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.41 % (1329)Termination reason: Unknown
% 1.83/1.41 % (1329)Termination phase: Property scanning
% 1.83/1.41
% 1.83/1.41 % (1329)Memory used [KB]: 1023
% 1.83/1.41 % (1329)Time elapsed: 0.004 s
% 1.83/1.41 % (1329)Instructions burned: 7 (million)
% 1.83/1.41 % (1329)------------------------------
% 1.83/1.41 % (1329)------------------------------
% 1.83/1.41 % (1330)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_923 for (2999ds/902Mi)
% 1.83/1.41 % (1331)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_923 for (2999ds/21Mi)
% 1.83/1.42 % (1332)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/5Mi)
% 1.83/1.42 % (1327)Instruction limit reached!
% 1.83/1.42 % (1327)------------------------------
% 1.83/1.42 % (1327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.42 % (1327)Termination reason: Unknown
% 1.83/1.42 % (1327)Termination phase: Saturation
% 1.83/1.42
% 1.83/1.42 % (1327)Memory used [KB]: 5628
% 1.83/1.42 % (1327)Time elapsed: 0.013 s
% 1.83/1.42 % (1327)Instructions burned: 19 (million)
% 1.83/1.42 % (1327)------------------------------
% 1.83/1.42 % (1327)------------------------------
% 1.83/1.42 % (1332)Instruction limit reached!
% 1.83/1.42 % (1332)------------------------------
% 1.83/1.42 % (1332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.42 % (1332)Termination reason: Unknown
% 1.83/1.42 % (1332)Termination phase: Property scanning
% 1.83/1.42
% 1.83/1.42 % (1332)Memory used [KB]: 1023
% 1.83/1.42 % (1332)Time elapsed: 0.003 s
% 1.83/1.42 % (1332)Instructions burned: 5 (million)
% 1.83/1.42 % (1332)------------------------------
% 1.83/1.42 % (1332)------------------------------
% 1.83/1.42 % (1331)Instruction limit reached!
% 1.83/1.42 % (1331)------------------------------
% 1.83/1.42 % (1331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.42 % (1331)Termination reason: Unknown
% 1.83/1.42 % (1331)Termination phase: Saturation
% 1.83/1.42
% 1.83/1.42 % (1331)Memory used [KB]: 5628
% 1.83/1.42 % (1331)Time elapsed: 0.009 s
% 1.83/1.42 % (1331)Instructions burned: 21 (million)
% 1.83/1.42 % (1331)------------------------------
% 1.83/1.42 % (1331)------------------------------
% 1.83/1.42 % (1330)Refutation not found, incomplete strategy
% 1.83/1.42 % (1330)------------------------------
% 1.83/1.42 % (1330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.42 % (1330)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.42
% 1.83/1.42
% 1.83/1.42 % (1330)Memory used [KB]: 5628
% 1.83/1.42 % (1330)Time elapsed: 0.012 s
% 1.83/1.42 % (1330)Instructions burned: 17 (million)
% 1.83/1.42 % (1330)------------------------------
% 1.83/1.42 % (1330)------------------------------
% 1.83/1.43 % (1334)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/377Mi)
% 1.83/1.43 % (1335)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_923 for (2999ds/779Mi)
% 1.83/1.43 % (1333)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_923 for (2999ds/6Mi)
% 1.83/1.44 % (1333)Instruction limit reached!
% 1.83/1.44 % (1333)------------------------------
% 1.83/1.44 % (1333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.44 % (1333)Termination reason: Unknown
% 1.83/1.44 % (1333)Termination phase: Property scanning
% 1.83/1.44
% 1.83/1.44 % (1333)Memory used [KB]: 1023
% 1.83/1.44 % (1333)Time elapsed: 0.004 s
% 1.83/1.44 % (1333)Instructions burned: 6 (million)
% 1.83/1.44 % (1333)------------------------------
% 1.83/1.44 % (1333)------------------------------
% 1.83/1.44 % (1336)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_923 for (2999ds/19Mi)
% 1.83/1.44 % (1336)Instruction limit reached!
% 1.83/1.44 % (1336)------------------------------
% 1.83/1.44 % (1336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.44 % (1336)Termination reason: Unknown
% 1.83/1.44 % (1336)Termination phase: Saturation
% 1.83/1.44
% 1.83/1.44 % (1336)Memory used [KB]: 5628
% 1.83/1.44 % (1336)Time elapsed: 0.008 s
% 1.83/1.44 % (1336)Instructions burned: 19 (million)
% 1.83/1.44 % (1336)------------------------------
% 1.83/1.44 % (1336)------------------------------
% 1.83/1.45 % (1308)Instruction limit reached!
% 1.83/1.45 % (1308)------------------------------
% 1.83/1.45 % (1308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.45 % (1308)Termination reason: Unknown
% 1.83/1.45 % (1308)Termination phase: Saturation
% 1.83/1.45
% 1.83/1.45 % (1308)Memory used [KB]: 6268
% 1.83/1.45 % (1308)Time elapsed: 0.099 s
% 1.83/1.45 % (1308)Instructions burned: 183 (million)
% 1.83/1.45 % (1308)------------------------------
% 1.83/1.45 % (1308)------------------------------
% 1.83/1.45 % (1337)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_923 for (2999ds/879Mi)
% 1.83/1.45 % (1338)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_923 for (2998ds/17Mi)
% 1.83/1.46 % (1339)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_923 for (2998ds/3Mi)
% 1.83/1.46 % (1339)Instruction limit reached!
% 1.83/1.46 % (1339)------------------------------
% 1.83/1.46 % (1339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.46 % (1339)Termination reason: Unknown
% 1.83/1.46 % (1339)Termination phase: Property scanning
% 1.83/1.46
% 1.83/1.46 % (1339)Memory used [KB]: 1023
% 1.83/1.46 % (1339)Time elapsed: 0.003 s
% 1.83/1.46 % (1339)Instructions burned: 4 (million)
% 1.83/1.46 % (1339)------------------------------
% 1.83/1.46 % (1339)------------------------------
% 1.83/1.46 % (1338)Instruction limit reached!
% 1.83/1.46 % (1338)------------------------------
% 1.83/1.46 % (1338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.46 % (1338)Termination reason: Unknown
% 1.83/1.46 % (1338)Termination phase: Saturation
% 1.83/1.46
% 1.83/1.46 % (1338)Memory used [KB]: 5628
% 1.83/1.46 % (1338)Time elapsed: 0.008 s
% 1.83/1.46 % (1338)Instructions burned: 17 (million)
% 1.83/1.46 % (1338)------------------------------
% 1.83/1.46 % (1338)------------------------------
% 1.83/1.47 % (1340)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_923 for (2998ds/30Mi)
% 1.83/1.47 % (1341)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_923 for (2998ds/127Mi)
% 1.83/1.48 % (1340)Instruction limit reached!
% 1.83/1.48 % (1340)------------------------------
% 1.83/1.48 % (1340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.48 % (1340)Termination reason: Unknown
% 1.83/1.48 % (1340)Termination phase: Saturation
% 1.83/1.48
% 1.83/1.48 % (1340)Memory used [KB]: 5756
% 1.83/1.48 % (1340)Time elapsed: 0.012 s
% 1.83/1.48 % (1340)Instructions burned: 30 (million)
% 1.83/1.48 % (1340)------------------------------
% 1.83/1.48 % (1340)------------------------------
% 1.83/1.49 % (1342)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_923 for (2998ds/100Mi)
% 1.83/1.51 % (1341)Instruction limit reached!
% 1.83/1.51 % (1341)------------------------------
% 1.83/1.51 % (1341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.51 % (1341)Termination reason: Unknown
% 1.83/1.51 % (1341)Termination phase: Saturation
% 1.83/1.51
% 1.83/1.51 % (1341)Memory used [KB]: 6268
% 1.83/1.51 % (1341)Time elapsed: 0.044 s
% 1.83/1.51 % (1341)Instructions burned: 129 (million)
% 1.83/1.51 % (1341)------------------------------
% 1.83/1.51 % (1341)------------------------------
% 1.83/1.52 % (1342)Instruction limit reached!
% 1.83/1.52 % (1342)------------------------------
% 1.83/1.52 % (1342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.52 % (1342)Termination reason: Unknown
% 1.83/1.52 % (1342)Termination phase: Saturation
% 1.83/1.52
% 1.83/1.52 % (1342)Memory used [KB]: 6012
% 1.83/1.52 % (1342)Time elapsed: 0.035 s
% 1.83/1.52 % (1342)Instructions burned: 102 (million)
% 1.83/1.52 % (1342)------------------------------
% 1.83/1.52 % (1342)------------------------------
% 1.83/1.52 % (1343)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_923 for (2998ds/3Mi)
% 1.83/1.52 % (1343)Instruction limit reached!
% 1.83/1.52 % (1343)------------------------------
% 1.83/1.52 % (1343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.52 % (1343)Termination reason: Unknown
% 1.83/1.52 % (1343)Termination phase: Property scanning
% 1.83/1.52
% 1.83/1.52 % (1343)Memory used [KB]: 1023
% 1.83/1.52 % (1343)Time elapsed: 0.003 s
% 1.83/1.52 % (1343)Instructions burned: 5 (million)
% 1.83/1.52 % (1343)------------------------------
% 1.83/1.52 % (1343)------------------------------
% 1.83/1.53 % (1344)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_923 for (2998ds/20Mi)
% 1.83/1.53 % (1345)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_923 for (2998ds/86Mi)
% 1.83/1.54 % (1344)Instruction limit reached!
% 1.83/1.54 % (1344)------------------------------
% 1.83/1.54 % (1344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (1344)Termination reason: Unknown
% 1.83/1.54 % (1344)Termination phase: Saturation
% 1.83/1.54
% 1.83/1.54 % (1344)Memory used [KB]: 5628
% 1.83/1.54 % (1344)Time elapsed: 0.009 s
% 1.83/1.54 % (1344)Instructions burned: 22 (million)
% 1.83/1.54 % (1344)------------------------------
% 1.83/1.54 % (1344)------------------------------
% 1.83/1.55 % (1346)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_923 for (2998ds/107Mi)
% 1.83/1.56 % (1334)Instruction limit reached!
% 1.83/1.56 % (1334)------------------------------
% 1.83/1.56 % (1334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.56 % (1334)Termination reason: Unknown
% 1.83/1.56 % (1334)Termination phase: Saturation
% 1.83/1.56
% 1.83/1.56 % (1334)Memory used [KB]: 6140
% 1.83/1.56 % (1334)Time elapsed: 0.130 s
% 1.83/1.56 % (1334)Instructions burned: 378 (million)
% 1.83/1.56 % (1334)------------------------------
% 1.83/1.56 % (1334)------------------------------
% 1.83/1.56 % (1345)Instruction limit reached!
% 1.83/1.56 % (1345)------------------------------
% 1.83/1.56 % (1345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.56 % (1345)Termination reason: Unknown
% 1.83/1.56 % (1345)Termination phase: Saturation
% 1.83/1.56
% 1.83/1.56 % (1345)Memory used [KB]: 6012
% 1.83/1.56 % (1345)Time elapsed: 0.030 s
% 1.83/1.56 % (1345)Instructions burned: 86 (million)
% 1.83/1.56 % (1345)------------------------------
% 1.83/1.56 % (1345)------------------------------
% 1.83/1.57 % (1347)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_923 for (2997ds/39Mi)
% 1.83/1.57 % (1348)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_923 for (2997ds/448Mi)
% 1.83/1.58 % (1347)Instruction limit reached!
% 1.83/1.58 % (1347)------------------------------
% 1.83/1.58 % (1347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.58 % (1347)Termination reason: Unknown
% 1.83/1.58 % (1347)Termination phase: Saturation
% 1.83/1.58
% 1.83/1.58 % (1347)Memory used [KB]: 5756
% 1.83/1.58 % (1347)Time elapsed: 0.015 s
% 1.83/1.58 % (1347)Instructions burned: 39 (million)
% 1.83/1.58 % (1347)------------------------------
% 1.83/1.58 % (1347)------------------------------
% 1.83/1.58 % (1346)Instruction limit reached!
% 1.83/1.58 % (1346)------------------------------
% 1.83/1.58 % (1346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.58 % (1346)Termination reason: Unknown
% 1.83/1.58 % (1346)Termination phase: Saturation
% 1.83/1.58
% 1.83/1.58 % (1346)Memory used [KB]: 6012
% 1.83/1.58 % (1346)Time elapsed: 0.039 s
% 1.83/1.58 % (1346)Instructions burned: 109 (million)
% 1.83/1.58 % (1346)------------------------------
% 1.83/1.58 % (1346)------------------------------
% 1.83/1.59 % (1350)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_923 for (2997ds/46Mi)
% 1.83/1.60 % (1351)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_923 for (2997ds/98Mi)
% 1.83/1.61 % (1350)Instruction limit reached!
% 1.83/1.61 % (1350)------------------------------
% 1.83/1.61 % (1350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.61 % (1350)Termination reason: Unknown
% 1.83/1.61 % (1350)Termination phase: Saturation
% 1.83/1.61
% 1.83/1.61 % (1350)Memory used [KB]: 5884
% 1.83/1.61 % (1350)Time elapsed: 0.039 s
% 1.83/1.61 % (1350)Instructions burned: 47 (million)
% 1.83/1.61 % (1350)------------------------------
% 1.83/1.61 % (1350)------------------------------
% 1.83/1.62 % (1352)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_923 for (2997ds/507Mi)
% 1.83/1.62 % (1352)Refutation not found, incomplete strategy
% 1.83/1.62 % (1352)------------------------------
% 1.83/1.62 % (1352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.62 % (1352)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.62
% 1.83/1.62
% 1.83/1.62 % (1352)Memory used [KB]: 5756
% 1.83/1.62 % (1352)Time elapsed: 0.009 s
% 1.83/1.62 % (1352)Instructions burned: 22 (million)
% 1.83/1.62 % (1352)------------------------------
% 1.83/1.62 % (1352)------------------------------
% 1.83/1.63 % (1328)Instruction limit reached!
% 1.83/1.63 % (1328)------------------------------
% 1.83/1.63 % (1328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.63 % (1328)Termination reason: Unknown
% 1.83/1.63 % (1328)Termination phase: Saturation
% 1.83/1.63
% 1.83/1.63 % (1328)Memory used [KB]: 7036
% 1.83/1.63 % (1328)Time elapsed: 0.223 s
% 1.83/1.63 % (1328)Instructions burned: 710 (million)
% 1.83/1.63 % (1328)------------------------------
% 1.83/1.63 % (1328)------------------------------
% 1.83/1.63 % (1351)Instruction limit reached!
% 1.83/1.63 % (1351)------------------------------
% 1.83/1.63 % (1351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.63 % (1351)Termination reason: Unknown
% 1.83/1.63 % (1351)Termination phase: Saturation
% 1.83/1.63
% 1.83/1.63 % (1351)Memory used [KB]: 1407
% 1.83/1.63 % (1351)Time elapsed: 0.034 s
% 1.83/1.63 % (1351)Instructions burned: 100 (million)
% 1.83/1.63 % (1351)------------------------------
% 1.83/1.63 % (1351)------------------------------
% 1.83/1.63 % (1353)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_923 for (2997ds/149Mi)
% 1.83/1.64 % (1354)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_923 for (2997ds/39Mi)
% 1.83/1.64 % (1355)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_923 for (2997ds/6Mi)
% 1.83/1.64 % (1355)Instruction limit reached!
% 1.83/1.64 % (1355)------------------------------
% 1.83/1.64 % (1355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.64 % (1355)Termination reason: Unknown
% 1.83/1.64 % (1355)Termination phase: Property scanning
% 1.83/1.64
% 1.83/1.64 % (1355)Memory used [KB]: 1023
% 1.83/1.64 % (1355)Time elapsed: 0.004 s
% 1.83/1.64 % (1355)Instructions burned: 8 (million)
% 1.83/1.64 % (1355)------------------------------
% 1.83/1.64 % (1355)------------------------------
% 1.83/1.65 % (1356)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_923 for (2996ds/1087Mi)
% 1.83/1.65 % (1354)Instruction limit reached!
% 1.83/1.65 % (1354)------------------------------
% 1.83/1.65 % (1354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.65 % (1354)Termination reason: Unknown
% 1.83/1.65 % (1354)Termination phase: Saturation
% 1.83/1.65
% 1.83/1.65 % (1354)Memory used [KB]: 5756
% 1.83/1.65 % (1354)Time elapsed: 0.016 s
% 1.83/1.65 % (1354)Instructions burned: 41 (million)
% 1.83/1.65 % (1354)------------------------------
% 1.83/1.65 % (1354)------------------------------
% 1.83/1.66 % (1357)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_923 for (2996ds/47Mi)
% 1.83/1.68 % (1357)Instruction limit reached!
% 1.83/1.68 % (1357)------------------------------
% 1.83/1.68 % (1357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.68 % (1357)Termination reason: Unknown
% 1.83/1.68 % (1357)Termination phase: Saturation
% 1.83/1.68
% 1.83/1.68 % (1357)Memory used [KB]: 5756
% 1.83/1.68 % (1357)Time elapsed: 0.017 s
% 1.83/1.68 % (1357)Instructions burned: 49 (million)
% 1.83/1.68 % (1357)------------------------------
% 1.83/1.68 % (1357)------------------------------
% 1.83/1.68 % (1335)Instruction limit reached!
% 1.83/1.68 % (1335)------------------------------
% 1.83/1.68 % (1335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.68 % (1335)Termination reason: Unknown
% 1.83/1.68 % (1335)Termination phase: Saturation
% 1.83/1.68
% 1.83/1.68 % (1335)Memory used [KB]: 7036
% 1.83/1.68 % (1335)Time elapsed: 0.250 s
% 1.83/1.68 % (1335)Instructions burned: 781 (million)
% 1.83/1.68 % (1335)------------------------------
% 1.83/1.68 % (1335)------------------------------
% 1.83/1.68 % (1358)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_923 for (2996ds/44Mi)
% 1.83/1.69 % (1353)Instruction limit reached!
% 1.83/1.69 % (1353)------------------------------
% 1.83/1.69 % (1353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.69 % (1353)Termination reason: Unknown
% 1.83/1.69 % (1353)Termination phase: Saturation
% 1.83/1.69
% 1.83/1.69 % (1353)Memory used [KB]: 6140
% 1.83/1.69 % (1353)Time elapsed: 0.053 s
% 1.83/1.69 % (1353)Instructions burned: 151 (million)
% 1.83/1.69 % (1353)------------------------------
% 1.83/1.69 % (1353)------------------------------
% 1.83/1.69 % (1319)Instruction limit reached!
% 1.83/1.69 % (1319)------------------------------
% 1.83/1.69 % (1319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.69 % (1319)Termination reason: Unknown
% 1.83/1.69 % (1319)Termination phase: Saturation
% 1.83/1.69
% 1.83/1.69 % (1319)Memory used [KB]: 7164
% 1.83/1.69 % (1319)Time elapsed: 0.318 s
% 1.83/1.69 % (1319)Instructions burned: 1043 (million)
% 1.83/1.69 % (1319)------------------------------
% 1.83/1.69 % (1319)------------------------------
% 1.83/1.69 % (1359)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_923 for (2996ds/432Mi)
% 1.83/1.70 % (1361)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_923 for (2996ds/31Mi)
% 1.83/1.70 % (1360)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_923 for (2996ds/62Mi)
% 1.83/1.70 % (1358)Instruction limit reached!
% 1.83/1.70 % (1358)------------------------------
% 1.83/1.70 % (1358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.70 % (1358)Termination reason: Unknown
% 1.83/1.70 % (1358)Termination phase: Saturation
% 1.83/1.70
% 1.83/1.70 % (1358)Memory used [KB]: 1279
% 1.83/1.70 % (1358)Time elapsed: 0.015 s
% 1.83/1.70 % (1358)Instructions burned: 46 (million)
% 1.83/1.70 % (1358)------------------------------
% 1.83/1.70 % (1358)------------------------------
% 1.83/1.71 % (1361)Instruction limit reached!
% 1.83/1.71 % (1361)------------------------------
% 1.83/1.71 % (1361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.71 % (1361)Termination reason: Unknown
% 1.83/1.71 % (1361)Termination phase: Saturation
% 1.83/1.71
% 1.83/1.71 % (1361)Memory used [KB]: 5756
% 1.83/1.71 % (1361)Time elapsed: 0.011 s
% 1.83/1.71 % (1361)Instructions burned: 32 (million)
% 1.83/1.71 % (1361)------------------------------
% 1.83/1.71 % (1361)------------------------------
% 1.83/1.71 % (1356)First to succeed.
% 1.83/1.71 % (1362)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_923 for (2996ds/96Mi)
% 1.83/1.71 % (1356)Refutation found. Thanks to Tanya!
% 1.83/1.71 % SZS status Theorem for DTF2THF_923
% 1.83/1.71 % SZS output start Proof for DTF2THF_923
% 1.83/1.71 thf(type_def_6, type, nat: $tType).
% 1.83/1.71 thf(type_def_7, type, list: ($tType) > $tType).
% 1.83/1.71 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.83/1.71 thf(func_def_2, type, nat: $tType).
% 1.83/1.71 thf(func_def_3, type, natStar: nat > nat > $o).
% 1.83/1.71 thf(func_def_4, type, zero: nat).
% 1.83/1.71 thf(func_def_5, type, suc: nat > nat).
% 1.83/1.71 thf(func_def_6, type, plus: nat > nat > nat).
% 1.83/1.71 thf(func_def_7, type, list: ($tType) > $tType).
% 1.83/1.71 thf(func_def_8, type, listStar: !>[X0: $tType]:((X0 > X0 > $o) > nat > list @ X0 > list @ X0 > $o)).
% 1.83/1.71 thf(func_def_9, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.83/1.71 thf(func_def_10, type, cons: !>[X0: $tType]:(nat > X0 > list @ X0 > list @ X0)).
% 1.83/1.71 thf(func_def_11, type, app: !>[X0: $tType]:(nat > nat > list @ X0 > list @ X0 > list @ X0)).
% 1.83/1.71 thf(func_def_12, type, rev: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 1.83/1.71 thf(func_def_15, type, sP0: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.83/1.71 thf(func_def_16, type, sP1: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.83/1.71 thf(func_def_17, type, sK2: nat).
% 1.83/1.71 thf(func_def_18, type, sK3: list @ list @ list @ nat).
% 1.83/1.71 thf(func_def_19, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.83/1.71 thf(func_def_20, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.83/1.71 thf(func_def_21, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.83/1.71 thf(func_def_22, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.83/1.71 thf(func_def_23, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.83/1.71 thf(func_def_24, type, sK9: (nat > $o) > nat).
% 1.83/1.71 thf(func_def_27, type, ph11: !>[X0: $tType]:(X0)).
% 1.83/1.71 thf(f646,plain,(
% 1.83/1.71 $false),
% 1.83/1.71 inference(avatar_sat_refutation,[status(thm)],[f321,f363,f370,f427,f469,f482,f572,f598,f645])).
% 1.83/1.71 thf(f645,plain,(
% 1.83/1.71 ~spl10_17 | ~spl10_11),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f644,f361,f547])).
% 1.83/1.71 thf(f547,definition,(
% 1.83/1.71 spl10_17 <=> ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) = $true)),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_17])],[avatar_definition])).
% 1.83/1.71 thf(f361,definition,(
% 1.83/1.71 spl10_11 <=> ! [X0 : list @ list @ list @ nat] : (($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ X0)) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ X0 @ sK3) != $true))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_11])],[avatar_definition])).
% 1.83/1.71 thf(f644,plain,(
% 1.83/1.71 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ~spl10_11),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f633,f77])).
% 1.83/1.71 thf(f77,plain,(
% 1.83/1.71 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ sK3 @ sK3))),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f61])).
% 1.83/1.71 thf(f61,plain,(
% 1.83/1.71 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ (app @ list @ list @ nat @ zero @ sK2 @ nil @ list @ list @ nat @ sK3))) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ sK3 @ sK3)) & ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ sK3))),
% 1.83/1.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f49,f60])).
% 1.83/1.71 thf(f60,plain,(
% 1.83/1.71 ? [X0 : nat,X1 : list @ 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 @ nil @ list @ list @ nat @ X1)) = $true) & ($true = (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) != $true)) => (($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ (app @ list @ list @ nat @ zero @ sK2 @ nil @ list @ list @ nat @ sK3))) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ sK3 @ sK3)) & ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ sK3)))),
% 1.83/1.71 introduced(definition,[],[choice_axiom])).
% 1.83/1.71 thf(f49,plain,(
% 1.83/1.71 ? [X0 : nat,X1 : list @ 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 @ nil @ list @ list @ nat @ X1)) = $true) & ($true = (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) != $true))),
% 1.83/1.71 inference(flattening,[status(thm)],[f48])).
% 1.83/1.71 thf(f48,plain,(
% 1.83/1.71 ? [X0 : nat,X1 : list @ 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)) @ X1) != $true) & ((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)) = $true)) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1)))),
% 1.83/1.71 inference(ennf_transformation,[status(thm)],[f28])).
% 1.83/1.71 thf(f28,plain,(
% 1.83/1.71 ~! [X0 : nat,X1 : list @ list @ list @ nat] : (($true = (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)) = $true) => ((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) = $true)))),
% 1.83/1.71 inference(fool_elimination,[status(thm)],[f27])).
% 1.83/1.71 thf(f27,plain,(
% 1.83/1.71 ~! [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)))),
% 1.83/1.71 inference(rectify,[status(thm)],[f17])).
% 1.83/1.71 thf(f17,negated_conjecture,(
% 1.83/1.71 ~! [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)))),
% 1.83/1.71 inference(negated_conjecture,[status(cth)],[f16])).
% 1.83/1.71 thf(f16,conjecture,(
% 1.83/1.71 ! [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)))),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p',list_rev_invol_step4)).
% 1.83/1.71 thf(f633,plain,(
% 1.83/1.71 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ sK3 @ sK3)) | ~spl10_11),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f630])).
% 1.83/1.71 thf(f630,plain,(
% 1.83/1.71 ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ sK3 @ sK3)) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != $true) | ~spl10_11),
% 1.83/1.71 inference(superposition,[status(thm)],[f542,f438])).
% 1.83/1.71 thf(f438,plain,(
% 1.83/1.71 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (((listStar @ X0 @ X1 @ X2 @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true) | ((isPer @ X0 @ X1) != $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3))) )),
% 1.83/1.71 inference(forward_demodulation,[status(thm)],[f79,f98])).
% 1.83/1.71 thf(f98,plain,(
% 1.83/1.71 ( ! [X0 : nat] : (((plus @ zero @ X0) = X0)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f41])).
% 1.83/1.71 thf(f41,plain,(
% 1.83/1.71 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 1.83/1.71 inference(rectify,[status(thm)],[f11])).
% 1.83/1.71 thf(f11,axiom,(
% 1.83/1.71 ! [X8 : nat] : ((plus @ zero @ X8) = X8)),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p',ax1)).
% 1.83/1.71 thf(f79,plain,(
% 1.83/1.71 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true) | ((isPer @ X0 @ X1) != $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f47])).
% 1.83/1.71 thf(f47,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : list @ X0] : (($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3)) | ((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true)) | ((isPer @ X0 @ X1) != $true))),
% 1.83/1.71 inference(ennf_transformation,[status(thm)],[f36])).
% 1.83/1.71 thf(f36,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : list @ X0] : (($true = (listStar @ X0 @ X1 @ X2 @ X3 @ X3)) => ((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true)))),
% 1.83/1.71 inference(fool_elimination,[status(thm)],[f35])).
% 1.83/1.71 thf(f35,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X3 @ X3) => (listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3)))),
% 1.83/1.71 inference(rectify,[status(thm)],[f13])).
% 1.83/1.71 thf(f13,axiom,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X2 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X2 @ X2) => (listStar @ X0 @ X1 @ (plus @ zero @ X8) @ (app @ X0 @ zero @ X8 @ nil @ X0 @ X2) @ X2)))),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p',ax3)).
% 1.83/1.71 thf(f542,plain,(
% 1.83/1.71 ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (app @ list @ list @ nat @ zero @ sK2 @ nil @ list @ list @ nat @ sK3) @ sK3)) | ~spl10_11),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f535])).
% 1.83/1.71 thf(f535,plain,(
% 1.83/1.71 ($true != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (app @ list @ list @ nat @ zero @ sK2 @ nil @ list @ list @ nat @ sK3) @ sK3)) | ~spl10_11),
% 1.83/1.71 inference(superposition,[status(thm)],[f362,f78])).
% 1.83/1.71 thf(f78,plain,(
% 1.83/1.71 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ (app @ list @ list @ nat @ zero @ sK2 @ nil @ list @ list @ nat @ sK3)))),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f61])).
% 1.83/1.71 thf(f362,plain,(
% 1.83/1.71 ( ! [X0 : list @ list @ list @ nat] : (($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ X0)) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ X0 @ sK3) != $true)) ) | ~spl10_11),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f361])).
% 1.83/1.71 thf(f598,plain,(
% 1.83/1.71 ~spl10_13 | spl10_17),
% 1.83/1.71 inference(avatar_contradiction_clause,[status(thm)],[f597])).
% 1.83/1.71 thf(f597,plain,(
% 1.83/1.71 $false | (~spl10_13 | spl10_17)),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f596,f417])).
% 1.83/1.71 thf(f417,plain,(
% 1.83/1.71 ($true = (sP1 @ nat @ natStar)) | ~spl10_13),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f416])).
% 1.83/1.71 thf(f416,definition,(
% 1.83/1.71 spl10_13 <=> ($true = (sP1 @ nat @ natStar))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_13])],[avatar_definition])).
% 1.83/1.71 thf(f596,plain,(
% 1.83/1.71 ($true != (sP1 @ nat @ natStar)) | spl10_17),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f595])).
% 1.83/1.71 thf(f595,plain,(
% 1.83/1.71 ($true != (sP1 @ nat @ natStar)) | ($true != $true) | spl10_17),
% 1.83/1.71 inference(superposition,[status(thm)],[f580,f94])).
% 1.83/1.71 thf(f94,plain,(
% 1.83/1.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f72])).
% 1.83/1.71 thf(f72,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)))),
% 1.83/1.71 inference(nnf_transformation,[status(thm)],[f59])).
% 1.83/1.71 thf(f59,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((sP1 @ X0 @ X1) = $true) <=> ((isPer @ X0 @ X1) = $true))),
% 1.83/1.71 inference(definition_folding,[status(thm)],[f56,f58,f57])).
% 1.83/1.71 thf(f57,plain,(
% 1.83/1.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : (($true = (sP0 @ X0 @ X1)) <=> ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X6) = $true)))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.83/1.71 thf(f58,plain,(
% 1.83/1.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : (((sP1 @ X0 @ X1) = $true) <=> (($true = (sP0 @ X0 @ X1)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.83/1.71 thf(f56,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X6) = $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.83/1.71 inference(flattening,[status(thm)],[f55])).
% 1.83/1.71 thf(f55,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X5 @ X6))) | ((X1 @ X4 @ X5) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.83/1.71 inference(ennf_transformation,[status(thm)],[f34])).
% 1.83/1.71 thf(f34,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) => (($true = (X1 @ X5 @ X6)) => ((X1 @ X4 @ X6) = $true)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.83/1.71 inference(fool_elimination,[status(thm)],[f33])).
% 1.83/1.71 thf(f33,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((X1 @ X4 @ X5) => ((X1 @ X5 @ X6) => (X1 @ X4 @ X6)))) <=> (isPer @ X0 @ X1))),
% 1.83/1.71 inference(rectify,[status(thm)],[f1])).
% 1.83/1.71 thf(f1,axiom,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))) <=> (isPer @ X0 @ X1))),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p',is_per)).
% 1.83/1.71 thf(f580,plain,(
% 1.83/1.71 ($true != (isPer @ nat @ natStar)) | spl10_17),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f578])).
% 1.83/1.71 thf(f578,plain,(
% 1.83/1.71 ($true != $true) | ($true != (isPer @ nat @ natStar)) | spl10_17),
% 1.83/1.71 inference(superposition,[status(thm)],[f575,f82])).
% 1.83/1.71 thf(f82,plain,(
% 1.83/1.71 ( ! [X0 : $tType,X2 : nat,X1 : X0 > X0 > $o] : (($true = (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2))) | ((isPer @ X0 @ X1) != $true)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f52])).
% 1.83/1.71 thf(f52,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat] : ($true = (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2))))),
% 1.83/1.71 inference(ennf_transformation,[status(thm)],[f38])).
% 1.83/1.71 thf(f38,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat] : ($true = (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2))))),
% 1.83/1.71 inference(fool_elimination,[status(thm)],[f37])).
% 1.83/1.71 thf(f37,plain,(
% 1.83/1.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat] : (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)))),
% 1.83/1.71 inference(rectify,[status(thm)],[f3])).
% 1.83/1.71 thf(f3,axiom,(
% 1.83/1.71 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : nat] : (isPer @ list @ X5 @ (listStar @ X5 @ X6 @ X7)))),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p','\'listStar\'_is_per')).
% 1.83/1.71 thf(f575,plain,(
% 1.83/1.71 ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | spl10_17),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f574])).
% 1.83/1.71 thf(f574,plain,(
% 1.83/1.71 ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | ($true != $true) | spl10_17),
% 1.83/1.71 inference(superposition,[status(thm)],[f548,f82])).
% 1.83/1.71 thf(f548,plain,(
% 1.83/1.71 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_17),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f547])).
% 1.83/1.71 thf(f572,plain,(
% 1.83/1.71 spl10_13 | ~spl10_8 | ~spl10_14),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f571,f419,f298,f416])).
% 1.83/1.71 thf(f298,definition,(
% 1.83/1.71 spl10_8 <=> ($true = (sP0 @ nat @ natStar))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_8])],[avatar_definition])).
% 1.83/1.71 thf(f419,definition,(
% 1.83/1.71 spl10_14 <=> ((sK4 @ nat @ natStar) = (sK5 @ nat @ natStar))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_14])],[avatar_definition])).
% 1.83/1.71 thf(f571,plain,(
% 1.83/1.71 ($true = (sP1 @ nat @ natStar)) | (~spl10_8 | ~spl10_14)),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f570,f299])).
% 1.83/1.71 thf(f299,plain,(
% 1.83/1.71 ($true = (sP0 @ nat @ natStar)) | ~spl10_8),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f298])).
% 1.83/1.71 thf(f570,plain,(
% 1.83/1.71 ($true != (sP0 @ nat @ natStar)) | ($true = (sP1 @ nat @ natStar)) | ~spl10_14),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f568,f103])).
% 1.83/1.71 thf(f103,plain,(
% 1.83/1.71 ( ! [X1 : nat] : (((natStar @ X1 @ X1) = $true)) )),
% 1.83/1.71 inference(equality_resolution,[status(thm)],[f85])).
% 1.83/1.71 thf(f85,plain,(
% 1.83/1.71 ( ! [X0 : nat,X1 : nat] : (($true = (natStar @ X0 @ X1)) | (X0 != X1)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f62])).
% 1.83/1.71 thf(f62,plain,(
% 1.83/1.71 ! [X0 : nat,X1 : nat] : ((($true = (natStar @ X0 @ X1)) | (X0 != X1)) & ((X0 = X1) | ($true != (natStar @ X0 @ X1))))),
% 1.83/1.71 inference(nnf_transformation,[status(thm)],[f20])).
% 1.83/1.71 thf(f20,plain,(
% 1.83/1.71 ! [X0 : nat,X1 : nat] : (($true = (natStar @ X0 @ X1)) <=> (X0 = X1))),
% 1.83/1.71 inference(fool_elimination,[status(thm)],[f19])).
% 1.83/1.71 thf(f19,plain,(
% 1.83/1.71 ! [X0 : nat,X1 : nat] : ((natStar @ X0 @ X1) <=> (X0 = X1))),
% 1.83/1.71 inference(rectify,[status(thm)],[f2])).
% 1.83/1.71 thf(f2,axiom,(
% 1.83/1.71 ! [X2 : nat,X3 : nat] : ((natStar @ X2 @ X3) <=> (X2 = X3))),
% 1.83/1.71 file('/export/starexec/sandbox/tmp/tmp.3FRRtBxG5G/DTF2THF_923.p',natStar_is_eq)).
% 1.83/1.71 thf(f568,plain,(
% 1.83/1.71 ($true != (natStar @ (sK4 @ nat @ natStar) @ (sK4 @ nat @ natStar))) | ($true != (sP0 @ nat @ natStar)) | ($true = (sP1 @ nat @ natStar)) | ~spl10_14),
% 1.83/1.71 inference(superposition,[status(thm)],[f88,f420])).
% 1.83/1.71 thf(f420,plain,(
% 1.83/1.71 ((sK4 @ nat @ natStar) = (sK5 @ nat @ natStar)) | ~spl10_14),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f419])).
% 1.83/1.71 thf(f88,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true != (X0 @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) | ($true != (sP0 @ X1 @ X0)) | ($true = (sP1 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f67])).
% 1.83/1.71 thf(f67,plain,(
% 1.83/1.71 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP1 @ X1 @ X0)) | ($true != (sP0 @ X1 @ X0)) | (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X0 @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))))) & ((($true = (sP0 @ X1 @ X0)) & ! [X4 : X1,X5 : X1] : (($true != (X0 @ X4 @ X5)) | ($true = (X0 @ X5 @ X4)))) | ($true != (sP1 @ X1 @ X0))))),
% 1.83/1.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f65,f66])).
% 1.83/1.71 thf(f66,plain,(
% 1.83/1.71 ! [X1 : $tType,X0 : X1 > X1 > $o] : (? [X2 : X1,X3 : X1] : (($true = (X0 @ X2 @ X3)) & ((X0 @ X3 @ X2) != $true)) => (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X0 @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))))),
% 1.83/1.71 introduced(definition,[],[choice_axiom])).
% 1.83/1.71 thf(f65,plain,(
% 1.83/1.71 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP1 @ X1 @ X0)) | ($true != (sP0 @ X1 @ X0)) | ? [X2 : X1,X3 : X1] : (($true = (X0 @ X2 @ X3)) & ((X0 @ X3 @ X2) != $true))) & ((($true = (sP0 @ X1 @ X0)) & ! [X4 : X1,X5 : X1] : (($true != (X0 @ X4 @ X5)) | ($true = (X0 @ X5 @ X4)))) | ($true != (sP1 @ X1 @ X0))))),
% 1.83/1.71 inference(rectify,[status(thm)],[f64])).
% 1.83/1.71 thf(f64,plain,(
% 1.83/1.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | ($true != (sP0 @ X0 @ X1)) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true))) & ((($true = (sP0 @ X0 @ X1)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) | ((sP1 @ X0 @ X1) != $true)))),
% 1.83/1.71 inference(flattening,[status(thm)],[f63])).
% 1.83/1.71 thf(f63,plain,(
% 1.83/1.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | (($true != (sP0 @ X0 @ X1)) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)))) & ((($true = (sP0 @ X0 @ X1)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))) | ((sP1 @ X0 @ X1) != $true)))),
% 1.83/1.71 inference(nnf_transformation,[status(thm)],[f58])).
% 1.83/1.71 thf(f482,plain,(
% 1.83/1.71 spl10_4 | ~spl10_13),
% 1.83/1.71 inference(avatar_contradiction_clause,[status(thm)],[f481])).
% 1.83/1.71 thf(f481,plain,(
% 1.83/1.71 $false | (spl10_4 | ~spl10_13)),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f417,f437])).
% 1.83/1.71 thf(f437,plain,(
% 1.83/1.71 ($true != (sP1 @ nat @ natStar)) | spl10_4),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f436])).
% 1.83/1.71 thf(f436,plain,(
% 1.83/1.71 ($true != (sP1 @ nat @ natStar)) | ($true != $true) | spl10_4),
% 1.83/1.71 inference(superposition,[status(thm)],[f435,f94])).
% 1.83/1.71 thf(f435,plain,(
% 1.83/1.71 ($true != (isPer @ nat @ natStar)) | spl10_4),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f433])).
% 1.83/1.71 thf(f433,plain,(
% 1.83/1.71 ($true != $true) | ($true != (isPer @ nat @ natStar)) | spl10_4),
% 1.83/1.71 inference(superposition,[status(thm)],[f430,f82])).
% 1.83/1.71 thf(f430,plain,(
% 1.83/1.71 ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | spl10_4),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f429])).
% 1.83/1.71 thf(f429,plain,(
% 1.83/1.71 ($true != $true) | ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | spl10_4),
% 1.83/1.71 inference(superposition,[status(thm)],[f396,f82])).
% 1.83/1.71 thf(f396,plain,(
% 1.83/1.71 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_4),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f394])).
% 1.83/1.71 thf(f394,plain,(
% 1.83/1.71 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != $true) | spl10_4),
% 1.83/1.71 inference(superposition,[status(thm)],[f372,f82])).
% 1.83/1.71 thf(f372,plain,(
% 1.83/1.71 ($true != (isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2))) | spl10_4),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f371])).
% 1.83/1.71 thf(f371,plain,(
% 1.83/1.71 ($true != $true) | ($true != (isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2))) | spl10_4),
% 1.83/1.71 inference(superposition,[status(thm)],[f248,f95])).
% 1.83/1.71 thf(f95,plain,(
% 1.83/1.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f72])).
% 1.83/1.71 thf(f248,plain,(
% 1.83/1.71 ($true != (sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2))) | spl10_4),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f247])).
% 1.83/1.71 thf(f247,definition,(
% 1.83/1.71 spl10_4 <=> ($true = (sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2)))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 1.83/1.71 thf(f469,plain,(
% 1.83/1.71 spl10_8 | ~spl10_9),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f468,f319,f298])).
% 1.83/1.71 thf(f319,definition,(
% 1.83/1.71 spl10_9 <=> ((sK7 @ nat @ natStar) = (sK6 @ nat @ natStar))),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_9])],[avatar_definition])).
% 1.83/1.71 thf(f468,plain,(
% 1.83/1.71 ($true = (sP0 @ nat @ natStar)) | ~spl10_9),
% 1.83/1.71 inference(subsumption_resolution,[status(thm)],[f458,f91])).
% 1.83/1.71 thf(f91,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true != (X0 @ (sK6 @ X1 @ X0) @ (sK8 @ X1 @ X0))) | ($true = (sP0 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f71])).
% 1.83/1.71 thf(f71,plain,(
% 1.83/1.71 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP0 @ X1 @ X0)) | (($true = (X0 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) & ($true = (X0 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0))) & ($true != (X0 @ (sK6 @ X1 @ X0) @ (sK8 @ X1 @ X0))))) & (! [X5 : X1,X6 : X1,X7 : X1] : (($true != (X0 @ X5 @ X6)) | ($true != (X0 @ X6 @ X7)) | ($true = (X0 @ X5 @ X7))) | ($true != (sP0 @ X1 @ X0))))),
% 1.83/1.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f69,f70])).
% 1.83/1.71 thf(f70,plain,(
% 1.83/1.71 ! [X1 : $tType,X0 : X1 > X1 > $o] : (? [X2 : X1,X3 : X1,X4 : X1] : (($true = (X0 @ X2 @ X3)) & ($true = (X0 @ X3 @ X4)) & ((X0 @ X2 @ X4) != $true)) => (($true = (X0 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) & ($true = (X0 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0))) & ($true != (X0 @ (sK6 @ X1 @ X0) @ (sK8 @ X1 @ X0)))))),
% 1.83/1.71 introduced(definition,[],[choice_axiom])).
% 1.83/1.71 thf(f69,plain,(
% 1.83/1.71 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP0 @ X1 @ X0)) | ? [X2 : X1,X3 : X1,X4 : X1] : (($true = (X0 @ X2 @ X3)) & ($true = (X0 @ X3 @ X4)) & ((X0 @ X2 @ X4) != $true))) & (! [X5 : X1,X6 : X1,X7 : X1] : (($true != (X0 @ X5 @ X6)) | ($true != (X0 @ X6 @ X7)) | ($true = (X0 @ X5 @ X7))) | ($true != (sP0 @ X1 @ X0))))),
% 1.83/1.71 inference(rectify,[status(thm)],[f68])).
% 1.83/1.71 thf(f68,plain,(
% 1.83/1.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((($true = (sP0 @ X0 @ X1)) | ? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) & ($true = (X1 @ X5 @ X6)) & ((X1 @ X4 @ X6) != $true))) & (! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ($true != (X1 @ X5 @ X6)) | ((X1 @ X4 @ X6) = $true)) | ($true != (sP0 @ X0 @ X1))))),
% 1.83/1.71 inference(nnf_transformation,[status(thm)],[f57])).
% 1.83/1.71 thf(f458,plain,(
% 1.83/1.71 ($true = (natStar @ (sK6 @ nat @ natStar) @ (sK8 @ nat @ natStar))) | ($true = (sP0 @ nat @ natStar)) | ~spl10_9),
% 1.83/1.71 inference(superposition,[status(thm)],[f92,f320])).
% 1.83/1.71 thf(f320,plain,(
% 1.83/1.71 ((sK7 @ nat @ natStar) = (sK6 @ nat @ natStar)) | ~spl10_9),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f319])).
% 1.83/1.71 thf(f92,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (X0 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0))) | ($true = (sP0 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f71])).
% 1.83/1.71 thf(f427,plain,(
% 1.83/1.71 spl10_13 | spl10_14 | ~spl10_8),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f411,f298,f419,f416])).
% 1.83/1.71 thf(f411,plain,(
% 1.83/1.71 ($true != (sP0 @ nat @ natStar)) | ((sK4 @ nat @ natStar) = (sK5 @ nat @ natStar)) | ($true = (sP1 @ nat @ natStar))),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f402])).
% 1.83/1.71 thf(f402,plain,(
% 1.83/1.71 ($true != $true) | ((sK4 @ nat @ natStar) = (sK5 @ nat @ natStar)) | ($true != (sP0 @ nat @ natStar)) | ($true = (sP1 @ nat @ natStar))),
% 1.83/1.71 inference(superposition,[status(thm)],[f84,f89])).
% 1.83/1.71 thf(f89,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (sP1 @ X1 @ X0)) | ($true != (sP0 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f67])).
% 1.83/1.71 thf(f84,plain,(
% 1.83/1.71 ( ! [X0 : nat,X1 : nat] : (($true != (natStar @ X0 @ X1)) | (X0 = X1)) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f62])).
% 1.83/1.71 thf(f370,plain,(
% 1.83/1.71 ~spl10_4 | spl10_10),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f369,f358,f247])).
% 1.83/1.71 thf(f358,definition,(
% 1.83/1.71 spl10_10 <=> ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2)) = $true)),
% 1.83/1.71 introduced(definition,[new_symbols(naming,[spl10_10])],[avatar_definition])).
% 1.83/1.71 thf(f369,plain,(
% 1.83/1.71 ($true != (sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2))) | spl10_10),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.83/1.71 thf(f368,plain,(
% 1.83/1.71 ($true != $true) | ($true != (sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2))) | spl10_10),
% 1.83/1.71 inference(superposition,[status(thm)],[f359,f87])).
% 1.83/1.71 thf(f87,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (sP0 @ X1 @ X0)) | ($true != (sP1 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f67])).
% 1.83/1.71 thf(f359,plain,(
% 1.83/1.71 ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2)) != $true) | spl10_10),
% 1.83/1.71 inference(avatar_component_clause,[status(thm)],[f358])).
% 1.83/1.71 thf(f363,plain,(
% 1.83/1.71 ~spl10_10 | spl10_11),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f345,f361,f358])).
% 1.83/1.71 thf(f345,plain,(
% 1.83/1.71 ( ! [X0 : list @ list @ list @ nat] : (((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2)) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ X0)) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ X0 @ sK3) != $true)) )),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f329])).
% 1.83/1.71 thf(f329,plain,(
% 1.83/1.71 ( ! [X0 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ X0 @ sK3) != $true) | ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2)) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ X0)) | ($true != $true)) )),
% 1.83/1.71 inference(superposition,[status(thm)],[f76,f90])).
% 1.83/1.71 thf(f90,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o,X6 : X1,X7 : X1,X5 : X1] : (($true = (X0 @ X5 @ X7)) | ($true != (sP0 @ X1 @ X0)) | ($true != (X0 @ X6 @ X7)) | ($true != (X0 @ X5 @ X6))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f71])).
% 1.83/1.71 thf(f76,plain,(
% 1.83/1.71 ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK2 @ (rev @ list @ list @ nat @ sK2 @ (rev @ list @ list @ nat @ sK2 @ sK3)) @ sK3))),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f61])).
% 1.83/1.71 thf(f321,plain,(
% 1.83/1.71 spl10_8 | spl10_9),
% 1.83/1.71 inference(avatar_split_clause,[status(thm)],[f314,f319,f298])).
% 1.83/1.71 thf(f314,plain,(
% 1.83/1.71 ((sK7 @ nat @ natStar) = (sK6 @ nat @ natStar)) | ($true = (sP0 @ nat @ natStar))),
% 1.83/1.71 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.83/1.71 thf(f306,plain,(
% 1.83/1.71 ($true = (sP0 @ nat @ natStar)) | ((sK7 @ nat @ natStar) = (sK6 @ nat @ natStar)) | ($true != $true)),
% 1.83/1.71 inference(superposition,[status(thm)],[f84,f93])).
% 1.83/1.71 thf(f93,plain,(
% 1.83/1.71 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (X0 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) | ($true = (sP0 @ X1 @ X0))) )),
% 1.83/1.71 inference(cnf_transformation,[status(thm)],[f71])).
% 1.83/1.71 % SZS output end Proof for DTF2THF_923
% 1.83/1.71 % (1356)------------------------------
% 1.83/1.71 % (1356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.71 % (1356)Termination reason: Refutation
% 1.83/1.71
% 1.83/1.71 % (1356)Memory used [KB]: 6140
% 1.83/1.71 % (1356)Time elapsed: 0.060 s
% 1.83/1.71 % (1356)Instructions burned: 159 (million)
% 1.83/1.71 % (1356)------------------------------
% 1.83/1.71 % (1356)------------------------------
% 1.83/1.71 % (1307)Success in time 0.375 s
%------------------------------------------------------------------------------