%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT402^1 : 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 : n018.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 08:45:40 AM UTC 2026
% Result : Theorem 1.89s 1.73s
% Output : Refutation 1.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT402^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 06:17:16 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : DAT402^1 : TPTP v9.2.1. Released v9.2.0.
% 0.21/0.45 % Domain : Data Structures
% 0.21/0.45 % Problem : List reversal involution polymorphic, step 1 type instantiated
% 0.21/0.45 % Version : Especial.
% 0.21/0.45 % English : List reversal involution for polymorphic fixed-length lists. The
% 0.21/0.45 % proof is split into smaller steps. To simplify proof search, the
% 0.21/0.45 % axioms in each problem file have been preselected.
% 0.21/0.45
% 0.21/0.45 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.21/0.45 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.21/0.45 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.21/0.45 % Source : [Rot25]
% 0.21/0.45 % Names : ListReversalInvolution/list-rev-invol-step1-typeInstantiated.p [Rot25]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % Rating : ? v9.2.0
% 0.21/0.45 % Syntax : Number of formulae : 22 ( 11 unt; 9 typ; 0 def)
% 0.21/0.45 % Number of atoms : 13 ( 13 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 2 ( 1 avg)
% 0.21/0.45 % Number of connectives : 184 ( 3 ~; 0 |; 0 &; 177 @)
% 0.21/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 8 ( 4 avg)
% 0.21/0.45 % Number of types : 2 ( 1 usr)
% 0.21/0.45 % Number of type decls : 9 ( 4 !>P; 3 !>D)
% 0.21/0.45 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 9 ( 8 usr; 1 con; 0-5 aty)
% 0.21/0.45 % Number of variables : 39 ( 0 ^; 31 !; 0 ?; 39 :)
% 0.21/0.45 % ( 8 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.45 % SPC : DH1_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments :
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(nat_type,type,
% 0.21/0.45 nat: $tType ).
% 0.21/0.45
% 0.21/0.45 thf(zero_type,type,
% 0.21/0.45 zero: nat ).
% 0.21/0.45
% 0.21/0.45 thf(suc_type,type,
% 0.21/0.45 suc: nat > nat ).
% 0.21/0.45
% 0.21/0.45 thf(plus_type,type,
% 0.21/0.45 plus: nat > nat > nat ).
% 0.21/0.45
% 0.21/0.45 thf(list_type,type,
% 0.21/0.45 list: $tType > nat > $tType ).
% 0.21/0.45
% 0.21/0.45 thf(nil_type,type,
% 0.21/0.45 nil:
% 0.21/0.45 !>[A: $tType] : ( list @ A @ zero ) ).
% 0.21/0.45
% 0.21/0.45 thf(cons_type,type,
% 0.21/0.45 cons:
% 0.21/0.45 !>[A: $tType,N: nat] : ( A > ( list @ A @ N ) > ( list @ A @ ( suc @ N ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(app_type,type,
% 0.21/0.45 app:
% 0.21/0.45 !>[A: $tType,N: nat,M: nat] : ( ( list @ A @ N ) > ( list @ A @ M ) > ( list @ A @ ( plus @ N @ M ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(rev_type,type,
% 0.21/0.45 rev:
% 0.21/0.45 !>[A: $tType,N: nat] : ( ( list @ A @ N ) > ( list @ A @ N ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(peano1,axiom,
% 0.21/0.45 ! [N: nat] :
% 0.21/0.45 ( ( suc @ N )
% 0.21/0.45 != zero ) ).
% 0.21/0.45
% 0.21/0.45 thf(peano2,axiom,
% 0.21/0.45 ! [N: nat,M: nat] :
% 0.21/0.45 ( ( N != M )
% 0.21/0.45 => ( ( suc @ N )
% 0.21/0.45 != ( suc @ M ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(peano3,axiom,
% 0.21/0.45 ! [P: nat > $o] :
% 0.21/0.45 ( ( P @ zero )
% 0.21/0.45 => ( ! [M: nat] :
% 0.21/0.45 ( ( P @ M )
% 0.21/0.45 => ( P @ ( suc @ M ) ) )
% 0.21/0.45 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax1,axiom,
% 0.21/0.45 ! [N: nat] :
% 0.21/0.45 ( ( plus @ zero @ N )
% 0.21/0.45 = N ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax2,axiom,
% 0.21/0.45 ! [N: nat,M: nat] :
% 0.21/0.45 ( ( plus @ ( suc @ N ) @ M )
% 0.21/0.45 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax3,axiom,
% 0.21/0.45 ! [A: $tType,N: nat,X: list @ A @ N] :
% 0.21/0.45 ( ( app @ A @ zero @ N @ ( nil @ A ) @ X )
% 0.21/0.45 = X ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax4,axiom,
% 0.21/0.45 ! [A: $tType,N: nat,M: nat,X: A,Y: list @ A @ N,Z: list @ A @ M] :
% 0.21/0.45 ( ( app @ A @ ( suc @ N ) @ M @ ( cons @ A @ N @ X @ Y ) @ Z )
% 0.21/0.45 = ( cons @ A @ ( plus @ N @ M ) @ X @ ( app @ A @ N @ M @ Y @ Z ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax5,axiom,
% 0.21/0.45 ! [A: $tType] :
% 0.21/0.45 ( ( rev @ A @ zero @ ( nil @ A ) )
% 0.21/0.45 = ( nil @ A ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(ax6,axiom,
% 0.21/0.45 ! [A: $tType,N: nat,X: A,Y: list @ A @ N] :
% 0.21/0.45 ( ( rev @ A @ ( suc @ N ) @ ( cons @ A @ N @ X @ Y ) )
% 0.21/0.45 = ( app @ A @ N @ ( suc @ zero ) @ ( rev @ A @ N @ Y ) @ ( cons @ A @ zero @ X @ ( nil @ A ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(plus_com,axiom,
% 0.21/0.45 ! [N: nat,M: nat] :
% 0.21/0.45 ( ( plus @ N @ M )
% 0.21/0.45 = ( plus @ M @ N ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(plus1r,axiom,
% 0.21/0.45 ! [N: nat] :
% 0.21/0.45 ( ( suc @ N )
% 0.21/0.45 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(list_app_nil,axiom,
% 0.21/0.45 ! [A: $tType,N: nat,L: list @ A @ N] :
% 0.21/0.45 ( ( app @ A @ N @ zero @ L @ ( nil @ A ) )
% 0.21/0.45 = L ) ).
% 0.21/0.45
% 0.21/0.45 thf(list_rev_invol_step1,conjecture,
% 0.21/0.45 ! [N: nat,L: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N] :
% 0.21/0.45 ( ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ ( rev @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L ) )
% 0.21/0.45 = ( 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 ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.82/1.33 ---- Embedded in THF ---
% 1.82/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.82/1.33 %%% Generated on Tue Feb 24 06:17:17 EST 2026
% 1.82/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.82/1.33 %%% Logic specification used:
% 1.82/1.33 %%% thf(spec, logic, $$dhol).
% 1.82/1.33
% 1.82/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2DTF2655.p
% 1.82/1.33 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.82/1.33 thf(is_per, definition, (! [A:$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)))))))))).
% 1.82/1.33 thf(nat_type, type, nat: $tType).
% 1.82/1.33 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.82/1.33 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.82/1.33 thf(zero_type, type, zero: nat).
% 1.82/1.33 thf(suc_type, type, suc: (nat > nat)).
% 1.82/1.33 thf(plus_type, type, plus: (nat > (nat > nat))).
% 1.82/1.33 thf(list_type, type, list: ($tType > $tType)).
% 1.82/1.33 thf(listStar, type, 'listStar': (!> [A:$tType]: (((A > (A > $o)) > (nat > ((list @ A) > ((list @ A) > $o))))))).
% 1.82/1.33 thf('\'listStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:nat]: (((isPer @ (list @ B)) @ (((listStar @ B) @ BStar) @ C)))))))).
% 1.82/1.33 thf(nil_type, type, nil: (!> [A:$tType]: ((list @ A)))).
% 1.82/1.33 thf(nil_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (nil @ A)) @ (nil @ A)))))).
% 1.82/1.33 thf(cons_type, type, cons: (!> [A:$tType]: ((nat > (A > ((list @ A) > (list @ A))))))).
% 1.82/1.33 thf(cons_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:A,D_prime:A]: (((D = D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ ((((cons @ A) @ N) @ D) @ D0)) @ ((((cons @ A) @ N) @ D_prime) @ D0_prime)))))))))))))).
% 1.82/1.33 thf(app_type, type, app: (!> [A:$tType]: ((nat > (nat > ((list @ A) > ((list @ A) > (list @ A)))))))).
% 1.82/1.33 thf(app_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ M) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ M)) @ (((((app @ A) @ N) @ M) @ D) @ D0)) @ (((((app @ A) @ N) @ M) @ D_prime) @ D0_prime)))))))))))))))).
% 1.82/1.33 thf(rev_type, type, rev: (!> [A:$tType]: ((nat > ((list @ A) > (list @ A)))))).
% 1.82/1.33 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))))))))))).
% 1.82/1.33 thf(peano1, axiom, (! [N:nat]: (((suc @ N) != zero)))).
% 1.82/1.33 thf(peano2, axiom, (! [N:nat]: ((! [M:nat]: (((N != M) => ((suc @ N) != (suc @ M)))))))).
% 1.82/1.33 thf(peano3, axiom, (! [P:(nat > $o)]: (((P @ zero) => ((! [M:nat]: (((P @ M) => (P @ (suc @ M))))) => (! [N:nat]: ((P @ N)))))))).
% 1.82/1.33 thf(ax1, axiom, (! [N:nat]: ((((plus @ zero) @ N) = N)))).
% 1.82/1.33 thf(ax2, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ (suc @ N)) @ M) = (suc @ ((plus @ N) @ M)))))))).
% 1.82/1.33 thf(ax3, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [X:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ X) @ X) => (((((listStar @ A) @ AStar) @ ((plus @ zero) @ N)) @ (((((app @ A) @ zero) @ N) @ (nil @ A)) @ X)) @ X)))))))))).
% 1.82/1.33 thf(ax4, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [X:A]: ((! [Y:(list @ A),Z:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ Y) @ Y) => ((((((listStar @ A) @ AStar) @ M) @ Z) @ Z) => (((((listStar @ A) @ AStar) @ ((plus @ (suc @ N)) @ M)) @ (((((app @ A) @ (suc @ N)) @ M) @ ((((cons @ A) @ N) @ X) @ Y)) @ Z)) @ ((((cons @ A) @ ((plus @ N) @ M)) @ X) @ (((((app @ A) @ N) @ M) @ Y) @ Z))))))))))))))))).
% 1.82/1.33 thf(ax5, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (((rev @ A) @ zero) @ (nil @ A))) @ (nil @ A)))))).
% 1.82/1.33 thf(ax6, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [X:A]: ((! [Y:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ Y) @ Y) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ (((rev @ A) @ (suc @ N)) @ ((((cons @ A) @ N) @ X) @ Y))) @ (((((app @ A) @ N) @ (suc @ zero)) @ (((rev @ A) @ N) @ Y)) @ ((((cons @ A) @ zero) @ X) @ (nil @ A))))))))))))))).
% 1.82/1.33 thf(plus_com, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ N) @ M) = ((plus @ M) @ N))))))).
% 1.82/1.33 thf(plus1r, axiom, (! [N:nat]: (((suc @ N) = ((plus @ N) @ (suc @ zero)))))).
% 1.82/1.33 thf(list_app_nil, axiom, (! [A:$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)))))))))).
% 1.82/1.33 thf(list_rev_invol_step1, 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))) @ (((rev @ (list @ (list @ nat))) @ ((plus @ N) @ zero)) @ (((((app @ (list @ (list @ nat))) @ N) @ zero) @ (((rev @ (list @ (list @ nat))) @ N) @ L)) @ (nil @ (list @ (list @ nat)))))))))))).
% 1.82/1.33 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2DTF2655.p
% 1.82/1.33 ------------------------
% 1.82/1.34 ---- Cleaned THF ---
% 1.82/1.34 thf(is_per_type,type,
% 1.82/1.34 isPer:
% 1.82/1.34 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.82/1.34
% 1.82/1.34 thf(is_per,definition,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 <=> ( ! [X: A,Y: A] :
% 1.82/1.34 ( ( AStar @ X @ Y )
% 1.82/1.34 => ( AStar @ Y @ X ) )
% 1.82/1.34 & ! [X: A,Y: A,Z: A] :
% 1.82/1.34 ( ( AStar @ X @ Y )
% 1.82/1.34 => ( ( AStar @ Y @ Z )
% 1.82/1.34 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(nat_type,type,
% 1.82/1.34 nat: $tType ).
% 1.82/1.34
% 1.82/1.34 thf(natStar,type,
% 1.82/1.34 natStar: nat > nat > $o ).
% 1.82/1.34
% 1.82/1.34 thf(natStar_is_eq,axiom,
% 1.82/1.34 ! [X: nat,Y: nat] :
% 1.82/1.34 ( ( natStar @ X @ Y )
% 1.82/1.34 <=> ( X = Y ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(zero_type,type,
% 1.82/1.34 zero: nat ).
% 1.82/1.34
% 1.82/1.34 thf(suc_type,type,
% 1.82/1.34 suc: nat > nat ).
% 1.82/1.34
% 1.82/1.34 thf(plus_type,type,
% 1.82/1.34 plus: nat > nat > nat ).
% 1.82/1.34
% 1.82/1.34 thf(list_type,type,
% 1.82/1.34 list: $tType > $tType ).
% 1.82/1.34
% 1.82/1.34 thf(listStar,type,
% 1.82/1.34 listStar:
% 1.82/1.34 !>[A: $tType] : ( ( A > A > $o ) > nat > ( list @ A ) > ( list @ A ) > $o ) ).
% 1.82/1.34
% 1.82/1.34 thf('\'listStar\'_is_per',axiom,
% 1.82/1.34 ! [B: $tType,BStar: B > B > $o] :
% 1.82/1.34 ( ( isPer @ B @ BStar )
% 1.82/1.34 => ! [C: nat] : ( isPer @ ( list @ B ) @ ( listStar @ B @ BStar @ C ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(nil_type,type,
% 1.82/1.34 nil:
% 1.82/1.34 !>[A: $tType] : ( list @ A ) ).
% 1.82/1.34
% 1.82/1.34 thf(nil_tp_ax,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ( listStar @ A @ AStar @ zero @ ( nil @ A ) @ ( nil @ A ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(cons_type,type,
% 1.82/1.34 cons:
% 1.82/1.34 !>[A: $tType] : ( nat > A > ( list @ A ) > ( list @ A ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(cons_tp_ax,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,D: A,D_prime: A] :
% 1.82/1.34 ( ( D = D_prime )
% 1.82/1.34 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ D0 @ D0_prime )
% 1.82/1.34 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( cons @ A @ N @ D @ D0 ) @ ( cons @ A @ N @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(app_type,type,
% 1.82/1.34 app:
% 1.82/1.34 !>[A: $tType] : ( nat > nat > ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(app_tp_ax,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,M: nat,D: list @ A,D_prime: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.82/1.34 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ M @ D0 @ D0_prime )
% 1.82/1.34 => ( listStar @ A @ AStar @ ( plus @ N @ M ) @ ( app @ A @ N @ M @ D @ D0 ) @ ( app @ A @ N @ M @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(rev_type,type,
% 1.82/1.34 rev:
% 1.82/1.34 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ A ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(rev_tp_ax,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,D: list @ A,D_prime: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.82/1.34 => ( listStar @ A @ AStar @ N @ ( rev @ A @ N @ D ) @ ( rev @ A @ N @ D_prime ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(peano1,axiom,
% 1.82/1.34 ! [N: nat] :
% 1.82/1.34 ( ( suc @ N )
% 1.82/1.34 != zero ) ).
% 1.82/1.34
% 1.82/1.34 thf(peano2,axiom,
% 1.82/1.34 ! [N: nat,M: nat] :
% 1.82/1.34 ( ( N != M )
% 1.82/1.34 => ( ( suc @ N )
% 1.82/1.34 != ( suc @ M ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(peano3,axiom,
% 1.82/1.34 ! [P: nat > $o] :
% 1.82/1.34 ( ( P @ zero )
% 1.82/1.34 => ( ! [M: nat] :
% 1.82/1.34 ( ( P @ M )
% 1.82/1.34 => ( P @ ( suc @ M ) ) )
% 1.82/1.34 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax1,axiom,
% 1.82/1.34 ! [N: nat] :
% 1.82/1.34 ( ( plus @ zero @ N )
% 1.82/1.34 = N ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax2,axiom,
% 1.82/1.34 ! [N: nat,M: nat] :
% 1.82/1.34 ( ( plus @ ( suc @ N ) @ M )
% 1.82/1.34 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax3,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,X: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ X @ X )
% 1.82/1.34 => ( listStar @ A @ AStar @ ( plus @ zero @ N ) @ ( app @ A @ zero @ N @ ( nil @ A ) @ X ) @ X ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax4,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,M: nat,X: A,Y: list @ A,Z: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ Y @ Y )
% 1.82/1.34 => ( ( listStar @ A @ AStar @ M @ Z @ Z )
% 1.82/1.34 => ( 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 ) ) ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax5,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ( listStar @ A @ AStar @ zero @ ( rev @ A @ zero @ ( nil @ A ) ) @ ( nil @ A ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(ax6,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,X: A,Y: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ Y @ Y )
% 1.82/1.34 => ( 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 ) ) ) ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(plus_com,axiom,
% 1.82/1.34 ! [N: nat,M: nat] :
% 1.82/1.34 ( ( plus @ N @ M )
% 1.82/1.34 = ( plus @ M @ N ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(plus1r,axiom,
% 1.82/1.34 ! [N: nat] :
% 1.82/1.34 ( ( suc @ N )
% 1.82/1.34 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(list_app_nil,axiom,
% 1.82/1.34 ! [A: $tType,AStar: A > A > $o] :
% 1.82/1.34 ( ( isPer @ A @ AStar )
% 1.82/1.34 => ! [N: nat,L: list @ A] :
% 1.82/1.34 ( ( listStar @ A @ AStar @ N @ L @ L )
% 1.82/1.34 => ( listStar @ A @ AStar @ ( plus @ N @ zero ) @ ( app @ A @ N @ zero @ L @ ( nil @ A ) ) @ L ) ) ) ).
% 1.82/1.34
% 1.82/1.34 thf(list_rev_invol_step1,conjecture,
% 1.82/1.34 ! [N: nat,L: list @ ( list @ ( list @ nat ) )] :
% 1.82/1.34 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ N @ L @ L )
% 1.82/1.34 => ( 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 ) ) ) ) ) ) ) ).
% 1.82/1.34 ------------------------
% 1.82/1.36 % (2989)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/18Mi)
% 1.82/1.36 % (2983)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/183Mi)
% 1.82/1.36 % (2986)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/2Mi)
% 1.82/1.36 % (2986)Instruction limit reached!
% 1.82/1.36 % (2986)------------------------------
% 1.82/1.36 % (2986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.36 % (2986)Termination reason: Unknown
% 1.82/1.36 % (2986)Termination phase: shuffling
% 1.82/1.36
% 1.82/1.36 % (2986)Memory used [KB]: 1023
% 1.82/1.36 % (2986)Time elapsed: 0.002 s
% 1.82/1.36 % (2986)Instructions burned: 3 (million)
% 1.82/1.36 % (2986)------------------------------
% 1.82/1.36 % (2986)------------------------------
% 1.82/1.36 % (2989)Instruction limit reached!
% 1.82/1.36 % (2989)------------------------------
% 1.82/1.36 % (2989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.36 % (2989)Termination reason: Unknown
% 1.82/1.36 % (2989)Termination phase: Saturation
% 1.82/1.36
% 1.82/1.36 % (2989)Memory used [KB]: 5628
% 1.82/1.36 % (2989)Time elapsed: 0.007 s
% 1.82/1.36 % (2989)Instructions burned: 18 (million)
% 1.82/1.36 % (2989)------------------------------
% 1.82/1.36 % (2989)------------------------------
% 1.82/1.37 % (2984)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_2655 for (2999ds/4Mi)
% 1.82/1.37 % (2985)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_2655 for (2999ds/27Mi)
% 1.82/1.37 % (2987)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_2655 for (2999ds/2Mi)
% 1.82/1.37 % (2988)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_2655 for (2999ds/275Mi)
% 1.82/1.37 % (2987)Instruction limit reached!
% 1.82/1.37 % (2987)------------------------------
% 1.82/1.37 % (2987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.37 % (2987)Termination reason: Unknown
% 1.82/1.37 % (2987)Termination phase: shuffling
% 1.82/1.37
% 1.82/1.37 % (2987)Memory used [KB]: 1023
% 1.82/1.37 % (2987)Time elapsed: 0.003 s
% 1.82/1.37 % (2987)Instructions burned: 2 (million)
% 1.82/1.37 % (2987)------------------------------
% 1.82/1.37 % (2987)------------------------------
% 1.82/1.37 % (2984)Instruction limit reached!
% 1.82/1.37 % (2984)------------------------------
% 1.82/1.37 % (2984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.37 % (2984)Termination reason: Unknown
% 1.82/1.37 % (2984)Termination phase: shuffling
% 1.82/1.37
% 1.82/1.37 % (2984)Memory used [KB]: 1023
% 1.82/1.37 % (2984)Time elapsed: 0.004 s
% 1.82/1.37 % (2984)Instructions burned: 4 (million)
% 1.82/1.37 % (2984)------------------------------
% 1.82/1.37 % (2984)------------------------------
% 1.82/1.37 % (2990)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/3Mi)
% 1.82/1.37 % (2990)Instruction limit reached!
% 1.82/1.37 % (2990)------------------------------
% 1.82/1.37 % (2990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.37 % (2990)Termination reason: Unknown
% 1.82/1.37 % (2990)Termination phase: shuffling
% 1.82/1.37
% 1.82/1.37 % (2990)Memory used [KB]: 1023
% 1.82/1.37 % (2990)Time elapsed: 0.003 s
% 1.82/1.37 % (2990)Instructions burned: 4 (million)
% 1.82/1.37 % (2990)------------------------------
% 1.82/1.37 % (2990)------------------------------
% 1.82/1.37 % (2991)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_2655 for (2999ds/37Mi)
% 1.82/1.38 % (2988)Refutation not found, incomplete strategy
% 1.82/1.38 % (2988)------------------------------
% 1.82/1.38 % (2988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.38 % (2988)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.38
% 1.82/1.38
% 1.82/1.38 % (2988)Memory used [KB]: 5628
% 1.82/1.38 % (2988)Time elapsed: 0.015 s
% 1.82/1.38 % (2988)Instructions burned: 21 (million)
% 1.82/1.38 % (2988)------------------------------
% 1.82/1.38 % (2988)------------------------------
% 1.82/1.38 % (2994)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_2655 for (2999ds/1041Mi)
% 1.82/1.38 % (2985)Instruction limit reached!
% 1.82/1.38 % (2985)------------------------------
% 1.82/1.38 % (2985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.38 % (2985)Termination reason: Unknown
% 1.82/1.38 % (2985)Termination phase: Saturation
% 1.82/1.38
% 1.82/1.38 % (2985)Memory used [KB]: 5628
% 1.82/1.38 % (2985)Time elapsed: 0.020 s
% 1.82/1.38 % (2985)Instructions burned: 28 (million)
% 1.82/1.38 % (2985)------------------------------
% 1.82/1.38 % (2985)------------------------------
% 1.82/1.38 % (2991)Instruction limit reached!
% 1.82/1.38 % (2991)------------------------------
% 1.82/1.38 % (2991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.38 % (2991)Termination reason: Unknown
% 1.82/1.38 % (2991)Termination phase: Saturation
% 1.82/1.38
% 1.82/1.38 % (2991)Memory used [KB]: 5756
% 1.82/1.38 % (2991)Time elapsed: 0.012 s
% 1.82/1.38 % (2991)Instructions burned: 38 (million)
% 1.82/1.38 % (2991)------------------------------
% 1.82/1.38 % (2991)------------------------------
% 1.82/1.38 % (2992)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_2655 for (2999ds/15Mi)
% 1.82/1.39 % (2993)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_2655 for (2999ds/3Mi)
% 1.82/1.39 % (2993)Instruction limit reached!
% 1.82/1.39 % (2993)------------------------------
% 1.82/1.39 % (2993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.39 % (2993)Termination reason: Unknown
% 1.82/1.39 % (2993)Termination phase: shuffling
% 1.82/1.39
% 1.82/1.39 % (2993)Memory used [KB]: 1023
% 1.82/1.39 % (2993)Time elapsed: 0.004 s
% 1.82/1.39 % (2993)Instructions burned: 4 (million)
% 1.82/1.39 % (2993)------------------------------
% 1.82/1.39 % (2993)------------------------------
% 1.82/1.39 % (2992)Instruction limit reached!
% 1.82/1.39 % (2992)------------------------------
% 1.82/1.39 % (2992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.39 % (2992)Termination reason: Unknown
% 1.82/1.39 % (2992)Termination phase: Saturation
% 1.82/1.39
% 1.82/1.39 % (2992)Memory used [KB]: 1151
% 1.82/1.39 % (2992)Time elapsed: 0.011 s
% 1.82/1.39 % (2992)Instructions burned: 16 (million)
% 1.82/1.39 % (2992)------------------------------
% 1.82/1.39 % (2992)------------------------------
% 1.82/1.39 % (2997)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_2655 for (2999ds/3Mi)
% 1.82/1.39 % (2997)Instruction limit reached!
% 1.82/1.39 % (2997)------------------------------
% 1.82/1.39 % (2997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.39 % (2997)Termination reason: Unknown
% 1.82/1.39 % (2997)Termination phase: shuffling
% 1.82/1.39
% 1.82/1.39 % (2997)Memory used [KB]: 1023
% 1.82/1.39 % (2997)Time elapsed: 0.002 s
% 1.82/1.39 % (2997)Instructions burned: 3 (million)
% 1.82/1.39 % (2997)------------------------------
% 1.82/1.39 % (2997)------------------------------
% 1.89/1.40 % (2995)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/7Mi)
% 1.89/1.40 % (2995)Instruction limit reached!
% 1.89/1.40 % (2995)------------------------------
% 1.89/1.40 % (2995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.40 % (2995)Termination reason: Unknown
% 1.89/1.40 % (2995)Termination phase: Preprocessing 3
% 1.89/1.40
% 1.89/1.40 % (2995)Memory used [KB]: 1023
% 1.89/1.40 % (2995)Time elapsed: 0.006 s
% 1.89/1.40 % (2995)Instructions burned: 7 (million)
% 1.89/1.40 % (2995)------------------------------
% 1.89/1.40 % (2995)------------------------------
% 1.89/1.40 % (2996)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/16Mi)
% 1.89/1.40 % (3000)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/3Mi)
% 1.89/1.40 % (2998)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_2655 for (2999ds/3Mi)
% 1.89/1.41 % (3000)Instruction limit reached!
% 1.89/1.41 % (3000)------------------------------
% 1.89/1.41 % (3000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (3000)Termination reason: Unknown
% 1.89/1.41 % (3000)Termination phase: shuffling
% 1.89/1.41
% 1.89/1.41 % (3000)Memory used [KB]: 1023
% 1.89/1.41 % (3000)Time elapsed: 0.002 s
% 1.89/1.41 % (3000)Instructions burned: 4 (million)
% 1.89/1.41 % (3000)------------------------------
% 1.89/1.41 % (3000)------------------------------
% 1.89/1.41 % (2998)Instruction limit reached!
% 1.89/1.41 % (2998)------------------------------
% 1.89/1.41 % (2998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (2998)Termination reason: Unknown
% 1.89/1.41 % (2998)Termination phase: shuffling
% 1.89/1.41
% 1.89/1.41 % (2998)Memory used [KB]: 1023
% 1.89/1.41 % (2998)Time elapsed: 0.004 s
% 1.89/1.41 % (2998)Instructions burned: 4 (million)
% 1.89/1.41 % (2998)------------------------------
% 1.89/1.41 % (2998)------------------------------
% 1.89/1.41 % (2999)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/7Mi)
% 1.89/1.41 % (2996)Instruction limit reached!
% 1.89/1.41 % (2996)------------------------------
% 1.89/1.41 % (2996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (2996)Termination reason: Unknown
% 1.89/1.41 % (2996)Termination phase: Saturation
% 1.89/1.41
% 1.89/1.41 % (2996)Memory used [KB]: 5628
% 1.89/1.41 % (2996)Time elapsed: 0.012 s
% 1.89/1.41 % (2996)Instructions burned: 16 (million)
% 1.89/1.41 % (2996)------------------------------
% 1.89/1.41 % (2996)------------------------------
% 1.89/1.41 % (3002)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/18Mi)
% 1.89/1.41 % (2999)Instruction limit reached!
% 1.89/1.41 % (2999)------------------------------
% 1.89/1.41 % (2999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (2999)Termination reason: Unknown
% 1.89/1.41 % (2999)Termination phase: Preprocessing 3
% 1.89/1.41
% 1.89/1.41 % (2999)Memory used [KB]: 1023
% 1.89/1.41 % (2999)Time elapsed: 0.006 s
% 1.89/1.41 % (2999)Instructions burned: 7 (million)
% 1.89/1.41 % (2999)------------------------------
% 1.89/1.41 % (2999)------------------------------
% 1.89/1.42 % (3001)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/4Mi)
% 1.89/1.42 % (3002)Instruction limit reached!
% 1.89/1.42 % (3002)------------------------------
% 1.89/1.42 % (3002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (3002)Termination reason: Unknown
% 1.89/1.42 % (3002)Termination phase: Saturation
% 1.89/1.42
% 1.89/1.42 % (3002)Memory used [KB]: 5628
% 1.89/1.42 % (3002)Time elapsed: 0.007 s
% 1.89/1.42 % (3002)Instructions burned: 20 (million)
% 1.89/1.42 % (3002)------------------------------
% 1.89/1.42 % (3002)------------------------------
% 1.89/1.42 % (2983)Instruction limit reached!
% 1.89/1.42 % (2983)------------------------------
% 1.89/1.42 % (2983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (2983)Termination reason: Unknown
% 1.89/1.42 % (2983)Termination phase: Saturation
% 1.89/1.42
% 1.89/1.42 % (2983)Memory used [KB]: 6396
% 1.89/1.42 % (2983)Time elapsed: 0.063 s
% 1.89/1.42 % (2983)Instructions burned: 184 (million)
% 1.89/1.42 % (2983)------------------------------
% 1.89/1.42 % (2983)------------------------------
% 1.89/1.42 % (3001)Instruction limit reached!
% 1.89/1.42 % (3001)------------------------------
% 1.89/1.42 % (3001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (3001)Termination reason: Unknown
% 1.89/1.42 % (3001)Termination phase: shuffling
% 1.89/1.42
% 1.89/1.42 % (3001)Memory used [KB]: 1023
% 1.89/1.42 % (3001)Time elapsed: 0.004 s
% 1.89/1.42 % (3001)Instructions burned: 4 (million)
% 1.89/1.42 % (3001)------------------------------
% 1.89/1.42 % (3001)------------------------------
% 1.89/1.42 % (3003)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/710Mi)
% 1.89/1.43 % (3004)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/6Mi)
% 1.89/1.43 % (3006)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_2655 for (2999ds/21Mi)
% 1.89/1.43 % (3007)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/5Mi)
% 1.89/1.43 % (3004)Instruction limit reached!
% 1.89/1.43 % (3004)------------------------------
% 1.89/1.43 % (3004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.43 % (3004)Termination reason: Unknown
% 1.89/1.43 % (3004)Termination phase: Property scanning
% 1.89/1.43
% 1.89/1.43 % (3004)Memory used [KB]: 1023
% 1.89/1.43 % (3004)Time elapsed: 0.005 s
% 1.89/1.43 % (3004)Instructions burned: 6 (million)
% 1.89/1.43 % (3004)------------------------------
% 1.89/1.43 % (3004)------------------------------
% 1.89/1.43 % (3007)Instruction limit reached!
% 1.89/1.43 % (3007)------------------------------
% 1.89/1.43 % (3007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.43 % (3007)Termination reason: Unknown
% 1.89/1.43 % (3007)Termination phase: shuffling
% 1.89/1.43
% 1.89/1.43 % (3007)Memory used [KB]: 1023
% 1.89/1.43 % (3007)Time elapsed: 0.003 s
% 1.89/1.43 % (3007)Instructions burned: 5 (million)
% 1.89/1.43 % (3007)------------------------------
% 1.89/1.43 % (3007)------------------------------
% 1.89/1.43 % (3005)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_2655 for (2999ds/902Mi)
% 1.89/1.44 % (3006)Instruction limit reached!
% 1.89/1.44 % (3006)------------------------------
% 1.89/1.44 % (3006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.44 % (3006)Termination reason: Unknown
% 1.89/1.44 % (3006)Termination phase: Saturation
% 1.89/1.44
% 1.89/1.44 % (3006)Memory used [KB]: 5628
% 1.89/1.44 % (3006)Time elapsed: 0.008 s
% 1.89/1.44 % (3006)Instructions burned: 21 (million)
% 1.89/1.44 % (3006)------------------------------
% 1.89/1.44 % (3006)------------------------------
% 1.89/1.44 % (3008)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_2655 for (2999ds/6Mi)
% 1.89/1.44 % (3008)Instruction limit reached!
% 1.89/1.44 % (3008)------------------------------
% 1.89/1.44 % (3008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.44 % (3008)Termination reason: Unknown
% 1.89/1.44 % (3008)Termination phase: Property scanning
% 1.89/1.44
% 1.89/1.44 % (3008)Memory used [KB]: 1023
% 1.89/1.44 % (3008)Time elapsed: 0.005 s
% 1.89/1.44 % (3008)Instructions burned: 6 (million)
% 1.89/1.44 % (3008)------------------------------
% 1.89/1.44 % (3008)------------------------------
% 1.89/1.44 % (3009)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/377Mi)
% 1.89/1.45 % (3005)Refutation not found, incomplete strategy
% 1.89/1.45 % (3005)------------------------------
% 1.89/1.45 % (3005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (3005)Termination reason: Refutation not found, incomplete strategy
% 1.89/1.45
% 1.89/1.45
% 1.89/1.45 % (3005)Memory used [KB]: 5628
% 1.89/1.45 % (3005)Time elapsed: 0.014 s
% 1.89/1.45 % (3005)Instructions burned: 21 (million)
% 1.89/1.45 % (3005)------------------------------
% 1.89/1.45 % (3005)------------------------------
% 1.89/1.45 % (3011)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_2655 for (2999ds/19Mi)
% 1.89/1.45 % (3010)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_2655 for (2999ds/779Mi)
% 1.89/1.45 % (3011)Instruction limit reached!
% 1.89/1.45 % (3011)------------------------------
% 1.89/1.45 % (3011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (3011)Termination reason: Unknown
% 1.89/1.45 % (3011)Termination phase: Saturation
% 1.89/1.45
% 1.89/1.45 % (3011)Memory used [KB]: 5628
% 1.89/1.45 % (3011)Time elapsed: 0.007 s
% 1.89/1.45 % (3011)Instructions burned: 20 (million)
% 1.89/1.45 % (3011)------------------------------
% 1.89/1.45 % (3011)------------------------------
% 1.89/1.46 % (3012)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/879Mi)
% 1.89/1.46 % (3014)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/3Mi)
% 1.89/1.46 % (3013)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2655 for (2999ds/17Mi)
% 1.89/1.46 % (3014)Instruction limit reached!
% 1.89/1.46 % (3014)------------------------------
% 1.89/1.46 % (3014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.46 % (3014)Termination reason: Unknown
% 1.89/1.46 % (3014)Termination phase: shuffling
% 1.89/1.46
% 1.89/1.46 % (3014)Memory used [KB]: 1023
% 1.89/1.46 % (3014)Time elapsed: 0.002 s
% 1.89/1.46 % (3014)Instructions burned: 4 (million)
% 1.89/1.46 % (3014)------------------------------
% 1.89/1.46 % (3014)------------------------------
% 1.89/1.47 % (3013)Instruction limit reached!
% 1.89/1.47 % (3013)------------------------------
% 1.89/1.47 % (3013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.47 % (3013)Termination reason: Unknown
% 1.89/1.47 % (3013)Termination phase: Saturation
% 1.89/1.47
% 1.89/1.47 % (3013)Memory used [KB]: 5628
% 1.89/1.47 % (3013)Time elapsed: 0.010 s
% 1.89/1.47 % (3013)Instructions burned: 17 (million)
% 1.89/1.47 % (3013)------------------------------
% 1.89/1.47 % (3013)------------------------------
% 1.89/1.47 % (3015)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2655 for (2998ds/30Mi)
% 1.89/1.48 % (3016)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2655 for (2998ds/127Mi)
% 1.89/1.48 % (3015)Instruction limit reached!
% 1.89/1.48 % (3015)------------------------------
% 1.89/1.48 % (3015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.48 % (3015)Termination reason: Unknown
% 1.89/1.48 % (3015)Termination phase: Saturation
% 1.89/1.48
% 1.89/1.48 % (3015)Memory used [KB]: 5756
% 1.89/1.48 % (3015)Time elapsed: 0.011 s
% 1.89/1.48 % (3015)Instructions burned: 32 (million)
% 1.89/1.48 % (3015)------------------------------
% 1.89/1.48 % (3015)------------------------------
% 1.89/1.49 % (3017)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2655 for (2998ds/100Mi)
% 1.89/1.52 % (3017)Instruction limit reached!
% 1.89/1.52 % (3017)------------------------------
% 1.89/1.52 % (3017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.52 % (3017)Termination reason: Unknown
% 1.89/1.52 % (3017)Termination phase: Saturation
% 1.89/1.52
% 1.89/1.52 % (3017)Memory used [KB]: 6012
% 1.89/1.52 % (3017)Time elapsed: 0.031 s
% 1.89/1.52 % (3017)Instructions burned: 102 (million)
% 1.89/1.52 % (3017)------------------------------
% 1.89/1.52 % (3017)------------------------------
% 1.89/1.52 % (3016)Instruction limit reached!
% 1.89/1.52 % (3016)------------------------------
% 1.89/1.52 % (3016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.52 % (3016)Termination reason: Unknown
% 1.89/1.52 % (3016)Termination phase: Saturation
% 1.89/1.52
% 1.89/1.52 % (3016)Memory used [KB]: 6012
% 1.89/1.52 % (3016)Time elapsed: 0.043 s
% 1.89/1.52 % (3016)Instructions burned: 127 (million)
% 1.89/1.52 % (3016)------------------------------
% 1.89/1.52 % (3016)------------------------------
% 1.89/1.53 % (3018)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_2655 for (2998ds/3Mi)
% 1.89/1.53 % (3018)Instruction limit reached!
% 1.89/1.53 % (3018)------------------------------
% 1.89/1.53 % (3018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (3018)Termination reason: Unknown
% 1.89/1.53 % (3018)Termination phase: shuffling
% 1.89/1.53
% 1.89/1.53 % (3018)Memory used [KB]: 1023
% 1.89/1.53 % (3018)Time elapsed: 0.002 s
% 1.89/1.53 % (3018)Instructions burned: 3 (million)
% 1.89/1.53 % (3018)------------------------------
% 1.89/1.53 % (3018)------------------------------
% 1.89/1.53 % (3019)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_2655 for (2998ds/20Mi)
% 1.89/1.54 % (3019)Instruction limit reached!
% 1.89/1.54 % (3019)------------------------------
% 1.89/1.54 % (3019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.54 % (3019)Termination reason: Unknown
% 1.89/1.54 % (3019)Termination phase: Saturation
% 1.89/1.54
% 1.89/1.54 % (3019)Memory used [KB]: 5628
% 1.89/1.54 % (3019)Time elapsed: 0.009 s
% 1.89/1.54 % (3019)Instructions burned: 22 (million)
% 1.89/1.54 % (3019)------------------------------
% 1.89/1.54 % (3019)------------------------------
% 1.89/1.54 % (3020)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_2655 for (2998ds/86Mi)
% 1.89/1.55 % (3021)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_2655 for (2998ds/107Mi)
% 1.89/1.57 % (3020)Instruction limit reached!
% 1.89/1.57 % (3020)------------------------------
% 1.89/1.57 % (3020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (3020)Termination reason: Unknown
% 1.89/1.57 % (3020)Termination phase: Saturation
% 1.89/1.57
% 1.89/1.57 % (3020)Memory used [KB]: 6268
% 1.89/1.57 % (3020)Time elapsed: 0.028 s
% 1.89/1.57 % (3020)Instructions burned: 87 (million)
% 1.89/1.57 % (3020)------------------------------
% 1.89/1.57 % (3020)------------------------------
% 1.89/1.57 % (3009)Instruction limit reached!
% 1.89/1.57 % (3009)------------------------------
% 1.89/1.57 % (3009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (3009)Termination reason: Unknown
% 1.89/1.57 % (3009)Termination phase: Saturation
% 1.89/1.57
% 1.89/1.57 % (3009)Memory used [KB]: 6140
% 1.89/1.57 % (3009)Time elapsed: 0.131 s
% 1.89/1.57 % (3009)Instructions burned: 379 (million)
% 1.89/1.57 % (3009)------------------------------
% 1.89/1.57 % (3009)------------------------------
% 1.89/1.58 % (3022)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_2655 for (2997ds/39Mi)
% 1.89/1.58 % (3023)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_2655 for (2997ds/448Mi)
% 1.89/1.59 % (3021)Instruction limit reached!
% 1.89/1.59 % (3021)------------------------------
% 1.89/1.59 % (3021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (3021)Termination reason: Unknown
% 1.89/1.59 % (3021)Termination phase: Saturation
% 1.89/1.59
% 1.89/1.59 % (3021)Memory used [KB]: 6012
% 1.89/1.59 % (3021)Time elapsed: 0.039 s
% 1.89/1.59 % (3021)Instructions burned: 109 (million)
% 1.89/1.59 % (3021)------------------------------
% 1.89/1.59 % (3021)------------------------------
% 1.89/1.59 % (3022)Instruction limit reached!
% 1.89/1.59 % (3022)------------------------------
% 1.89/1.59 % (3022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (3022)Termination reason: Unknown
% 1.89/1.59 % (3022)Termination phase: Saturation
% 1.89/1.59
% 1.89/1.59 % (3022)Memory used [KB]: 5756
% 1.89/1.59 % (3022)Time elapsed: 0.014 s
% 1.89/1.59 % (3022)Instructions burned: 41 (million)
% 1.89/1.59 % (3022)------------------------------
% 1.89/1.59 % (3022)------------------------------
% 1.89/1.60 % (3024)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_2655 for (2997ds/46Mi)
% 1.89/1.60 % (3025)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_2655 for (2997ds/98Mi)
% 1.89/1.61 % (3024)Instruction limit reached!
% 1.89/1.61 % (3024)------------------------------
% 1.89/1.61 % (3024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (3024)Termination reason: Unknown
% 1.89/1.61 % (3024)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (3024)Memory used [KB]: 5884
% 1.89/1.61 % (3024)Time elapsed: 0.018 s
% 1.89/1.61 % (3024)Instructions burned: 48 (million)
% 1.89/1.61 % (3024)------------------------------
% 1.89/1.61 % (3024)------------------------------
% 1.89/1.62 % (3026)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_2655 for (2997ds/507Mi)
% 1.89/1.63 % (3025)Instruction limit reached!
% 1.89/1.63 % (3025)------------------------------
% 1.89/1.63 % (3025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.63 % (3025)Termination reason: Unknown
% 1.89/1.63 % (3025)Termination phase: Saturation
% 1.89/1.63
% 1.89/1.63 % (3025)Memory used [KB]: 1407
% 1.89/1.63 % (3025)Time elapsed: 0.052 s
% 1.89/1.63 % (3025)Instructions burned: 99 (million)
% 1.89/1.63 % (3025)------------------------------
% 1.89/1.63 % (3025)------------------------------
% 1.89/1.63 % (3026)Refutation not found, incomplete strategy
% 1.89/1.63 % (3026)------------------------------
% 1.89/1.63 % (3026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.63 % (3026)Termination reason: Refutation not found, incomplete strategy
% 1.89/1.63
% 1.89/1.63
% 1.89/1.63 % (3026)Memory used [KB]: 5756
% 1.89/1.63 % (3026)Time elapsed: 0.011 s
% 1.89/1.63 % (3026)Instructions burned: 28 (million)
% 1.89/1.63 % (3026)------------------------------
% 1.89/1.63 % (3026)------------------------------
% 1.89/1.64 % (3027)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_2655 for (2997ds/149Mi)
% 1.89/1.64 % (3028)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2655 for (2997ds/39Mi)
% 1.89/1.66 % (3028)Instruction limit reached!
% 1.89/1.66 % (3028)------------------------------
% 1.89/1.66 % (3028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.66 % (3028)Termination reason: Unknown
% 1.89/1.66 % (3028)Termination phase: Saturation
% 1.89/1.66
% 1.89/1.66 % (3028)Memory used [KB]: 5756
% 1.89/1.66 % (3028)Time elapsed: 0.041 s
% 1.89/1.66 % (3028)Instructions burned: 39 (million)
% 1.89/1.66 % (3028)------------------------------
% 1.89/1.66 % (3028)------------------------------
% 1.89/1.66 % (3003)Instruction limit reached!
% 1.89/1.66 % (3003)------------------------------
% 1.89/1.66 % (3003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.66 % (3003)Termination reason: Unknown
% 1.89/1.66 % (3003)Termination phase: Saturation
% 1.89/1.66
% 1.89/1.66 % (3003)Memory used [KB]: 7419
% 1.89/1.66 % (3003)Time elapsed: 0.234 s
% 1.89/1.66 % (3003)Instructions burned: 711 (million)
% 1.89/1.66 % (3003)------------------------------
% 1.89/1.66 % (3003)------------------------------
% 1.89/1.67 % (3029)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_2655 for (2996ds/6Mi)
% 1.89/1.67 % (3030)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_2655 for (2996ds/1087Mi)
% 1.89/1.67 % (3029)Instruction limit reached!
% 1.89/1.67 % (3029)------------------------------
% 1.89/1.67 % (3029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.67 % (3029)Termination reason: Unknown
% 1.89/1.67 % (3029)Termination phase: Preprocessing 3
% 1.89/1.67
% 1.89/1.67 % (3029)Memory used [KB]: 1023
% 1.89/1.67 % (3029)Time elapsed: 0.004 s
% 1.89/1.67 % (3029)Instructions burned: 8 (million)
% 1.89/1.67 % (3029)------------------------------
% 1.89/1.67 % (3029)------------------------------
% 1.89/1.68 % (3031)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2655 for (2996ds/47Mi)
% 1.89/1.69 % (3027)Instruction limit reached!
% 1.89/1.69 % (3027)------------------------------
% 1.89/1.69 % (3027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.69 % (3027)Termination reason: Unknown
% 1.89/1.69 % (3027)Termination phase: Saturation
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% 1.89/1.69 % (3027)Time elapsed: 0.073 s
% 1.89/1.69 % (3027)Instructions burned: 149 (million)
% 1.89/1.69 % (3027)------------------------------
% 1.89/1.69 % (3027)------------------------------
% 1.89/1.69 % (3031)Instruction limit reached!
% 1.89/1.69 % (3031)------------------------------
% 1.89/1.69 % (3031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.69 % (3031)Termination reason: Unknown
% 1.89/1.69 % (3031)Termination phase: Saturation
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% 1.89/1.69 % (3031)Time elapsed: 0.018 s
% 1.89/1.69 % (3031)Instructions burned: 48 (million)
% 1.89/1.69 % (3031)------------------------------
% 1.89/1.69 % (3031)------------------------------
% 1.89/1.70 % (3032)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_2655 for (2996ds/44Mi)
% 1.89/1.70 % (3010)Instruction limit reached!
% 1.89/1.70 % (3010)------------------------------
% 1.89/1.70 % (3010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.70 % (3010)Termination reason: Unknown
% 1.89/1.70 % (3010)Termination phase: Saturation
% 1.89/1.70
% 1.89/1.70 % (3010)Memory used [KB]: 7036
% 1.89/1.70 % (3010)Time elapsed: 0.253 s
% 1.89/1.70 % (3010)Instructions burned: 780 (million)
% 1.89/1.70 % (3010)------------------------------
% 1.89/1.70 % (3010)------------------------------
% 1.89/1.70 % (2994)Instruction limit reached!
% 1.89/1.70 % (2994)------------------------------
% 1.89/1.70 % (2994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.70 % (2994)Termination reason: Unknown
% 1.89/1.70 % (2994)Termination phase: Saturation
% 1.89/1.70
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% 1.89/1.70 % (2994)Time elapsed: 0.321 s
% 1.89/1.70 % (2994)Instructions burned: 1041 (million)
% 1.89/1.70 % (2994)------------------------------
% 1.89/1.70 % (2994)------------------------------
% 1.89/1.70 % (3033)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_2655 for (2996ds/432Mi)
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% 1.89/1.71 % (3032)------------------------------
% 1.89/1.71 % (3032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.71 % (3032)Termination reason: Unknown
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% 1.89/1.71
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% 1.89/1.71 % (3032)Time elapsed: 0.014 s
% 1.89/1.71 % (3032)Instructions burned: 45 (million)
% 1.89/1.71 % (3032)------------------------------
% 1.89/1.71 % (3032)------------------------------
% 1.89/1.71 % (3035)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_2655 for (2996ds/31Mi)
% 1.89/1.71 % (3034)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2655 for (2996ds/62Mi)
% 1.89/1.72 % (3023)Instruction limit reached!
% 1.89/1.72 % (3023)------------------------------
% 1.89/1.72 % (3023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.72 % (3023)Termination reason: Unknown
% 1.89/1.72 % (3023)Termination phase: Saturation
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% 1.89/1.72 % (3023)Time elapsed: 0.158 s
% 1.89/1.72 % (3023)Instructions burned: 451 (million)
% 1.89/1.72 % (3023)------------------------------
% 1.89/1.72 % (3023)------------------------------
% 1.89/1.72 % (3036)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2655 for (2996ds/96Mi)
% 1.89/1.72 % (3035)Instruction limit reached!
% 1.89/1.72 % (3035)------------------------------
% 1.89/1.72 % (3035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.72 % (3035)Termination reason: Unknown
% 1.89/1.72 % (3035)Termination phase: Saturation
% 1.89/1.72
% 1.89/1.72 % (3035)Memory used [KB]: 5756
% 1.89/1.72 % (3035)Time elapsed: 0.011 s
% 1.89/1.72 % (3035)Instructions burned: 32 (million)
% 1.89/1.72 % (3035)------------------------------
% 1.89/1.72 % (3035)------------------------------
% 1.89/1.73 % (3037)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_2655 for (2996ds/453Mi)
% 1.89/1.73 % (3030)First to succeed.
% 1.89/1.73 % (3030)Refutation found. Thanks to Tanya!
% 1.89/1.73 % SZS status Theorem for DTF2THF_2655
% 1.89/1.73 % SZS output start Proof for DTF2THF_2655
% 1.89/1.73 thf(type_def_6, type, nat: $tType).
% 1.89/1.73 thf(type_def_7, type, list: ($tType) > $tType).
% 1.89/1.73 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.89/1.73 thf(func_def_2, type, nat: $tType).
% 1.89/1.73 thf(func_def_3, type, natStar: nat > nat > $o).
% 1.89/1.73 thf(func_def_4, type, zero: nat).
% 1.89/1.73 thf(func_def_5, type, suc: nat > nat).
% 1.89/1.73 thf(func_def_6, type, plus: nat > nat > nat).
% 1.89/1.73 thf(func_def_7, type, list: ($tType) > $tType).
% 1.89/1.73 thf(func_def_8, type, listStar: !>[X0: $tType]:((X0 > X0 > $o) > nat > list @ X0 > list @ X0 > $o)).
% 1.89/1.73 thf(func_def_9, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.89/1.73 thf(func_def_10, type, cons: !>[X0: $tType]:(nat > X0 > list @ X0 > list @ X0)).
% 1.89/1.73 thf(func_def_11, type, app: !>[X0: $tType]:(nat > nat > list @ X0 > list @ X0 > list @ X0)).
% 1.89/1.73 thf(func_def_12, type, rev: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 1.89/1.73 thf(func_def_15, type, sP0: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.89/1.73 thf(func_def_16, type, sP1: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.89/1.73 thf(func_def_17, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.73 thf(func_def_18, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.73 thf(func_def_19, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.73 thf(func_def_20, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.73 thf(func_def_21, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.73 thf(func_def_22, type, sK7: (nat > $o) > nat).
% 1.89/1.73 thf(func_def_23, type, sK8: nat).
% 1.89/1.73 thf(func_def_24, type, sK9: list @ list @ list @ nat).
% 1.89/1.73 thf(func_def_27, type, ph11: !>[X0: $tType]:(X0)).
% 1.89/1.73 thf(f572,plain,(
% 1.89/1.73 $false),
% 1.89/1.73 inference(avatar_sat_refutation,[status(thm)],[f403,f425,f432,f447,f475,f479,f504,f515,f549,f567])).
% 1.89/1.73 thf(f567,plain,(
% 1.89/1.73 ~spl10_14 | spl10_19),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f566,f513,f430])).
% 1.89/1.73 thf(f430,definition,(
% 1.89/1.73 spl10_14 <=> ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_14])],[avatar_definition])).
% 1.89/1.73 thf(f513,definition,(
% 1.89/1.73 spl10_19 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (rev @ list @ list @ nat @ sK8 @ sK9)) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_19])],[avatar_definition])).
% 1.89/1.73 thf(f566,plain,(
% 1.89/1.73 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_19),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f565,f114])).
% 1.89/1.73 thf(f114,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ sK9 @ sK9) = $true)),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f91])).
% 1.89/1.73 thf(f91,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9)) @ (rev @ list @ list @ nat @ (plus @ sK8 @ zero) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat))) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ sK9 @ sK9) = $true)),
% 1.89/1.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f62,f90])).
% 1.89/1.73 thf(f90,plain,(
% 1.89/1.73 ? [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)) @ (rev @ list @ list @ nat @ (plus @ X0 @ zero) @ (app @ list @ list @ nat @ X0 @ zero @ (rev @ list @ list @ nat @ X0 @ X1) @ nil @ list @ list @ nat))) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) = $true)) => (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9)) @ (rev @ list @ list @ nat @ (plus @ sK8 @ zero) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat))) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ sK9 @ sK9) = $true))),
% 1.89/1.73 introduced(definition,[],[choice_axiom])).
% 1.89/1.73 thf(f62,plain,(
% 1.89/1.73 ? [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)) @ (rev @ list @ list @ nat @ (plus @ X0 @ zero) @ (app @ list @ list @ nat @ X0 @ zero @ (rev @ list @ list @ nat @ X0 @ X1) @ nil @ list @ list @ nat))) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1) = $true))),
% 1.89/1.73 inference(ennf_transformation,[status(thm)],[f44])).
% 1.89/1.73 thf(f44,plain,(
% 1.89/1.73 ~! [X0 : nat,X1 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ 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)) @ (rev @ list @ list @ nat @ (plus @ X0 @ zero) @ (app @ list @ list @ nat @ X0 @ zero @ (rev @ list @ list @ nat @ X0 @ X1) @ nil @ list @ list @ nat))) = $true))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f43])).
% 1.89/1.73 thf(f43,plain,(
% 1.89/1.73 ~! [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))))),
% 1.89/1.73 inference(rectify,[status(thm)],[f21])).
% 1.89/1.73 thf(f21,negated_conjecture,(
% 1.89/1.73 ~! [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))))),
% 1.89/1.73 inference(negated_conjecture,[status(cth)],[f20])).
% 1.89/1.73 thf(f20,conjecture,(
% 1.89/1.73 ! [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))))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',list_rev_invol_step1)).
% 1.89/1.73 thf(f565,plain,(
% 1.89/1.73 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ sK9 @ sK9) != $true) | spl10_19),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f560])).
% 1.89/1.73 thf(f560,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ sK9 @ sK9) != $true) | ($true != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_19),
% 1.89/1.73 inference(superposition,[status(thm)],[f514,f120])).
% 1.89/1.73 thf(f120,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ (rev @ X0 @ X2 @ X3) @ (rev @ X0 @ X2 @ X4)) = $true) | ((listStar @ X0 @ X1 @ X2 @ X3 @ X4) != $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f64])).
% 1.89/1.73 thf(f64,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat,X3 : list @ X0,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ (rev @ X0 @ X2 @ X3) @ (rev @ X0 @ X2 @ X4)) = $true) | ((listStar @ X0 @ X1 @ X2 @ X3 @ X4) != $true)))),
% 1.89/1.73 inference(ennf_transformation,[status(thm)],[f50])).
% 1.89/1.73 thf(f50,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : list @ X0,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X3 @ X4) = $true) => ((listStar @ X0 @ X1 @ X2 @ (rev @ X0 @ X2 @ X3) @ (rev @ X0 @ X2 @ X4)) = $true)))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f49])).
% 1.89/1.73 thf(f49,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : list @ X0,X4 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X3 @ X4) => (listStar @ X0 @ X1 @ X2 @ (rev @ X0 @ X2 @ X3) @ (rev @ X0 @ X2 @ X4))))),
% 1.89/1.73 inference(rectify,[status(thm)],[f7])).
% 1.89/1.73 thf(f7,axiom,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X9 : list @ X0,X10 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X9 @ X10) => (listStar @ X0 @ X1 @ X8 @ (rev @ X0 @ X8 @ X9) @ (rev @ X0 @ X8 @ X10))))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',rev_tp_ax)).
% 1.89/1.73 thf(f514,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | spl10_19),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f513])).
% 1.89/1.73 thf(f549,plain,(
% 1.89/1.73 ~spl10_11 | spl10_14),
% 1.89/1.73 inference(avatar_contradiction_clause,[status(thm)],[f548])).
% 1.89/1.73 thf(f548,plain,(
% 1.89/1.73 $false | (~spl10_11 | spl10_14)),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f547,f399])).
% 1.89/1.73 thf(f399,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) = $true) | ~spl10_11),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f398])).
% 1.89/1.73 thf(f398,definition,(
% 1.89/1.73 spl10_11 <=> ((sP1 @ nat @ natStar) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_11])],[avatar_definition])).
% 1.89/1.73 thf(f547,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) != $true) | spl10_14),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f546])).
% 1.89/1.73 thf(f546,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) != $true) | ($true != $true) | spl10_14),
% 1.89/1.73 inference(superposition,[status(thm)],[f526,f103])).
% 1.89/1.73 thf(f103,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f86])).
% 1.89/1.73 thf(f86,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)) & (((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)))),
% 1.89/1.73 inference(nnf_transformation,[status(thm)],[f76])).
% 1.89/1.73 thf(f76,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> ((sP1 @ X0 @ X1) = $true))),
% 1.89/1.73 inference(definition_folding,[status(thm)],[f69,f75,f74])).
% 1.89/1.73 thf(f74,plain,(
% 1.89/1.73 ! [X1 : X0 > X0 > $o,X0 : $tType] : (((sP0 @ X0 @ X1) = $true) <=> ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X6) = $true)))),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.89/1.73 thf(f75,plain,(
% 1.89/1.73 ! [X1 : X0 > X0 > $o,X0 : $tType] : (((sP1 @ X0 @ X1) = $true) <=> (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ((sP0 @ X0 @ X1) = $true)))),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.89/1.73 thf(f69,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X6) = $true))))),
% 1.89/1.73 inference(flattening,[status(thm)],[f68])).
% 1.89/1.73 thf(f68,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X4 : X0,X5 : X0,X6 : X0] : ((((X1 @ X4 @ X6) = $true) | ((X1 @ X5 @ X6) != $true)) | ((X1 @ X4 @ X5) != $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))))),
% 1.89/1.73 inference(ennf_transformation,[status(thm)],[f34])).
% 1.89/1.73 thf(f34,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) => (((X1 @ X5 @ X6) = $true) => ((X1 @ X4 @ X6) = $true))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true))))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f33])).
% 1.89/1.73 thf(f33,plain,(
% 1.89/1.73 ! [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))),
% 1.89/1.73 inference(rectify,[status(thm)],[f1])).
% 1.89/1.73 thf(f1,axiom,(
% 1.89/1.73 ! [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))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',is_per)).
% 1.89/1.73 thf(f526,plain,(
% 1.89/1.73 ((isPer @ nat @ natStar) != $true) | spl10_14),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f525])).
% 1.89/1.73 thf(f525,plain,(
% 1.89/1.73 ($true != $true) | ((isPer @ nat @ natStar) != $true) | spl10_14),
% 1.89/1.73 inference(superposition,[status(thm)],[f522,f113])).
% 1.89/1.73 thf(f113,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X2 : nat,X1 : X0 > X0 > $o] : (((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f71])).
% 1.89/1.73 thf(f71,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true))),
% 1.89/1.73 inference(ennf_transformation,[status(thm)],[f26])).
% 1.89/1.73 thf(f26,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f25])).
% 1.89/1.73 thf(f25,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat] : (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)))),
% 1.89/1.73 inference(rectify,[status(thm)],[f3])).
% 1.89/1.73 thf(f3,axiom,(
% 1.89/1.73 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : nat] : (isPer @ list @ X5 @ (listStar @ X5 @ X6 @ X7)))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p','\'listStar\'_is_per')).
% 1.89/1.73 thf(f522,plain,(
% 1.89/1.73 ((isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero))) != $true) | spl10_14),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f521])).
% 1.89/1.73 thf(f521,plain,(
% 1.89/1.73 ((isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero))) != $true) | ($true != $true) | spl10_14),
% 1.89/1.73 inference(superposition,[status(thm)],[f431,f113])).
% 1.89/1.73 thf(f431,plain,(
% 1.89/1.73 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_14),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f430])).
% 1.89/1.73 thf(f515,plain,(
% 1.89/1.73 ~spl10_19 | ~spl10_14 | spl10_15),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f511,f445,f430,f513])).
% 1.89/1.73 thf(f445,definition,(
% 1.89/1.73 spl10_15 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat) @ (rev @ list @ list @ nat @ sK8 @ sK9)) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_15])],[avatar_definition])).
% 1.89/1.73 thf(f511,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_15),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f506])).
% 1.89/1.73 thf(f506,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != $true) | spl10_15),
% 1.89/1.73 inference(superposition,[status(thm)],[f446,f418])).
% 1.89/1.73 thf(f418,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (((listStar @ X0 @ X1 @ X2 @ (app @ X0 @ X2 @ zero @ X3 @ nil @ X0) @ X3) = $true) | ((isPer @ X0 @ X1) != $true) | ((listStar @ X0 @ X1 @ X2 @ X3 @ X3) != $true)) )),
% 1.89/1.73 inference(forward_demodulation,[status(thm)],[f111,f129])).
% 1.89/1.73 thf(f129,plain,(
% 1.89/1.73 ( ! [X0 : nat] : (((plus @ X0 @ zero) = X0)) )),
% 1.89/1.73 inference(superposition,[status(thm)],[f122,f116])).
% 1.89/1.73 thf(f116,plain,(
% 1.89/1.73 ( ! [X0 : nat] : (((plus @ zero @ X0) = X0)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f55])).
% 1.89/1.73 thf(f55,plain,(
% 1.89/1.73 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 1.89/1.73 inference(rectify,[status(thm)],[f11])).
% 1.89/1.73 thf(f11,axiom,(
% 1.89/1.73 ! [X8 : nat] : ((plus @ zero @ X8) = X8)),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',ax1)).
% 1.89/1.73 thf(f122,plain,(
% 1.89/1.73 ( ! [X0 : nat,X1 : nat] : (((plus @ X1 @ X0) = (plus @ X0 @ X1))) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f51])).
% 1.89/1.73 thf(f51,plain,(
% 1.89/1.73 ! [X0 : nat,X1 : nat] : ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 1.89/1.73 inference(rectify,[status(thm)],[f17])).
% 1.89/1.73 thf(f17,axiom,(
% 1.89/1.73 ! [X8 : nat,X13 : nat] : ((plus @ X8 @ X13) = (plus @ X13 @ X8))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',plus_com)).
% 1.89/1.73 thf(f111,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ((listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X3 @ nil @ X0) @ X3) = $true) | ((listStar @ X0 @ X1 @ X2 @ X3 @ X3) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f66])).
% 1.89/1.73 thf(f66,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat,X3 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X3 @ X3) != $true) | ((listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X3 @ nil @ X0) @ X3) = $true)))),
% 1.89/1.73 inference(ennf_transformation,[status(thm)],[f42])).
% 1.89/1.73 thf(f42,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X3 @ X3) = $true) => ((listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X3 @ nil @ X0) @ X3) = $true)))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f41])).
% 1.89/1.73 thf(f41,plain,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X3 @ X3) => (listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X3 @ nil @ X0) @ X3)))),
% 1.89/1.73 inference(rectify,[status(thm)],[f19])).
% 1.89/1.73 thf(f19,axiom,(
% 1.89/1.73 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X15 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X15 @ X15) => (listStar @ X0 @ X1 @ (plus @ X8 @ zero) @ (app @ X0 @ X8 @ zero @ X15 @ nil @ X0) @ X15)))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',list_app_nil)).
% 1.89/1.73 thf(f446,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | spl10_15),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f445])).
% 1.89/1.73 thf(f504,plain,(
% 1.89/1.73 spl10_7 | ~spl10_18),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f503,f477,f287])).
% 1.89/1.73 thf(f287,definition,(
% 1.89/1.73 spl10_7 <=> ((sP0 @ nat @ natStar) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_7])],[avatar_definition])).
% 1.89/1.73 thf(f477,definition,(
% 1.89/1.73 spl10_18 <=> ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar))),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_18])],[avatar_definition])).
% 1.89/1.73 thf(f503,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) = $true) | ~spl10_18),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f488,f99])).
% 1.89/1.73 thf(f99,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true) | ((sP0 @ X1 @ X0) = $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f85])).
% 1.89/1.73 thf(f85,plain,(
% 1.89/1.73 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP0 @ X1 @ X0) = $true) | (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)) = $true) & ((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true))) & (! [X5 : X1,X6 : X1,X7 : X1] : (((X0 @ X5 @ X6) != $true) | ((X0 @ X6 @ X7) != $true) | ((X0 @ X5 @ X7) = $true)) | ((sP0 @ X1 @ X0) != $true)))),
% 1.89/1.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f83,f84])).
% 1.89/1.73 thf(f84,plain,(
% 1.89/1.73 ! [X1 : $tType,X0 : X1 > X1 > $o] : (? [X2 : X1,X3 : X1,X4 : X1] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X3 @ X4) = $true) & ((X0 @ X2 @ X4) != $true)) => (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)) = $true) & ((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true)))),
% 1.89/1.73 introduced(definition,[],[choice_axiom])).
% 1.89/1.73 thf(f83,plain,(
% 1.89/1.73 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP0 @ X1 @ X0) = $true) | ? [X2 : X1,X3 : X1,X4 : X1] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X3 @ X4) = $true) & ((X0 @ X2 @ X4) != $true))) & (! [X5 : X1,X6 : X1,X7 : X1] : (((X0 @ X5 @ X6) != $true) | ((X0 @ X6 @ X7) != $true) | ((X0 @ X5 @ X7) = $true)) | ((sP0 @ X1 @ X0) != $true)))),
% 1.89/1.73 inference(rectify,[status(thm)],[f82])).
% 1.89/1.73 thf(f82,plain,(
% 1.89/1.73 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP0 @ X0 @ X1) = $true) | ? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) & ((X1 @ X5 @ X6) = $true) & ((X1 @ X4 @ X6) != $true))) & (! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) != $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X6) = $true)) | ((sP0 @ X0 @ X1) != $true)))),
% 1.89/1.73 inference(nnf_transformation,[status(thm)],[f74])).
% 1.89/1.73 thf(f488,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) = $true) | ((natStar @ (sK4 @ nat @ natStar) @ (sK6 @ nat @ natStar)) = $true) | ~spl10_18),
% 1.89/1.73 inference(superposition,[status(thm)],[f100,f478])).
% 1.89/1.73 thf(f478,plain,(
% 1.89/1.73 ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar)) | ~spl10_18),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f477])).
% 1.89/1.73 thf(f100,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)) = $true) | ((sP0 @ X1 @ X0) = $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f85])).
% 1.89/1.73 thf(f479,plain,(
% 1.89/1.73 spl10_7 | spl10_18),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f309,f477,f287])).
% 1.89/1.73 thf(f309,plain,(
% 1.89/1.73 ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar)) | ((sP0 @ nat @ natStar) = $true)),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f298])).
% 1.89/1.73 thf(f298,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) = $true) | ($true != $true) | ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar))),
% 1.89/1.73 inference(superposition,[status(thm)],[f124,f101])).
% 1.89/1.73 thf(f101,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((sP0 @ X1 @ X0) = $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f85])).
% 1.89/1.73 thf(f124,plain,(
% 1.89/1.73 ( ! [X0 : nat,X1 : nat] : (((natStar @ X0 @ X1) != $true) | (X0 = X1)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f92])).
% 1.89/1.73 thf(f92,plain,(
% 1.89/1.73 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ((natStar @ X0 @ X1) != $true)) & (((natStar @ X0 @ X1) = $true) | (X0 != X1)))),
% 1.89/1.73 inference(nnf_transformation,[status(thm)],[f36])).
% 1.89/1.73 thf(f36,plain,(
% 1.89/1.73 ! [X0 : nat,X1 : nat] : ((X0 = X1) <=> ((natStar @ X0 @ X1) = $true))),
% 1.89/1.73 inference(fool_elimination,[status(thm)],[f35])).
% 1.89/1.73 thf(f35,plain,(
% 1.89/1.73 ! [X0 : nat,X1 : nat] : ((X0 = X1) <=> (natStar @ X0 @ X1))),
% 1.89/1.73 inference(rectify,[status(thm)],[f2])).
% 1.89/1.73 thf(f2,axiom,(
% 1.89/1.73 ! [X2 : nat,X3 : nat] : ((X2 = X3) <=> (natStar @ X2 @ X3))),
% 1.89/1.73 file('/export/starexec/sandbox/tmp/tmp.KuP1xhDiAh/DTF2THF_2655.p',natStar_is_eq)).
% 1.89/1.73 thf(f475,plain,(
% 1.89/1.73 ~spl10_7 | spl10_11 | ~spl10_12),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f474,f401,f398,f287])).
% 1.89/1.73 thf(f401,definition,(
% 1.89/1.73 spl10_12 <=> ((sK3 @ nat @ natStar) = (sK2 @ nat @ natStar))),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_12])],[avatar_definition])).
% 1.89/1.73 thf(f474,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) != $true) | ((sP1 @ nat @ natStar) = $true) | ~spl10_12),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f464,f126])).
% 1.89/1.73 thf(f126,plain,(
% 1.89/1.73 ( ! [X1 : nat] : (((natStar @ X1 @ X1) = $true)) )),
% 1.89/1.73 inference(equality_resolution,[status(thm)],[f123])).
% 1.89/1.73 thf(f123,plain,(
% 1.89/1.73 ( ! [X0 : nat,X1 : nat] : (((natStar @ X0 @ X1) = $true) | (X0 != X1)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f92])).
% 1.89/1.73 thf(f464,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) = $true) | ((sP0 @ nat @ natStar) != $true) | ((natStar @ (sK2 @ nat @ natStar) @ (sK2 @ nat @ natStar)) != $true) | ~spl10_12),
% 1.89/1.73 inference(superposition,[status(thm)],[f96,f402])).
% 1.89/1.73 thf(f402,plain,(
% 1.89/1.73 ((sK3 @ nat @ natStar) = (sK2 @ nat @ natStar)) | ~spl10_12),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f401])).
% 1.89/1.73 thf(f96,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0)) != $true) | ((sP1 @ X1 @ X0) = $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f81])).
% 1.89/1.73 thf(f81,plain,(
% 1.89/1.73 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP1 @ X1 @ X0) = $true) | (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) = $true) & ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0)) != $true)) | ((sP0 @ X1 @ X0) != $true)) & ((! [X4 : X1,X5 : X1] : (((X0 @ X4 @ X5) != $true) | ((X0 @ X5 @ X4) = $true)) & ((sP0 @ X1 @ X0) = $true)) | ((sP1 @ X1 @ X0) != $true)))),
% 1.89/1.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f79,f80])).
% 1.89/1.73 thf(f80,plain,(
% 1.89/1.73 ! [X1 : $tType,X0 : X1 > X1 > $o] : (? [X2 : X1,X3 : X1] : (((X0 @ X2 @ X3) = $true) & ($true != (X0 @ X3 @ X2))) => (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) = $true) & ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0)) != $true)))),
% 1.89/1.73 introduced(definition,[],[choice_axiom])).
% 1.89/1.73 thf(f79,plain,(
% 1.89/1.73 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP1 @ X1 @ X0) = $true) | ? [X2 : X1,X3 : X1] : (((X0 @ X2 @ X3) = $true) & ($true != (X0 @ X3 @ X2))) | ((sP0 @ X1 @ X0) != $true)) & ((! [X4 : X1,X5 : X1] : (((X0 @ X4 @ X5) != $true) | ((X0 @ X5 @ X4) = $true)) & ((sP0 @ X1 @ X0) = $true)) | ((sP1 @ X1 @ X0) != $true)))),
% 1.89/1.73 inference(rectify,[status(thm)],[f78])).
% 1.89/1.73 thf(f78,plain,(
% 1.89/1.73 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)) | ((sP0 @ X0 @ X1) != $true)) & ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ((sP0 @ X0 @ X1) = $true)) | ((sP1 @ X0 @ X1) != $true)))),
% 1.89/1.73 inference(flattening,[status(thm)],[f77])).
% 1.89/1.73 thf(f77,plain,(
% 1.89/1.73 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | (? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)) | ((sP0 @ X0 @ X1) != $true))) & ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ((sP0 @ X0 @ X1) = $true)) | ((sP1 @ X0 @ X1) != $true)))),
% 1.89/1.73 inference(nnf_transformation,[status(thm)],[f75])).
% 1.89/1.73 thf(f447,plain,(
% 1.89/1.73 ~spl10_4 | ~spl10_15 | spl10_13),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f443,f427,f445,f241])).
% 1.89/1.73 thf(f241,definition,(
% 1.89/1.73 spl10_4 <=> ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 1.89/1.73 thf(f427,definition,(
% 1.89/1.73 spl10_13 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat)) = $true)),
% 1.89/1.73 introduced(definition,[new_symbols(naming,[spl10_13])],[avatar_definition])).
% 1.89/1.73 thf(f443,plain,(
% 1.89/1.73 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | spl10_13),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f440])).
% 1.89/1.73 thf(f440,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat) @ (rev @ list @ list @ nat @ sK8 @ sK9)) != $true) | ($true != $true) | ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) != $true) | spl10_13),
% 1.89/1.73 inference(superposition,[status(thm)],[f428,f95])).
% 1.89/1.73 thf(f95,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o,X4 : X1,X5 : X1] : (((X0 @ X5 @ X4) = $true) | ((sP1 @ X1 @ X0) != $true) | ((X0 @ X4 @ X5) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f81])).
% 1.89/1.73 thf(f428,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat)) != $true) | spl10_13),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f427])).
% 1.89/1.73 thf(f432,plain,(
% 1.89/1.73 ~spl10_13 | ~spl10_14),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f415,f430,f427])).
% 1.89/1.73 thf(f415,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat)) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true)),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f414])).
% 1.89/1.73 thf(f414,plain,(
% 1.89/1.73 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat)) != $true)),
% 1.89/1.73 inference(superposition,[status(thm)],[f166,f120])).
% 1.89/1.73 thf(f166,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9)) @ (rev @ list @ list @ nat @ sK8 @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat))) != $true)),
% 1.89/1.73 inference(forward_demodulation,[status(thm)],[f115,f129])).
% 1.89/1.73 thf(f115,plain,(
% 1.89/1.73 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8 @ (rev @ list @ list @ nat @ sK8 @ (rev @ list @ list @ nat @ sK8 @ sK9)) @ (rev @ list @ list @ nat @ (plus @ sK8 @ zero) @ (app @ list @ list @ nat @ sK8 @ zero @ (rev @ list @ list @ nat @ sK8 @ sK9) @ nil @ list @ list @ nat))) != $true)),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f91])).
% 1.89/1.73 thf(f425,plain,(
% 1.89/1.73 spl10_4 | ~spl10_11),
% 1.89/1.73 inference(avatar_contradiction_clause,[status(thm)],[f424])).
% 1.89/1.73 thf(f424,plain,(
% 1.89/1.73 $false | (spl10_4 | ~spl10_11)),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f399,f413])).
% 1.89/1.73 thf(f413,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) != $true) | spl10_4),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f412])).
% 1.89/1.73 thf(f412,plain,(
% 1.89/1.73 ($true != $true) | ((sP1 @ nat @ natStar) != $true) | spl10_4),
% 1.89/1.73 inference(superposition,[status(thm)],[f410,f103])).
% 1.89/1.73 thf(f410,plain,(
% 1.89/1.73 ((isPer @ nat @ natStar) != $true) | spl10_4),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f409])).
% 1.89/1.73 thf(f409,plain,(
% 1.89/1.73 ($true != $true) | ((isPer @ nat @ natStar) != $true) | spl10_4),
% 1.89/1.73 inference(superposition,[status(thm)],[f406,f113])).
% 1.89/1.73 thf(f406,plain,(
% 1.89/1.73 ((isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero))) != $true) | spl10_4),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f405])).
% 1.89/1.73 thf(f405,plain,(
% 1.89/1.73 ((isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero))) != $true) | ($true != $true) | spl10_4),
% 1.89/1.73 inference(superposition,[status(thm)],[f377,f113])).
% 1.89/1.73 thf(f377,plain,(
% 1.89/1.73 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_4),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.89/1.73 thf(f376,plain,(
% 1.89/1.73 ($true != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl10_4),
% 1.89/1.73 inference(superposition,[status(thm)],[f354,f113])).
% 1.89/1.73 thf(f354,plain,(
% 1.89/1.73 ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) != $true) | spl10_4),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.89/1.73 thf(f353,plain,(
% 1.89/1.73 ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) != $true) | ($true != $true) | spl10_4),
% 1.89/1.73 inference(superposition,[status(thm)],[f242,f102])).
% 1.89/1.73 thf(f102,plain,(
% 1.89/1.73 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f86])).
% 1.89/1.73 thf(f242,plain,(
% 1.89/1.73 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK8)) != $true) | spl10_4),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f241])).
% 1.89/1.73 thf(f403,plain,(
% 1.89/1.73 spl10_11 | spl10_12 | ~spl10_7),
% 1.89/1.73 inference(avatar_split_clause,[status(thm)],[f396,f287,f401,f398])).
% 1.89/1.73 thf(f396,plain,(
% 1.89/1.73 ((sP1 @ nat @ natStar) = $true) | ((sK3 @ nat @ natStar) = (sK2 @ nat @ natStar)) | ~spl10_7),
% 1.89/1.73 inference(subsumption_resolution,[status(thm)],[f385,f288])).
% 1.89/1.73 thf(f288,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) = $true) | ~spl10_7),
% 1.89/1.73 inference(avatar_component_clause,[status(thm)],[f287])).
% 1.89/1.73 thf(f385,plain,(
% 1.89/1.73 ((sK3 @ nat @ natStar) = (sK2 @ nat @ natStar)) | ((sP1 @ nat @ natStar) = $true) | ((sP0 @ nat @ natStar) != $true)),
% 1.89/1.73 inference(trivial_inequality_removal,[status(thm)],[f384])).
% 1.89/1.73 thf(f384,plain,(
% 1.89/1.73 ((sP0 @ nat @ natStar) != $true) | ($true != $true) | ((sK3 @ nat @ natStar) = (sK2 @ nat @ natStar)) | ((sP1 @ nat @ natStar) = $true)),
% 1.89/1.73 inference(superposition,[status(thm)],[f124,f97])).
% 1.89/1.73 thf(f97,plain,(
% 1.89/1.73 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) = $true) | ((sP1 @ X1 @ X0) = $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.89/1.73 inference(cnf_transformation,[status(thm)],[f81])).
% 1.89/1.73 % SZS output end Proof for DTF2THF_2655
% 1.89/1.73 % (3030)------------------------------
% 1.89/1.73 % (3030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.73 % (3030)Termination reason: Refutation
% 1.89/1.73
% 1.89/1.73 % (3030)Memory used [KB]: 6268
% 1.89/1.73 % (3030)Time elapsed: 0.064 s
% 1.89/1.73 % (3030)Instructions burned: 171 (million)
% 1.89/1.73 % (3030)------------------------------
% 1.89/1.73 % (3030)------------------------------
% 1.89/1.73 % (2982)Success in time 0.379 s
%------------------------------------------------------------------------------