%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT363^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.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 08:45:34 AM UTC 2026
% Result : Theorem 1.55s 1.76s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT363^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 06:16:34 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : DAT363^1 : TPTP v9.2.1. Released v9.2.0.
% 0.16/0.44 % Domain : Data Structures
% 0.16/0.44 % Problem : Associativity of list append polymorphic, base step typed
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.16/0.44 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.16/0.44 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.16/0.44 % Source : [Rot25]
% 0.16/0.44 % Names : ListAppAssoc/list-app-assoc-base-typeInstantiated.p [Rot25]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : ? v9.2.0
% 0.16/0.44 % Syntax : Number of formulae : 12 ( 4 unt; 8 typ; 0 def)
% 0.16/0.44 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.44 % Number of connectives : 111 ( 0 ~; 0 |; 0 &; 111 @)
% 0.16/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 5 ( 4 avg)
% 0.16/0.44 % Number of types : 1 ( 1 usr)
% 0.16/0.44 % Number of type decls : 8 ( 3 !>P; 2 !>D)
% 0.16/0.44 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 8 ( 7 usr; 1 con; 0-5 aty)
% 0.16/0.44 % Number of variables : 17 ( 0 ^; 11 !; 0 ?; 17 :)
% 0.16/0.44 % ( 6 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.44 % SPC : DH1_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments :
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(nat_type,type,
% 0.16/0.44 nat: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(zero_type,type,
% 0.16/0.44 zero: nat ).
% 0.16/0.44
% 0.16/0.44 thf(suc_type,type,
% 0.16/0.44 suc: nat > nat ).
% 0.16/0.44
% 0.16/0.44 thf(plus_type,type,
% 0.16/0.44 plus: nat > nat > nat ).
% 0.16/0.44
% 0.16/0.44 thf(list_type,type,
% 0.16/0.44 list: $tType > nat > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(nil_type,type,
% 0.16/0.44 nil:
% 0.16/0.44 !>[A: $tType] : ( list @ A @ zero ) ).
% 0.16/0.44
% 0.16/0.44 thf(cons_type,type,
% 0.16/0.44 cons:
% 0.16/0.44 !>[A: $tType,N: nat] : ( A > ( list @ A @ N ) > ( list @ A @ ( suc @ N ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(app_type,type,
% 0.16/0.44 app:
% 0.16/0.44 !>[A: $tType,N: nat,M: nat] : ( ( list @ A @ N ) > ( list @ A @ M ) > ( list @ A @ ( plus @ N @ M ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(ax1,axiom,
% 0.16/0.44 ! [N: nat] :
% 0.16/0.44 ( ( plus @ zero @ N )
% 0.16/0.44 = N ) ).
% 0.16/0.44
% 0.16/0.44 thf(ax3,axiom,
% 0.16/0.44 ! [A: $tType,N: nat,X: list @ A @ N] :
% 0.16/0.44 ( ( app @ A @ zero @ N @ ( nil @ A ) @ X )
% 0.16/0.44 = X ) ).
% 0.16/0.44
% 0.16/0.44 thf(plus_assoc,axiom,
% 0.16/0.44 ! [M1: nat,M2: nat,M3: nat] :
% 0.16/0.44 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.16/0.44 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(list_app_assoc_base,conjecture,
% 0.16/0.44 ! [M2: nat,L2: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ M2,M3: nat,L3: list @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ M3] :
% 0.16/0.44 ( ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ ( plus @ M2 @ M3 ) @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) @ ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ M2 @ M3 @ L2 @ L3 ) )
% 0.16/0.44 = ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ ( plus @ zero @ M2 ) @ M3 @ ( app @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ zero @ M2 @ ( nil @ ( list @ ( list @ nat @ ( suc @ zero ) ) @ ( suc @ zero ) ) ) @ L2 ) @ L3 ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 1.45/1.23 ---- Embedded in THF ---
% 1.45/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.24 %%% Generated on Tue Feb 24 06:16:35 EST 2026
% 1.45/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.24 %%% Logic specification used:
% 1.45/1.24 %%% thf(spec, logic, $$dhol).
% 1.45/1.24
% 1.45/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2DTF7357.p
% 1.45/1.24 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.45/1.24 thf(is_per, definition, (! [A:$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)))))))))).
% 1.45/1.24 thf(nat_type, type, nat: $tType).
% 1.45/1.24 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.45/1.24 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.45/1.24 thf(zero_type, type, zero: nat).
% 1.45/1.24 thf(suc_type, type, suc: (nat > nat)).
% 1.45/1.24 thf(plus_type, type, plus: (nat > (nat > nat))).
% 1.45/1.24 thf(list_type, type, list: ($tType > $tType)).
% 1.45/1.24 thf(listStar, type, 'listStar': (!> [A:$tType]: (((A > (A > $o)) > (nat > ((list @ A) > ((list @ A) > $o))))))).
% 1.45/1.24 thf('\'listStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:nat]: (((isPer @ (list @ B)) @ (((listStar @ B) @ BStar) @ C)))))))).
% 1.45/1.24 thf(nil_type, type, nil: (!> [A:$tType]: ((list @ A)))).
% 1.45/1.24 thf(nil_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (nil @ A)) @ (nil @ A)))))).
% 1.45/1.24 thf(cons_type, type, cons: (!> [A:$tType]: ((nat > (A > ((list @ A) > (list @ A))))))).
% 1.45/1.24 thf(cons_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:A,D_prime:A]: (((D = D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ ((((cons @ A) @ N) @ D) @ D0)) @ ((((cons @ A) @ N) @ D_prime) @ D0_prime)))))))))))))).
% 1.45/1.24 thf(app_type, type, app: (!> [A:$tType]: ((nat > (nat > ((list @ A) > ((list @ A) > (list @ A)))))))).
% 1.45/1.24 thf(app_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ M) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ M)) @ (((((app @ A) @ N) @ M) @ D) @ D0)) @ (((((app @ A) @ N) @ M) @ D_prime) @ D0_prime)))))))))))))))).
% 1.45/1.24 thf(ax1, axiom, (! [N:nat]: ((((plus @ zero) @ N) = N)))).
% 1.45/1.24 thf(ax3, axiom, (! [A:$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)))))))))).
% 1.45/1.24 thf(plus_assoc, axiom, (! [M1:nat]: ((! [M2:nat]: ((! [M3:nat]: ((((plus @ M1) @ ((plus @ M2) @ M3)) = ((plus @ ((plus @ M1) @ M2)) @ M3))))))))).
% 1.45/1.24 thf(list_app_assoc_base, conjecture, (! [M2:nat]: ((! [L2:(list @ (list @ (list @ nat))),M3:nat,L3:(list @ (list @ (list @ nat)))]: (((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ M2) @ L2) @ L2) => ((((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ M3) @ L3) @ L3) => (((((listStar @ (list @ (list @ nat))) @ (((listStar @ (list @ nat)) @ (((listStar @ nat) @ natStar) @ (suc @ zero))) @ (suc @ zero))) @ ((plus @ zero) @ ((plus @ M2) @ M3))) @ (((((app @ (list @ (list @ nat))) @ zero) @ ((plus @ M2) @ M3)) @ (nil @ (list @ (list @ nat)))) @ (((((app @ (list @ (list @ nat))) @ M2) @ M3) @ L2) @ L3))) @ (((((app @ (list @ (list @ nat))) @ ((plus @ zero) @ M2)) @ M3) @ (((((app @ (list @ (list @ nat))) @ zero) @ M2) @ (nil @ (list @ (list @ nat)))) @ L2)) @ L3))))))))).
% 1.45/1.24 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2DTF7357.p
% 1.45/1.24 ------------------------
% 1.45/1.24 ---- Cleaned THF ---
% 1.45/1.24 thf(is_per_type,type,
% 1.45/1.24 isPer:
% 1.45/1.24 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.45/1.24
% 1.45/1.24 thf(is_per,definition,
% 1.45/1.24 ! [A: $tType,AStar: A > A > $o] :
% 1.45/1.24 ( ( isPer @ A @ AStar )
% 1.45/1.24 <=> ( ! [X: A,Y: A] :
% 1.45/1.24 ( ( AStar @ X @ Y )
% 1.45/1.24 => ( AStar @ Y @ X ) )
% 1.45/1.24 & ! [X: A,Y: A,Z: A] :
% 1.45/1.24 ( ( AStar @ X @ Y )
% 1.45/1.24 => ( ( AStar @ Y @ Z )
% 1.45/1.24 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(nat_type,type,
% 1.45/1.24 nat: $tType ).
% 1.45/1.24
% 1.45/1.24 thf(natStar,type,
% 1.45/1.24 natStar: nat > nat > $o ).
% 1.45/1.24
% 1.45/1.24 thf(natStar_is_eq,axiom,
% 1.45/1.24 ! [X: nat,Y: nat] :
% 1.45/1.24 ( ( natStar @ X @ Y )
% 1.45/1.24 <=> ( X = Y ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(zero_type,type,
% 1.45/1.24 zero: nat ).
% 1.45/1.24
% 1.45/1.24 thf(suc_type,type,
% 1.45/1.24 suc: nat > nat ).
% 1.45/1.24
% 1.45/1.24 thf(plus_type,type,
% 1.45/1.24 plus: nat > nat > nat ).
% 1.45/1.24
% 1.45/1.24 thf(list_type,type,
% 1.45/1.24 list: $tType > $tType ).
% 1.45/1.24
% 1.45/1.24 thf(listStar,type,
% 1.45/1.24 listStar:
% 1.45/1.24 !>[A: $tType] : ( ( A > A > $o ) > nat > ( list @ A ) > ( list @ A ) > $o ) ).
% 1.45/1.24
% 1.45/1.24 thf('\'listStar\'_is_per',axiom,
% 1.45/1.24 ! [B: $tType,BStar: B > B > $o] :
% 1.45/1.24 ( ( isPer @ B @ BStar )
% 1.45/1.24 => ! [C: nat] : ( isPer @ ( list @ B ) @ ( listStar @ B @ BStar @ C ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(nil_type,type,
% 1.45/1.24 nil:
% 1.45/1.24 !>[A: $tType] : ( list @ A ) ).
% 1.45/1.24
% 1.45/1.24 thf(nil_tp_ax,axiom,
% 1.45/1.24 ! [A: $tType,AStar: A > A > $o] :
% 1.45/1.24 ( ( isPer @ A @ AStar )
% 1.45/1.24 => ( listStar @ A @ AStar @ zero @ ( nil @ A ) @ ( nil @ A ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(cons_type,type,
% 1.45/1.24 cons:
% 1.45/1.24 !>[A: $tType] : ( nat > A > ( list @ A ) > ( list @ A ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(cons_tp_ax,axiom,
% 1.45/1.24 ! [A: $tType,AStar: A > A > $o] :
% 1.45/1.24 ( ( isPer @ A @ AStar )
% 1.45/1.24 => ! [N: nat,D: A,D_prime: A] :
% 1.45/1.24 ( ( D = D_prime )
% 1.45/1.24 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.45/1.24 ( ( listStar @ A @ AStar @ N @ D0 @ D0_prime )
% 1.45/1.24 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( cons @ A @ N @ D @ D0 ) @ ( cons @ A @ N @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(app_type,type,
% 1.45/1.24 app:
% 1.45/1.24 !>[A: $tType] : ( nat > nat > ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(app_tp_ax,axiom,
% 1.45/1.24 ! [A: $tType,AStar: A > A > $o] :
% 1.45/1.24 ( ( isPer @ A @ AStar )
% 1.45/1.24 => ! [N: nat,M: nat,D: list @ A,D_prime: list @ A] :
% 1.45/1.24 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.45/1.24 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.45/1.24 ( ( listStar @ A @ AStar @ M @ D0 @ D0_prime )
% 1.45/1.24 => ( listStar @ A @ AStar @ ( plus @ N @ M ) @ ( app @ A @ N @ M @ D @ D0 ) @ ( app @ A @ N @ M @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(ax1,axiom,
% 1.45/1.24 ! [N: nat] :
% 1.45/1.24 ( ( plus @ zero @ N )
% 1.45/1.24 = N ) ).
% 1.45/1.24
% 1.45/1.24 thf(ax3,axiom,
% 1.45/1.24 ! [A: $tType,AStar: A > A > $o] :
% 1.45/1.24 ( ( isPer @ A @ AStar )
% 1.45/1.24 => ! [N: nat,X: list @ A] :
% 1.45/1.24 ( ( listStar @ A @ AStar @ N @ X @ X )
% 1.45/1.24 => ( listStar @ A @ AStar @ ( plus @ zero @ N ) @ ( app @ A @ zero @ N @ ( nil @ A ) @ X ) @ X ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(plus_assoc,axiom,
% 1.45/1.24 ! [M1: nat,M2: nat,M3: nat] :
% 1.45/1.24 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.45/1.24 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(list_app_assoc_base,conjecture,
% 1.45/1.24 ! [M2: nat,L2: list @ ( list @ ( list @ nat ) ),M3: nat,L3: list @ ( list @ ( list @ nat ) )] :
% 1.45/1.24 ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ M2 @ L2 @ L2 )
% 1.45/1.24 => ( ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ M3 @ L3 @ L3 )
% 1.45/1.24 => ( listStar @ ( list @ ( list @ nat ) ) @ ( listStar @ ( list @ nat ) @ ( listStar @ nat @ natStar @ ( suc @ zero ) ) @ ( suc @ zero ) ) @ ( plus @ zero @ ( plus @ M2 @ M3 ) ) @ ( app @ ( list @ ( list @ nat ) ) @ zero @ ( plus @ M2 @ M3 ) @ ( nil @ ( list @ ( list @ nat ) ) ) @ ( app @ ( list @ ( list @ nat ) ) @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( list @ ( list @ nat ) ) @ ( plus @ zero @ M2 ) @ M3 @ ( app @ ( list @ ( list @ nat ) ) @ zero @ M2 @ ( nil @ ( list @ ( list @ nat ) ) ) @ L2 ) @ L3 ) ) ) ) ).
% 1.45/1.24 ------------------------
% 1.45/1.26 % (7462)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/183Mi)
% 1.45/1.26 % (7463)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_7357 for (2999ds/4Mi)
% 1.45/1.26 % (7466)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_7357 for (2999ds/2Mi)
% 1.45/1.26 % (7464)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_7357 for (2999ds/27Mi)
% 1.45/1.26 % (7467)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_7357 for (2999ds/275Mi)
% 1.45/1.26 % (7465)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/2Mi)
% 1.45/1.26 % (7468)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/18Mi)
% 1.45/1.26 % (7466)Instruction limit reached!
% 1.45/1.26 % (7466)------------------------------
% 1.45/1.26 % (7466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (7466)Termination reason: Unknown
% 1.45/1.26 % (7466)Termination phase: shuffling
% 1.45/1.26
% 1.45/1.26 % (7466)Memory used [KB]: 1023
% 1.45/1.26 % (7466)Time elapsed: 0.002 s
% 1.45/1.26 % (7466)Instructions burned: 2 (million)
% 1.45/1.26 % (7466)------------------------------
% 1.45/1.26 % (7466)------------------------------
% 1.45/1.26 % (7463)Instruction limit reached!
% 1.45/1.26 % (7463)------------------------------
% 1.45/1.26 % (7463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (7463)Termination reason: Unknown
% 1.45/1.26 % (7463)Termination phase: Property scanning
% 1.45/1.26
% 1.45/1.26 % (7463)Memory used [KB]: 1023
% 1.45/1.26 % (7463)Time elapsed: 0.003 s
% 1.45/1.26 % (7465)Instruction limit reached!
% 1.45/1.26 % (7465)------------------------------
% 1.45/1.26 % (7465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (7465)Termination reason: Unknown
% 1.45/1.26 % (7465)Termination phase: Property scanning
% 1.45/1.26
% 1.45/1.26 % (7465)Memory used [KB]: 1023
% 1.45/1.26 % (7465)Time elapsed: 0.003 s
% 1.45/1.26 % (7465)Instructions burned: 4 (million)
% 1.45/1.26 % (7465)------------------------------
% 1.45/1.26 % (7465)------------------------------
% 1.45/1.26 % (7463)Instructions burned: 4 (million)
% 1.45/1.26 % (7463)------------------------------
% 1.45/1.26 % (7463)------------------------------
% 1.45/1.27 % (7468)Instruction limit reached!
% 1.45/1.27 % (7468)------------------------------
% 1.45/1.27 % (7468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (7468)Termination reason: Unknown
% 1.45/1.27 % (7467)Refutation not found, incomplete strategy
% 1.45/1.27 % (7467)------------------------------
% 1.45/1.27 % (7467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (7467)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.27
% 1.45/1.27
% 1.45/1.27 % (7467)Memory used [KB]: 5628
% 1.45/1.27 % (7467)Time elapsed: 0.011 s
% 1.45/1.27 % (7467)Instructions burned: 18 (million)
% 1.45/1.27 % (7467)------------------------------
% 1.45/1.27 % (7467)------------------------------
% 1.45/1.27 % (7468)Termination phase: Saturation
% 1.45/1.27
% 1.45/1.27 % (7468)Memory used [KB]: 5628
% 1.45/1.27 % (7468)Time elapsed: 0.011 s
% 1.45/1.27 % (7468)Instructions burned: 19 (million)
% 1.45/1.27 % (7468)------------------------------
% 1.45/1.27 % (7468)------------------------------
% 1.45/1.28 % (7464)Instruction limit reached!
% 1.45/1.28 % (7464)------------------------------
% 1.45/1.28 % (7464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (7464)Termination reason: Unknown
% 1.45/1.28 % (7464)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (7464)Memory used [KB]: 5756
% 1.45/1.28 % (7464)Time elapsed: 0.015 s
% 1.45/1.28 % (7464)Instructions burned: 27 (million)
% 1.45/1.28 % (7464)------------------------------
% 1.45/1.28 % (7464)------------------------------
% 1.45/1.28 % (7469)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/3Mi)
% 1.45/1.28 % (7470)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_7357 for (2999ds/37Mi)
% 1.45/1.28 % (7469)Instruction limit reached!
% 1.45/1.28 % (7469)------------------------------
% 1.45/1.28 % (7469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (7469)Termination reason: Unknown
% 1.45/1.28 % (7469)Termination phase: Property scanning
% 1.45/1.28
% 1.45/1.28 % (7469)Memory used [KB]: 1023
% 1.45/1.28 % (7469)Time elapsed: 0.003 s
% 1.45/1.28 % (7469)Instructions burned: 4 (million)
% 1.45/1.28 % (7469)------------------------------
% 1.45/1.28 % (7469)------------------------------
% 1.45/1.28 % (7471)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_7357 for (2999ds/15Mi)
% 1.45/1.29 % (7471)Instruction limit reached!
% 1.45/1.29 % (7471)------------------------------
% 1.45/1.29 % (7471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (7471)Termination reason: Unknown
% 1.45/1.29 % (7471)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (7471)Memory used [KB]: 5756
% 1.45/1.29 % (7473)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_7357 for (2999ds/1041Mi)
% 1.45/1.29 % (7471)Time elapsed: 0.009 s
% 1.45/1.29 % (7471)Instructions burned: 16 (million)
% 1.45/1.29 % (7471)------------------------------
% 1.45/1.29 % (7471)------------------------------
% 1.45/1.29 % (7472)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_7357 for (2999ds/3Mi)
% 1.45/1.29 % (7472)Instruction limit reached!
% 1.45/1.29 % (7472)------------------------------
% 1.45/1.29 % (7472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (7472)Termination reason: Unknown
% 1.45/1.29 % (7472)Termination phase: Property scanning
% 1.45/1.29
% 1.45/1.29 % (7472)Memory used [KB]: 1023
% 1.45/1.29 % (7472)Time elapsed: 0.003 s
% 1.45/1.29 % (7472)Instructions burned: 4 (million)
% 1.45/1.29 % (7472)------------------------------
% 1.45/1.29 % (7472)------------------------------
% 1.45/1.29 % (7474)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/7Mi)
% 1.45/1.30 % (7474)Instruction limit reached!
% 1.45/1.30 % (7474)------------------------------
% 1.45/1.30 % (7474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.30 % (7474)Termination reason: Unknown
% 1.45/1.30 % (7474)Termination phase: Saturation
% 1.45/1.30
% 1.45/1.30 % (7474)Memory used [KB]: 1023
% 1.45/1.30 % (7474)Time elapsed: 0.005 s
% 1.45/1.30 % (7474)Instructions burned: 8 (million)
% 1.45/1.30 % (7474)------------------------------
% 1.45/1.30 % (7474)------------------------------
% 1.55/1.30 % (7475)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/16Mi)
% 1.55/1.30 % (7470)Instruction limit reached!
% 1.55/1.30 % (7470)------------------------------
% 1.55/1.30 % (7470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (7470)Termination reason: Unknown
% 1.55/1.30 % (7470)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (7470)Memory used [KB]: 5756
% 1.55/1.30 % (7470)Time elapsed: 0.019 s
% 1.55/1.30 % (7470)Instructions burned: 38 (million)
% 1.55/1.30 % (7470)------------------------------
% 1.55/1.30 % (7470)------------------------------
% 1.55/1.30 % (7475)Instruction limit reached!
% 1.55/1.30 % (7475)------------------------------
% 1.55/1.30 % (7475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (7475)Termination reason: Unknown
% 1.55/1.30 % (7475)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (7475)Memory used [KB]: 5628
% 1.55/1.30 % (7475)Time elapsed: 0.009 s
% 1.55/1.30 % (7475)Instructions burned: 16 (million)
% 1.55/1.30 % (7475)------------------------------
% 1.55/1.30 % (7475)------------------------------
% 1.55/1.30 % (7476)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_7357 for (2999ds/3Mi)
% 1.55/1.31 % (7476)Instruction limit reached!
% 1.55/1.31 % (7476)------------------------------
% 1.55/1.31 % (7476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (7476)Termination reason: Unknown
% 1.55/1.31 % (7476)Termination phase: SInE selection
% 1.55/1.31
% 1.55/1.31 % (7476)Memory used [KB]: 1023
% 1.55/1.31 % (7476)Time elapsed: 0.003 s
% 1.55/1.31 % (7476)Instructions burned: 5 (million)
% 1.55/1.31 % (7476)------------------------------
% 1.55/1.31 % (7476)------------------------------
% 1.55/1.31 % (7477)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_7357 for (2999ds/3Mi)
% 1.55/1.31 % (7477)Instruction limit reached!
% 1.55/1.31 % (7477)------------------------------
% 1.55/1.31 % (7477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (7477)Termination reason: Unknown
% 1.55/1.31 % (7477)Termination phase: shuffling
% 1.55/1.31
% 1.55/1.31 % (7477)Memory used [KB]: 1023
% 1.55/1.31 % (7477)Time elapsed: 0.003 s
% 1.55/1.31 % (7477)Instructions burned: 4 (million)
% 1.55/1.31 % (7477)------------------------------
% 1.55/1.31 % (7477)------------------------------
% 1.55/1.31 % (7462)Instruction limit reached!
% 1.55/1.31 % (7462)------------------------------
% 1.55/1.31 % (7462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (7462)Termination reason: Unknown
% 1.55/1.31 % (7462)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (7462)Memory used [KB]: 7036
% 1.55/1.31 % (7462)Time elapsed: 0.054 s
% 1.55/1.31 % (7462)Instructions burned: 186 (million)
% 1.55/1.31 % (7462)------------------------------
% 1.55/1.31 % (7462)------------------------------
% 1.55/1.31 % (7478)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/7Mi)
% 1.55/1.32 % (7478)Instruction limit reached!
% 1.55/1.32 % (7478)------------------------------
% 1.55/1.32 % (7478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (7478)Termination reason: Unknown
% 1.55/1.32 % (7478)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (7478)Memory used [KB]: 5500
% 1.55/1.32 % (7478)Time elapsed: 0.005 s
% 1.55/1.32 % (7478)Instructions burned: 8 (million)
% 1.55/1.32 % (7478)------------------------------
% 1.55/1.32 % (7478)------------------------------
% 1.55/1.32 % (7483)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/6Mi)
% 1.55/1.32 % (7480)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/4Mi)
% 1.55/1.32 % (7479)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/3Mi)
% 1.55/1.32 % (7483)Instruction limit reached!
% 1.55/1.32 % (7483)------------------------------
% 1.55/1.32 % (7483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (7483)Termination reason: Unknown
% 1.55/1.32 % (7483)Termination phase: Property scanning
% 1.55/1.32
% 1.55/1.32 % (7483)Memory used [KB]: 1023
% 1.55/1.32 % (7483)Time elapsed: 0.003 s
% 1.55/1.32 % (7483)Instructions burned: 7 (million)
% 1.55/1.32 % (7483)------------------------------
% 1.55/1.32 % (7483)------------------------------
% 1.55/1.32 % (7481)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/18Mi)
% 1.55/1.32 % (7479)Instruction limit reached!
% 1.55/1.32 % (7479)------------------------------
% 1.55/1.32 % (7479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (7479)Termination reason: Unknown
% 1.55/1.32 % (7479)Termination phase: Property scanning
% 1.55/1.32
% 1.55/1.32 % (7479)Memory used [KB]: 1023
% 1.55/1.32 % (7479)Time elapsed: 0.003 s
% 1.55/1.32 % (7479)Instructions burned: 4 (million)
% 1.55/1.32 % (7479)------------------------------
% 1.55/1.32 % (7479)------------------------------
% 1.55/1.32 % (7480)Instruction limit reached!
% 1.55/1.32 % (7480)------------------------------
% 1.55/1.32 % (7480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (7480)Termination reason: Unknown
% 1.55/1.32 % (7480)Termination phase: Property scanning
% 1.55/1.32
% 1.55/1.32 % (7480)Memory used [KB]: 1023
% 1.55/1.32 % (7480)Time elapsed: 0.003 s
% 1.55/1.32 % (7480)Instructions burned: 4 (million)
% 1.55/1.32 % (7480)------------------------------
% 1.55/1.32 % (7480)------------------------------
% 1.55/1.32 % (7482)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/710Mi)
% 1.55/1.33 % (7485)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_7357 for (2999ds/21Mi)
% 1.55/1.33 % (7481)Instruction limit reached!
% 1.55/1.33 % (7481)------------------------------
% 1.55/1.33 % (7481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.33 % (7481)Termination reason: Unknown
% 1.55/1.33 % (7481)Termination phase: Saturation
% 1.55/1.33
% 1.55/1.33 % (7481)Memory used [KB]: 5628
% 1.55/1.33 % (7481)Time elapsed: 0.011 s
% 1.55/1.33 % (7481)Instructions burned: 18 (million)
% 1.55/1.33 % (7481)------------------------------
% 1.55/1.33 % (7481)------------------------------
% 1.55/1.33 % (7484)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_7357 for (2999ds/902Mi)
% 1.55/1.34 % (7486)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/5Mi)
% 1.55/1.34 % (7485)Instruction limit reached!
% 1.55/1.34 % (7485)------------------------------
% 1.55/1.34 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.34 % (7485)Termination reason: Unknown
% 1.55/1.34 % (7485)Termination phase: Saturation
% 1.55/1.34
% 1.55/1.34 % (7485)Memory used [KB]: 5756
% 1.55/1.34 % (7485)Time elapsed: 0.009 s
% 1.55/1.34 % (7485)Instructions burned: 23 (million)
% 1.55/1.34 % (7485)------------------------------
% 1.55/1.34 % (7485)------------------------------
% 1.55/1.34 % (7487)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_7357 for (2999ds/6Mi)
% 1.55/1.34 % (7484)Refutation not found, incomplete strategy
% 1.55/1.34 % (7484)------------------------------
% 1.55/1.34 % (7484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.34 % (7484)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.34
% 1.55/1.34
% 1.55/1.34 % (7484)Memory used [KB]: 5628
% 1.55/1.34 % (7484)Time elapsed: 0.010 s
% 1.55/1.34 % (7484)Instructions burned: 16 (million)
% 1.55/1.34 % (7484)------------------------------
% 1.55/1.34 % (7484)------------------------------
% 1.55/1.34 % (7486)Instruction limit reached!
% 1.55/1.34 % (7486)------------------------------
% 1.55/1.34 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.34 % (7486)Termination reason: Unknown
% 1.55/1.34 % (7486)Termination phase: Property scanning
% 1.55/1.34
% 1.55/1.34 % (7486)Memory used [KB]: 1023
% 1.55/1.34 % (7486)Time elapsed: 0.004 s
% 1.55/1.34 % (7486)Instructions burned: 6 (million)
% 1.55/1.34 % (7486)------------------------------
% 1.55/1.34 % (7486)------------------------------
% 1.55/1.34 % (7487)Instruction limit reached!
% 1.55/1.34 % (7487)------------------------------
% 1.55/1.34 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.34 % (7487)Termination reason: Unknown
% 1.55/1.34 % (7487)Termination phase: Property scanning
% 1.55/1.34
% 1.55/1.34 % (7487)Memory used [KB]: 1023
% 1.55/1.34 % (7487)Time elapsed: 0.004 s
% 1.55/1.34 % (7487)Instructions burned: 7 (million)
% 1.55/1.34 % (7487)------------------------------
% 1.55/1.34 % (7487)------------------------------
% 1.55/1.35 % (7488)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/377Mi)
% 1.55/1.35 % (7489)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_7357 for (2999ds/779Mi)
% 1.55/1.36 % (7490)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_7357 for (2999ds/19Mi)
% 1.55/1.36 % (7491)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/879Mi)
% 1.55/1.36 % (7492)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7357 for (2999ds/17Mi)
% 1.55/1.37 % (7490)Refutation not found, incomplete strategy
% 1.55/1.37 % (7490)------------------------------
% 1.55/1.37 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.37 % (7490)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.37
% 1.55/1.37
% 1.55/1.37 % (7490)Memory used [KB]: 5628
% 1.55/1.37 % (7490)Time elapsed: 0.010 s
% 1.55/1.37 % (7490)Instructions burned: 18 (million)
% 1.55/1.37 % (7490)------------------------------
% 1.55/1.37 % (7490)------------------------------
% 1.55/1.37 % (7492)Instruction limit reached!
% 1.55/1.37 % (7492)------------------------------
% 1.55/1.37 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.37 % (7492)Termination reason: Unknown
% 1.55/1.37 % (7492)Termination phase: Saturation
% 1.55/1.37
% 1.55/1.37 % (7492)Memory used [KB]: 5756
% 1.55/1.37 % (7492)Time elapsed: 0.010 s
% 1.55/1.37 % (7492)Instructions burned: 17 (million)
% 1.55/1.37 % (7492)------------------------------
% 1.55/1.37 % (7492)------------------------------
% 1.55/1.38 % (7493)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7357 for (2998ds/3Mi)
% 1.55/1.38 % (7493)Instruction limit reached!
% 1.55/1.38 % (7493)------------------------------
% 1.55/1.38 % (7493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (7493)Termination reason: Unknown
% 1.55/1.38 % (7493)Termination phase: Property scanning
% 1.55/1.38
% 1.55/1.38 % (7493)Memory used [KB]: 1023
% 1.55/1.38 % (7493)Time elapsed: 0.003 s
% 1.55/1.38 % (7493)Instructions burned: 4 (million)
% 1.55/1.38 % (7493)------------------------------
% 1.55/1.38 % (7493)------------------------------
% 1.55/1.38 % (7494)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7357 for (2998ds/30Mi)
% 1.55/1.40 % (7495)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7357 for (2998ds/127Mi)
% 1.55/1.40 % (7494)Instruction limit reached!
% 1.55/1.40 % (7494)------------------------------
% 1.55/1.40 % (7494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.40 % (7494)Termination reason: Unknown
% 1.55/1.40 % (7494)Termination phase: Saturation
% 1.55/1.40
% 1.55/1.40 % (7494)Memory used [KB]: 5756
% 1.55/1.40 % (7494)Time elapsed: 0.038 s
% 1.55/1.40 % (7494)Instructions burned: 31 (million)
% 1.55/1.40 % (7494)------------------------------
% 1.55/1.40 % (7494)------------------------------
% 1.55/1.42 % (7496)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7357 for (2998ds/100Mi)
% 1.55/1.46 % (7495)Instruction limit reached!
% 1.55/1.46 % (7495)------------------------------
% 1.55/1.46 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.46 % (7495)Termination reason: Unknown
% 1.55/1.46 % (7495)Termination phase: Saturation
% 1.55/1.46
% 1.55/1.46 % (7495)Memory used [KB]: 6140
% 1.55/1.46 % (7495)Time elapsed: 0.060 s
% 1.55/1.46 % (7495)Instructions burned: 129 (million)
% 1.55/1.46 % (7495)------------------------------
% 1.55/1.46 % (7495)------------------------------
% 1.55/1.46 % (7496)Instruction limit reached!
% 1.55/1.46 % (7496)------------------------------
% 1.55/1.46 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.46 % (7496)Termination reason: Unknown
% 1.55/1.46 % (7496)Termination phase: Saturation
% 1.55/1.46
% 1.55/1.46 % (7496)Memory used [KB]: 6012
% 1.55/1.46 % (7496)Time elapsed: 0.047 s
% 1.55/1.46 % (7496)Instructions burned: 100 (million)
% 1.55/1.46 % (7496)------------------------------
% 1.55/1.46 % (7496)------------------------------
% 1.55/1.47 % (7498)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_7357 for (2998ds/20Mi)
% 1.55/1.47 % (7497)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_7357 for (2998ds/3Mi)
% 1.55/1.48 % (7497)Instruction limit reached!
% 1.55/1.48 % (7497)------------------------------
% 1.55/1.48 % (7497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.48 % (7497)Termination reason: Unknown
% 1.55/1.48 % (7497)Termination phase: Property scanning
% 1.55/1.48
% 1.55/1.48 % (7497)Memory used [KB]: 1023
% 1.55/1.48 % (7497)Time elapsed: 0.003 s
% 1.55/1.48 % (7497)Instructions burned: 4 (million)
% 1.55/1.48 % (7497)------------------------------
% 1.55/1.48 % (7497)------------------------------
% 1.55/1.48 % (7498)Instruction limit reached!
% 1.55/1.48 % (7498)------------------------------
% 1.55/1.48 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.48 % (7498)Termination reason: Unknown
% 1.55/1.48 % (7498)Termination phase: Saturation
% 1.55/1.48
% 1.55/1.48 % (7498)Memory used [KB]: 5628
% 1.55/1.48 % (7498)Time elapsed: 0.008 s
% 1.55/1.48 % (7498)Instructions burned: 22 (million)
% 1.55/1.48 % (7498)------------------------------
% 1.55/1.48 % (7498)------------------------------
% 1.55/1.49 % (7500)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_7357 for (2997ds/107Mi)
% 1.55/1.49 % (7499)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_7357 for (2997ds/86Mi)
% 1.55/1.52 % (7488)Instruction limit reached!
% 1.55/1.52 % (7488)------------------------------
% 1.55/1.52 % (7488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.52 % (7488)Termination reason: Unknown
% 1.55/1.52 % (7488)Termination phase: Saturation
% 1.55/1.52
% 1.55/1.52 % (7488)Memory used [KB]: 6268
% 1.55/1.52 % (7488)Time elapsed: 0.180 s
% 1.55/1.52 % (7488)Instructions burned: 378 (million)
% 1.55/1.52 % (7488)------------------------------
% 1.55/1.52 % (7488)------------------------------
% 1.55/1.53 % (7500)Instruction limit reached!
% 1.55/1.53 % (7500)------------------------------
% 1.55/1.53 % (7500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.53 % (7500)Termination reason: Unknown
% 1.55/1.53 % (7500)Termination phase: Saturation
% 1.55/1.53
% 1.55/1.53 % (7500)Memory used [KB]: 6140
% 1.55/1.53 % (7500)Time elapsed: 0.065 s
% 1.55/1.53 % (7500)Instructions burned: 108 (million)
% 1.55/1.53 % (7500)------------------------------
% 1.55/1.53 % (7500)------------------------------
% 1.55/1.53 % (7499)Instruction limit reached!
% 1.55/1.53 % (7499)------------------------------
% 1.55/1.53 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.53 % (7499)Termination reason: Unknown
% 1.55/1.53 % (7499)Termination phase: Saturation
% 1.55/1.53
% 1.55/1.53 % (7499)Memory used [KB]: 6268
% 1.55/1.53 % (7499)Time elapsed: 0.043 s
% 1.55/1.53 % (7499)Instructions burned: 86 (million)
% 1.55/1.53 % (7499)------------------------------
% 1.55/1.53 % (7499)------------------------------
% 1.55/1.54 % (7501)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_7357 for (2997ds/39Mi)
% 1.55/1.55 % (7502)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_7357 for (2997ds/448Mi)
% 1.55/1.55 % (7503)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_7357 for (2997ds/46Mi)
% 1.55/1.56 % (7501)Instruction limit reached!
% 1.55/1.56 % (7501)------------------------------
% 1.55/1.56 % (7501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.56 % (7501)Termination reason: Unknown
% 1.55/1.56 % (7501)Termination phase: Saturation
% 1.55/1.56
% 1.55/1.56 % (7501)Memory used [KB]: 5756
% 1.55/1.56 % (7501)Time elapsed: 0.021 s
% 1.55/1.56 % (7501)Instructions burned: 40 (million)
% 1.55/1.56 % (7501)------------------------------
% 1.55/1.56 % (7501)------------------------------
% 1.55/1.57 % (7503)Instruction limit reached!
% 1.55/1.57 % (7503)------------------------------
% 1.55/1.57 % (7503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.57 % (7503)Termination reason: Unknown
% 1.55/1.57 % (7503)Termination phase: Saturation
% 1.55/1.57
% 1.55/1.57 % (7503)Memory used [KB]: 5756
% 1.55/1.57 % (7503)Time elapsed: 0.024 s
% 1.55/1.57 % (7503)Instructions burned: 47 (million)
% 1.55/1.57 % (7503)------------------------------
% 1.55/1.57 % (7503)------------------------------
% 1.55/1.58 % (7504)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_7357 for (2996ds/98Mi)
% 1.55/1.59 % (7505)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_7357 for (2996ds/507Mi)
% 1.55/1.60 % (7505)Refutation not found, incomplete strategy
% 1.55/1.60 % (7505)------------------------------
% 1.55/1.60 % (7505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.60 % (7505)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.60
% 1.55/1.60
% 1.55/1.60 % (7505)Memory used [KB]: 5756
% 1.55/1.60 % (7505)Time elapsed: 0.016 s
% 1.55/1.60 % (7505)Instructions burned: 26 (million)
% 1.55/1.60 % (7505)------------------------------
% 1.55/1.60 % (7505)------------------------------
% 1.55/1.62 % (7506)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_7357 for (2996ds/149Mi)
% 1.55/1.63 % (7504)Instruction limit reached!
% 1.55/1.63 % (7504)------------------------------
% 1.55/1.63 % (7504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.63 % (7504)Termination reason: Unknown
% 1.55/1.63 % (7504)Termination phase: Saturation
% 1.55/1.63
% 1.55/1.63 % (7504)Memory used [KB]: 1407
% 1.55/1.63 % (7504)Time elapsed: 0.039 s
% 1.55/1.63 % (7504)Instructions burned: 99 (million)
% 1.55/1.63 % (7504)------------------------------
% 1.55/1.63 % (7504)------------------------------
% 1.55/1.64 % (7489)Instruction limit reached!
% 1.55/1.64 % (7489)------------------------------
% 1.55/1.64 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.64 % (7489)Termination reason: Unknown
% 1.55/1.64 % (7489)Termination phase: Saturation
% 1.55/1.64
% 1.55/1.64 % (7489)Memory used [KB]: 7036
% 1.55/1.64 % (7489)Time elapsed: 0.289 s
% 1.55/1.64 % (7489)Instructions burned: 779 (million)
% 1.55/1.64 % (7489)------------------------------
% 1.55/1.64 % (7489)------------------------------
% 1.55/1.64 % (7507)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7357 for (2996ds/39Mi)
% 1.55/1.65 % (7508)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_7357 for (2996ds/6Mi)
% 1.55/1.65 % (7508)Instruction limit reached!
% 1.55/1.65 % (7508)------------------------------
% 1.55/1.65 % (7508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.65 % (7508)Termination reason: Unknown
% 1.55/1.65 % (7508)Termination phase: Property scanning
% 1.55/1.65
% 1.55/1.65 % (7508)Memory used [KB]: 1023
% 1.55/1.65 % (7508)Time elapsed: 0.004 s
% 1.55/1.65 % (7508)Instructions burned: 7 (million)
% 1.55/1.65 % (7508)------------------------------
% 1.55/1.65 % (7508)------------------------------
% 1.55/1.66 % (7507)Instruction limit reached!
% 1.55/1.66 % (7507)------------------------------
% 1.55/1.66 % (7507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.66 % (7507)Termination reason: Unknown
% 1.55/1.66 % (7507)Termination phase: Saturation
% 1.55/1.66
% 1.55/1.66 % (7507)Memory used [KB]: 5756
% 1.55/1.66 % (7507)Time elapsed: 0.020 s
% 1.55/1.66 % (7507)Instructions burned: 39 (million)
% 1.55/1.66 % (7507)------------------------------
% 1.55/1.66 % (7507)------------------------------
% 1.55/1.66 % (7482)Instruction limit reached!
% 1.55/1.66 % (7482)------------------------------
% 1.55/1.66 % (7482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.66 % (7482)Termination reason: Unknown
% 1.55/1.66 % (7482)Termination phase: Saturation
% 1.55/1.66
% 1.55/1.66 % (7482)Memory used [KB]: 6908
% 1.55/1.66 % (7482)Time elapsed: 0.341 s
% 1.55/1.66 % (7482)Instructions burned: 711 (million)
% 1.55/1.66 % (7482)------------------------------
% 1.55/1.66 % (7482)------------------------------
% 1.55/1.68 % (7510)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7357 for (2995ds/47Mi)
% 1.55/1.68 % (7506)Instruction limit reached!
% 1.55/1.68 % (7506)------------------------------
% 1.55/1.68 % (7506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.68 % (7506)Termination reason: Unknown
% 1.55/1.68 % (7506)Termination phase: Saturation
% 1.55/1.68
% 1.55/1.68 % (7506)Memory used [KB]: 6268
% 1.55/1.68 % (7506)Time elapsed: 0.049 s
% 1.55/1.68 % (7506)Instructions burned: 150 (million)
% 1.55/1.68 % (7506)------------------------------
% 1.55/1.68 % (7506)------------------------------
% 1.55/1.68 % (7509)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_7357 for (2995ds/1087Mi)
% 1.55/1.68 % (7511)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_7357 for (2995ds/44Mi)
% 1.55/1.69 % (7511)Refutation not found, incomplete strategy
% 1.55/1.69 % (7511)------------------------------
% 1.55/1.69 % (7511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.69 % (7511)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.69
% 1.55/1.69
% 1.55/1.69 % (7511)Memory used [KB]: 1279
% 1.55/1.69 % (7511)Time elapsed: 0.012 s
% 1.55/1.69 % (7511)Instructions burned: 22 (million)
% 1.55/1.69 % (7511)------------------------------
% 1.55/1.69 % (7511)------------------------------
% 1.55/1.69 % (7512)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_7357 for (2995ds/432Mi)
% 1.55/1.70 % (7510)Instruction limit reached!
% 1.55/1.70 % (7510)------------------------------
% 1.55/1.70 % (7510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.70 % (7510)Termination reason: Unknown
% 1.55/1.70 % (7510)Termination phase: Saturation
% 1.55/1.70
% 1.55/1.70 % (7510)Memory used [KB]: 5756
% 1.55/1.70 % (7510)Time elapsed: 0.024 s
% 1.55/1.70 % (7510)Instructions burned: 48 (million)
% 1.55/1.70 % (7510)------------------------------
% 1.55/1.70 % (7510)------------------------------
% 1.55/1.71 % (7515)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_7357 for (2995ds/31Mi)
% 1.55/1.72 % (7514)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7357 for (2995ds/62Mi)
% 1.55/1.72 % (7473)Instruction limit reached!
% 1.55/1.72 % (7473)------------------------------
% 1.55/1.72 % (7473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.72 % (7473)Termination reason: Unknown
% 1.55/1.72 % (7473)Termination phase: Saturation
% 1.55/1.72
% 1.55/1.72 % (7473)Memory used [KB]: 8059
% 1.55/1.72 % (7473)Time elapsed: 0.431 s
% 1.55/1.72 % (7473)Instructions burned: 1041 (million)
% 1.55/1.72 % (7473)------------------------------
% 1.55/1.72 % (7473)------------------------------
% 1.55/1.73 % (7515)Instruction limit reached!
% 1.55/1.73 % (7515)------------------------------
% 1.55/1.73 % (7515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.73 % (7515)Termination reason: Unknown
% 1.55/1.73 % (7515)Termination phase: Saturation
% 1.55/1.73
% 1.55/1.73 % (7515)Memory used [KB]: 5756
% 1.55/1.73 % (7515)Time elapsed: 0.017 s
% 1.55/1.73 % (7515)Instructions burned: 32 (million)
% 1.55/1.73 % (7515)------------------------------
% 1.55/1.73 % (7515)------------------------------
% 1.55/1.74 % (7516)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7357 for (2995ds/96Mi)
% 1.55/1.74 % (7514)Instruction limit reached!
% 1.55/1.74 % (7514)------------------------------
% 1.55/1.74 % (7514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.74 % (7514)Termination reason: Unknown
% 1.55/1.74 % (7514)Termination phase: Saturation
% 1.55/1.74
% 1.55/1.74 % (7514)Memory used [KB]: 5884
% 1.55/1.74 % (7514)Time elapsed: 0.043 s
% 1.55/1.74 % (7514)Instructions burned: 65 (million)
% 1.55/1.74 % (7514)------------------------------
% 1.55/1.74 % (7514)------------------------------
% 1.55/1.75 % (7518)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_7357 for (2995ds/71Mi)
% 1.55/1.75 % (7517)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_7357 for (2995ds/453Mi)
% 1.55/1.75 % (7502)Instruction limit reached!
% 1.55/1.75 % (7502)------------------------------
% 1.55/1.75 % (7502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.75 % (7502)Termination reason: Unknown
% 1.55/1.75 % (7502)Termination phase: Saturation
% 1.55/1.75
% 1.55/1.75 % (7502)Memory used [KB]: 6652
% 1.55/1.75 % (7502)Time elapsed: 0.208 s
% 1.55/1.75 % (7502)Instructions burned: 449 (million)
% 1.55/1.75 % (7502)------------------------------
% 1.55/1.75 % (7502)------------------------------
% 1.55/1.76 % (7509)First to succeed.
% 1.55/1.76 % (7509)Refutation found. Thanks to Tanya!
% 1.55/1.76 % SZS status Theorem for DTF2THF_7357
% 1.55/1.76 % SZS output start Proof for DTF2THF_7357
% 1.55/1.76 thf(type_def_6, type, nat: $tType).
% 1.55/1.76 thf(type_def_7, type, list: ($tType) > $tType).
% 1.55/1.76 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.55/1.76 thf(func_def_2, type, nat: $tType).
% 1.55/1.76 thf(func_def_3, type, natStar: nat > nat > $o).
% 1.55/1.76 thf(func_def_4, type, zero: nat).
% 1.55/1.76 thf(func_def_5, type, suc: nat > nat).
% 1.55/1.76 thf(func_def_6, type, plus: nat > nat > nat).
% 1.55/1.76 thf(func_def_7, type, list: ($tType) > $tType).
% 1.55/1.76 thf(func_def_8, type, listStar: !>[X0: $tType]:((X0 > X0 > $o) > nat > list @ X0 > list @ X0 > $o)).
% 1.55/1.76 thf(func_def_9, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.55/1.76 thf(func_def_10, type, cons: !>[X0: $tType]:(nat > X0 > list @ X0 > list @ X0)).
% 1.55/1.76 thf(func_def_11, type, app: !>[X0: $tType]:(nat > nat > list @ X0 > list @ X0 > list @ X0)).
% 1.55/1.76 thf(func_def_14, type, sP0: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.55/1.76 thf(func_def_15, type, sP1: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.55/1.76 thf(func_def_16, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.55/1.76 thf(func_def_17, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.55/1.76 thf(func_def_18, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.55/1.76 thf(func_def_19, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.55/1.76 thf(func_def_20, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.55/1.76 thf(func_def_21, type, sK7: nat).
% 1.55/1.76 thf(func_def_22, type, sK8: list @ list @ list @ nat).
% 1.55/1.76 thf(func_def_23, type, sK9: nat).
% 1.55/1.76 thf(func_def_24, type, sK10: list @ list @ list @ nat).
% 1.55/1.76 thf(func_def_27, type, ph12: !>[X0: $tType]:(X0)).
% 1.55/1.76 thf(f619,plain,(
% 1.55/1.76 $false),
% 1.55/1.76 inference(avatar_sat_refutation,[status(thm)],[f174,f222,f226,f280,f325,f332,f407,f420,f463,f476,f506,f527,f556,f614])).
% 1.55/1.76 thf(f614,plain,(
% 1.55/1.76 ~spl11_16 | spl11_24),
% 1.55/1.76 inference(avatar_split_clause,[status(thm)],[f613,f525,f402])).
% 1.55/1.76 thf(f402,definition,(
% 1.55/1.76 spl11_16 <=> ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) = $true)),
% 1.55/1.76 introduced(definition,[new_symbols(naming,[spl11_16])],[avatar_definition])).
% 1.55/1.77 thf(f525,definition,(
% 1.55/1.77 spl11_24 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK8) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_24])],[avatar_definition])).
% 1.55/1.77 thf(f613,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_24),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f612,f72])).
% 1.55/1.77 thf(f72,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) = $true)),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f55])).
% 1.55/1.77 thf(f55,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ sK7 @ sK9)) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ (app @ list @ list @ nat @ (plus @ zero @ sK7) @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) = $true) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10))),
% 1.55/1.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f35,f54])).
% 1.55/1.77 thf(f54,plain,(
% 1.55/1.77 ? [X0 : nat,X1 : list @ list @ list @ nat,X2 : nat,X3 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ list @ list @ nat @ zero @ (plus @ X0 @ X2) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X0 @ X2 @ X1 @ X3)) @ (app @ list @ list @ nat @ (plus @ zero @ X0) @ X2 @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1) @ X3)) != $true) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1)) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X3 @ X3) = $true)) => (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ sK7 @ sK9)) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ (app @ list @ list @ nat @ (plus @ zero @ sK7) @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) = $true) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10)))),
% 1.55/1.77 introduced(definition,[],[choice_axiom])).
% 1.55/1.77 thf(f35,plain,(
% 1.55/1.77 ? [X0 : nat,X1 : list @ list @ list @ nat,X2 : nat,X3 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ list @ list @ nat @ zero @ (plus @ X0 @ X2) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X0 @ X2 @ X1 @ X3)) @ (app @ list @ list @ nat @ (plus @ zero @ X0) @ X2 @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1) @ X3)) != $true) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1)) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X3 @ X3) = $true))),
% 1.55/1.77 inference(flattening,[status(thm)],[f34])).
% 1.55/1.77 thf(f34,plain,(
% 1.55/1.77 ? [X0 : nat,X1 : list @ list @ list @ nat,X2 : nat,X3 : list @ list @ list @ nat] : ((((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ list @ list @ nat @ zero @ (plus @ X0 @ X2) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X0 @ X2 @ X1 @ X3)) @ (app @ list @ list @ nat @ (plus @ zero @ X0) @ X2 @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1) @ X3)) != $true) & ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X3 @ X3) = $true)) & ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1)))),
% 1.55/1.77 inference(ennf_transformation,[status(thm)],[f26])).
% 1.55/1.77 thf(f26,plain,(
% 1.55/1.77 ~! [X0 : nat,X1 : list @ list @ list @ nat,X2 : nat,X3 : list @ list @ list @ nat] : (($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X0 @ X1 @ X1)) => (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X2 @ X3 @ X3) = $true) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ list @ list @ nat @ zero @ (plus @ X0 @ X2) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X0 @ X2 @ X1 @ X3)) @ (app @ list @ list @ nat @ (plus @ zero @ X0) @ X2 @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1) @ X3)) = $true)))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f25])).
% 1.55/1.77 thf(f25,plain,(
% 1.55/1.77 ~! [X0 : nat,X1 : list @ list @ list @ nat,X2 : nat,X3 : 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)) @ X2 @ X3 @ X3) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ list @ list @ nat @ zero @ (plus @ X0 @ X2) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X0 @ X2 @ X1 @ X3)) @ (app @ list @ list @ nat @ (plus @ zero @ X0) @ X2 @ (app @ list @ list @ nat @ zero @ X0 @ nil @ list @ list @ nat @ X1) @ X3))))),
% 1.55/1.77 inference(rectify,[status(thm)],[f11])).
% 1.55/1.77 thf(f11,negated_conjecture,(
% 1.55/1.77 ~! [X15 : nat,X17 : list @ list @ list @ nat,X16 : nat,X18 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X15 @ X17 @ X17) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X16 @ X18 @ X18) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X15 @ X16)) @ (app @ list @ list @ nat @ zero @ (plus @ X15 @ X16) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X15 @ X16 @ X17 @ X18)) @ (app @ list @ list @ nat @ (plus @ zero @ X15) @ X16 @ (app @ list @ list @ nat @ zero @ X15 @ nil @ list @ list @ nat @ X17) @ X18))))),
% 1.55/1.77 inference(negated_conjecture,[status(cth)],[f10])).
% 1.55/1.77 thf(f10,conjecture,(
% 1.55/1.77 ! [X15 : nat,X17 : list @ list @ list @ nat,X16 : nat,X18 : list @ list @ list @ nat] : ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X15 @ X17 @ X17) => ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ X16 @ X18 @ X18) => (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ X15 @ X16)) @ (app @ list @ list @ nat @ zero @ (plus @ X15 @ X16) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ X15 @ X16 @ X17 @ X18)) @ (app @ list @ list @ nat @ (plus @ zero @ X15) @ X16 @ (app @ list @ list @ nat @ zero @ X15 @ nil @ list @ list @ nat @ X17) @ X18))))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',list_app_assoc_base)).
% 1.55/1.77 thf(f612,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_24),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f607])).
% 1.55/1.77 thf(f607,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) != $true) | ($true != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_24),
% 1.55/1.77 inference(superposition,[status(thm)],[f526,f293])).
% 1.55/1.77 thf(f293,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (($true = (listStar @ X0 @ X1 @ X2 @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3)) | ((isPer @ X0 @ X1) != $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3))) )),
% 1.55/1.77 inference(forward_demodulation,[status(thm)],[f76,f75])).
% 1.55/1.77 thf(f75,plain,(
% 1.55/1.77 ( ! [X0 : nat] : (((plus @ zero @ X0) = X0)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.77 thf(f29,plain,(
% 1.55/1.77 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 1.55/1.77 inference(rectify,[status(thm)],[f7])).
% 1.55/1.77 thf(f7,axiom,(
% 1.55/1.77 ! [X8 : nat] : ((plus @ zero @ X8) = X8)),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',ax1)).
% 1.55/1.77 thf(f76,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X2 : nat,X3 : list @ X0,X1 : X0 > X0 > $o] : (($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3)) | ((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f33])).
% 1.55/1.77 thf(f33,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : list @ X0] : (((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X3 @ X3))) | ((isPer @ X0 @ X1) != $true))),
% 1.55/1.77 inference(ennf_transformation,[status(thm)],[f28])).
% 1.55/1.77 thf(f28,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : list @ X0] : (($true = (listStar @ X0 @ X1 @ X2 @ X3 @ X3)) => ((listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3) = $true)))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f27])).
% 1.55/1.77 thf(f27,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X3 @ X3) => (listStar @ X0 @ X1 @ (plus @ zero @ X2) @ (app @ X0 @ zero @ X2 @ nil @ X0 @ X3) @ X3)))),
% 1.55/1.77 inference(rectify,[status(thm)],[f8])).
% 1.55/1.77 thf(f8,axiom,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X2 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X2 @ X2) => (listStar @ X0 @ X1 @ (plus @ zero @ X8) @ (app @ X0 @ zero @ X8 @ nil @ X0 @ X2) @ X2)))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',ax3)).
% 1.55/1.77 thf(f526,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK8) != $true) | spl11_24),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f525])).
% 1.55/1.77 thf(f556,plain,(
% 1.55/1.77 ~spl11_16 | spl11_23),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f554,f522,f402])).
% 1.55/1.77 thf(f522,definition,(
% 1.55/1.77 spl11_23 <=> ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_23])],[avatar_definition])).
% 1.55/1.77 thf(f554,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_23),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f553])).
% 1.55/1.77 thf(f553,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != $true) | spl11_23),
% 1.55/1.77 inference(superposition,[status(thm)],[f547,f77])).
% 1.55/1.77 thf(f77,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X2 : nat,X1 : X0 > X0 > $o] : (((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f39])).
% 1.55/1.77 thf(f39,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true) | ((isPer @ X0 @ X1) != $true))),
% 1.55/1.77 inference(ennf_transformation,[status(thm)],[f24])).
% 1.55/1.77 thf(f24,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f23])).
% 1.55/1.77 thf(f23,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat] : (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)))),
% 1.55/1.77 inference(rectify,[status(thm)],[f3])).
% 1.55/1.77 thf(f3,axiom,(
% 1.55/1.77 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : nat] : (isPer @ list @ X5 @ (listStar @ X5 @ X6 @ X7)))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p','\'listStar\'_is_per')).
% 1.55/1.77 thf(f547,plain,(
% 1.55/1.77 ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) != $true) | spl11_23),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f546])).
% 1.55/1.77 thf(f546,plain,(
% 1.55/1.77 ($true != $true) | ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) != $true) | spl11_23),
% 1.55/1.77 inference(superposition,[status(thm)],[f523,f69])).
% 1.55/1.77 thf(f69,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f53])).
% 1.55/1.77 thf(f53,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)) & (((sP1 @ X0 @ X1) = $true) | ((isPer @ X0 @ X1) != $true)))),
% 1.55/1.77 inference(nnf_transformation,[status(thm)],[f42])).
% 1.55/1.77 thf(f42,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> ((sP1 @ X0 @ X1) = $true))),
% 1.55/1.77 inference(definition_folding,[status(thm)],[f32,f41,f40])).
% 1.55/1.77 thf(f40,plain,(
% 1.55/1.77 ! [X1 : X0 > X0 > $o,X0 : $tType] : (((sP0 @ X0 @ X1) = $true) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X4) = $true)))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.55/1.77 thf(f41,plain,(
% 1.55/1.77 ! [X1 : X0 > X0 > $o,X0 : $tType] : (((sP1 @ X0 @ X1) = $true) <=> (((sP0 @ X0 @ X1) = $true) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.55/1.77 thf(f32,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X4) = $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))))),
% 1.55/1.77 inference(flattening,[status(thm)],[f31])).
% 1.55/1.77 thf(f31,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : ((((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) | ((X1 @ X2 @ X3) != $true))))),
% 1.55/1.77 inference(ennf_transformation,[status(thm)],[f18])).
% 1.55/1.77 thf(f18,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) => ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) => (((X1 @ X3 @ X4) = $true) => ((X1 @ X2 @ X4) = $true)))))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f17])).
% 1.55/1.77 thf(f17,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X5 : X0,X6 : X0] : ((X1 @ X5 @ X6) => (X1 @ X6 @ X5))))),
% 1.55/1.77 inference(rectify,[status(thm)],[f1])).
% 1.55/1.77 thf(f1,axiom,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2))))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',is_per)).
% 1.55/1.77 thf(f523,plain,(
% 1.55/1.77 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) != $true) | spl11_23),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f522])).
% 1.55/1.77 thf(f527,plain,(
% 1.55/1.77 ~spl11_23 | ~spl11_24 | spl11_22),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f520,f504,f525,f522])).
% 1.55/1.77 thf(f504,definition,(
% 1.55/1.77 spl11_22 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8)) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_22])],[avatar_definition])).
% 1.55/1.77 thf(f520,plain,(
% 1.55/1.77 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK8) != $true) | spl11_22),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f518])).
% 1.55/1.77 thf(f518,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK8) != $true) | ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7)) != $true) | ($true != $true) | spl11_22),
% 1.55/1.77 inference(superposition,[status(thm)],[f505,f61])).
% 1.55/1.77 thf(f61,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o,X4 : X1,X5 : X1] : (((X0 @ X5 @ X4) = $true) | ((sP1 @ X1 @ X0) != $true) | ((X0 @ X4 @ X5) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f48])).
% 1.55/1.77 thf(f48,plain,(
% 1.55/1.77 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP1 @ X1 @ X0) = $true) | ($true != (sP0 @ X1 @ X0)) | (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) = $true) & ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0)) != $true))) & ((($true = (sP0 @ X1 @ X0)) & ! [X4 : X1,X5 : X1] : (((X0 @ X4 @ X5) != $true) | ((X0 @ X5 @ X4) = $true))) | ((sP1 @ X1 @ X0) != $true)))),
% 1.55/1.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f46,f47])).
% 1.55/1.77 thf(f47,plain,(
% 1.55/1.77 ! [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)))),
% 1.55/1.77 introduced(definition,[],[choice_axiom])).
% 1.55/1.77 thf(f46,plain,(
% 1.55/1.77 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((((sP1 @ X1 @ X0) = $true) | ($true != (sP0 @ X1 @ X0)) | ? [X2 : X1,X3 : X1] : (((X0 @ X2 @ X3) = $true) & ($true != (X0 @ X3 @ X2)))) & ((($true = (sP0 @ X1 @ X0)) & ! [X4 : X1,X5 : X1] : (((X0 @ X4 @ X5) != $true) | ((X0 @ X5 @ X4) = $true))) | ((sP1 @ X1 @ X0) != $true)))),
% 1.55/1.77 inference(rectify,[status(thm)],[f45])).
% 1.55/1.77 thf(f45,plain,(
% 1.55/1.77 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | ((sP0 @ X0 @ X1) != $true) | ? [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true != (X1 @ X6 @ X5)))) & ((((sP0 @ X0 @ X1) = $true) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((sP1 @ X0 @ X1) != $true)))),
% 1.55/1.77 inference(flattening,[status(thm)],[f44])).
% 1.55/1.77 thf(f44,plain,(
% 1.55/1.77 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP1 @ X0 @ X1) = $true) | (((sP0 @ X0 @ X1) != $true) | ? [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true != (X1 @ X6 @ X5))))) & ((((sP0 @ X0 @ X1) = $true) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((sP1 @ X0 @ X1) != $true)))),
% 1.55/1.77 inference(nnf_transformation,[status(thm)],[f41])).
% 1.55/1.77 thf(f505,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8)) != $true) | spl11_22),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f504])).
% 1.55/1.77 thf(f506,plain,(
% 1.55/1.77 ~spl11_22 | ~spl11_16 | spl11_15),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f502,f399,f402,f504])).
% 1.55/1.77 thf(f399,definition,(
% 1.55/1.77 spl11_15 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_15])],[avatar_definition])).
% 1.55/1.77 thf(f502,plain,(
% 1.55/1.77 ((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)) @ sK7 @ sK8 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8)) != $true) | spl11_15),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f491,f71])).
% 1.55/1.77 thf(f71,plain,(
% 1.55/1.77 ($true = (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10))),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f55])).
% 1.55/1.77 thf(f491,plain,(
% 1.55/1.77 ((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)) @ sK7 @ sK8 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8)) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10)) | spl11_15),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f488])).
% 1.55/1.77 thf(f488,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8)) != $true) | ($true != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10)) | spl11_15),
% 1.55/1.77 inference(superposition,[status(thm)],[f400,f56])).
% 1.55/1.77 thf(f56,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : X0 > X0 > $o,X6 : list @ X0,X7 : list @ X0,X4 : list @ X0,X5 : list @ X0] : (((listStar @ X0 @ X1 @ (plus @ X2 @ X3) @ (app @ X0 @ X2 @ X3 @ X4 @ X6) @ (app @ X0 @ X2 @ X3 @ X5 @ X7)) = $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X4 @ X5)) | ((listStar @ X0 @ X1 @ X3 @ X6 @ X7) != $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f36])).
% 1.55/1.77 thf(f36,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : nat,X4 : list @ X0,X5 : list @ X0] : (($true != (listStar @ X0 @ X1 @ X2 @ X4 @ X5)) | ! [X6 : list @ X0,X7 : list @ X0] : (((listStar @ X0 @ X1 @ X3 @ X6 @ X7) != $true) | ((listStar @ X0 @ X1 @ (plus @ X2 @ X3) @ (app @ X0 @ X2 @ X3 @ X4 @ X6) @ (app @ X0 @ X2 @ X3 @ X5 @ X7)) = $true))) | ((isPer @ X0 @ X1) != $true))),
% 1.55/1.77 inference(ennf_transformation,[status(thm)],[f20])).
% 1.55/1.77 thf(f20,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : nat,X4 : list @ X0,X5 : list @ X0] : (($true = (listStar @ X0 @ X1 @ X2 @ X4 @ X5)) => ! [X6 : list @ X0,X7 : list @ X0] : (((listStar @ X0 @ X1 @ X3 @ X6 @ X7) = $true) => ((listStar @ X0 @ X1 @ (plus @ X2 @ X3) @ (app @ X0 @ X2 @ X3 @ X4 @ X6) @ (app @ X0 @ X2 @ X3 @ X5 @ X7)) = $true))))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f19])).
% 1.55/1.77 thf(f19,plain,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : nat,X4 : list @ X0,X5 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X4 @ X5) => ! [X6 : list @ X0,X7 : list @ X0] : ((listStar @ X0 @ X1 @ X3 @ X6 @ X7) => (listStar @ X0 @ X1 @ (plus @ X2 @ X3) @ (app @ X0 @ X2 @ X3 @ X4 @ X6) @ (app @ X0 @ X2 @ X3 @ X5 @ X7)))))),
% 1.55/1.77 inference(rectify,[status(thm)],[f6])).
% 1.55/1.77 thf(f6,axiom,(
% 1.55/1.77 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X13 : nat,X9 : list @ X0,X10 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X9 @ X10) => ! [X11 : list @ X0,X12 : list @ X0] : ((listStar @ X0 @ X1 @ X13 @ X11 @ X12) => (listStar @ X0 @ X1 @ (plus @ X8 @ X13) @ (app @ X0 @ X8 @ X13 @ X9 @ X11) @ (app @ X0 @ X8 @ X13 @ X10 @ X12)))))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',app_tp_ax)).
% 1.55/1.77 thf(f400,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) | spl11_15),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f399])).
% 1.55/1.77 thf(f476,plain,(
% 1.55/1.77 ~spl11_16 | spl11_17),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f475,f405,f402])).
% 1.55/1.77 thf(f405,definition,(
% 1.55/1.77 spl11_17 <=> ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_17])],[avatar_definition])).
% 1.55/1.77 thf(f475,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_17),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f474,f72])).
% 1.55/1.77 thf(f474,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_17),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f468,f71])).
% 1.55/1.77 thf(f468,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10)) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) != $true) | spl11_17),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f464])).
% 1.55/1.77 thf(f464,plain,(
% 1.55/1.77 ($true != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK7 @ sK8 @ sK8) != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | ($true != (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ sK9 @ sK10 @ sK10)) | spl11_17),
% 1.55/1.77 inference(superposition,[status(thm)],[f406,f56])).
% 1.55/1.77 thf(f406,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) != $true) | spl11_17),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f405])).
% 1.55/1.77 thf(f463,plain,(
% 1.55/1.77 ~spl11_10 | spl11_16),
% 1.55/1.77 inference(avatar_contradiction_clause,[status(thm)],[f462])).
% 1.55/1.77 thf(f462,plain,(
% 1.55/1.77 $false | (~spl11_10 | spl11_16)),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f461,f274])).
% 1.55/1.77 thf(f274,plain,(
% 1.55/1.77 ($true = (sP1 @ nat @ natStar)) | ~spl11_10),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f273])).
% 1.55/1.77 thf(f273,definition,(
% 1.55/1.77 spl11_10 <=> ($true = (sP1 @ nat @ natStar))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_10])],[avatar_definition])).
% 1.55/1.77 thf(f461,plain,(
% 1.55/1.77 ($true != (sP1 @ nat @ natStar)) | spl11_16),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f460])).
% 1.55/1.77 thf(f460,plain,(
% 1.55/1.77 ($true != (sP1 @ nat @ natStar)) | ($true != $true) | spl11_16),
% 1.55/1.77 inference(superposition,[status(thm)],[f457,f70])).
% 1.55/1.77 thf(f70,plain,(
% 1.55/1.77 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) | ((sP1 @ X0 @ X1) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f53])).
% 1.55/1.77 thf(f457,plain,(
% 1.55/1.77 ((isPer @ nat @ natStar) != $true) | spl11_16),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f455])).
% 1.55/1.77 thf(f455,plain,(
% 1.55/1.77 ((isPer @ nat @ natStar) != $true) | ($true != $true) | spl11_16),
% 1.55/1.77 inference(superposition,[status(thm)],[f425,f77])).
% 1.55/1.77 thf(f425,plain,(
% 1.55/1.77 ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | spl11_16),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f424])).
% 1.55/1.77 thf(f424,plain,(
% 1.55/1.77 ($true != (isPer @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)))) | ($true != $true) | spl11_16),
% 1.55/1.77 inference(superposition,[status(thm)],[f403,f77])).
% 1.55/1.77 thf(f403,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_16),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f402])).
% 1.55/1.77 thf(f420,plain,(
% 1.55/1.77 ~spl11_16 | spl11_7),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f418,f184,f402])).
% 1.55/1.77 thf(f184,definition,(
% 1.55/1.77 spl11_7 <=> ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition])).
% 1.55/1.77 thf(f418,plain,(
% 1.55/1.77 ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_7),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f417])).
% 1.55/1.77 thf(f417,plain,(
% 1.55/1.77 ($true != $true) | ((isPer @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero))) != $true) | spl11_7),
% 1.55/1.77 inference(superposition,[status(thm)],[f413,f77])).
% 1.55/1.77 thf(f413,plain,(
% 1.55/1.77 ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | spl11_7),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f412])).
% 1.55/1.77 thf(f412,plain,(
% 1.55/1.77 ((isPer @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | ($true != $true) | spl11_7),
% 1.55/1.77 inference(superposition,[status(thm)],[f185,f69])).
% 1.55/1.77 thf(f185,plain,(
% 1.55/1.77 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | spl11_7),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f184])).
% 1.55/1.77 thf(f407,plain,(
% 1.55/1.77 ~spl11_15 | ~spl11_16 | ~spl11_17 | ~spl11_9),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f392,f220,f405,f402,f399])).
% 1.55/1.77 thf(f220,definition,(
% 1.55/1.77 spl11_9 <=> ! [X0 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ X0) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ X0 @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition])).
% 1.55/1.77 thf(f392,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) != $true) | ((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)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) | ~spl11_9),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f388])).
% 1.55/1.77 thf(f388,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) != $true) | ((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)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10) @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) | ~spl11_9),
% 1.55/1.77 inference(superposition,[status(thm)],[f221,f293])).
% 1.55/1.77 thf(f221,plain,(
% 1.55/1.77 ( ! [X0 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ X0) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ X0 @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true)) ) | ~spl11_9),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f220])).
% 1.55/1.77 thf(f332,plain,(
% 1.55/1.77 spl11_10 | ~spl11_3 | ~spl11_11),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f329,f276,f148,f273])).
% 1.55/1.77 thf(f148,definition,(
% 1.55/1.77 spl11_3 <=> ((sP0 @ nat @ natStar) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.55/1.77 thf(f276,definition,(
% 1.55/1.77 spl11_11 <=> ((sK2 @ nat @ natStar) = (sK3 @ nat @ natStar))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_11])],[avatar_definition])).
% 1.55/1.77 thf(f329,plain,(
% 1.55/1.77 ($true = (sP1 @ nat @ natStar)) | (~spl11_3 | ~spl11_11)),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f328,f79])).
% 1.55/1.77 thf(f79,plain,(
% 1.55/1.77 ( ! [X1 : nat] : (((natStar @ X1 @ X1) = $true)) )),
% 1.55/1.77 inference(equality_resolution,[status(thm)],[f59])).
% 1.55/1.77 thf(f59,plain,(
% 1.55/1.77 ( ! [X0 : nat,X1 : nat] : (((natStar @ X0 @ X1) = $true) | (X0 != X1)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f43])).
% 1.55/1.77 thf(f43,plain,(
% 1.55/1.77 ! [X0 : nat,X1 : nat] : ((((natStar @ X0 @ X1) = $true) | (X0 != X1)) & ((X0 = X1) | ((natStar @ X0 @ X1) != $true)))),
% 1.55/1.77 inference(nnf_transformation,[status(thm)],[f22])).
% 1.55/1.77 thf(f22,plain,(
% 1.55/1.77 ! [X0 : nat,X1 : nat] : (((natStar @ X0 @ X1) = $true) <=> (X0 = X1))),
% 1.55/1.77 inference(fool_elimination,[status(thm)],[f21])).
% 1.55/1.77 thf(f21,plain,(
% 1.55/1.77 ! [X0 : nat,X1 : nat] : ((natStar @ X0 @ X1) <=> (X0 = X1))),
% 1.55/1.77 inference(rectify,[status(thm)],[f2])).
% 1.55/1.77 thf(f2,axiom,(
% 1.55/1.77 ! [X2 : nat,X3 : nat] : ((natStar @ X2 @ X3) <=> (X2 = X3))),
% 1.55/1.77 file('/export/starexec/sandbox2/tmp/tmp.DUbZzavCME/DTF2THF_7357.p',natStar_is_eq)).
% 1.55/1.77 thf(f328,plain,(
% 1.55/1.77 ($true != (natStar @ (sK2 @ nat @ natStar) @ (sK2 @ nat @ natStar))) | ($true = (sP1 @ nat @ natStar)) | (~spl11_3 | ~spl11_11)),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f326,f149])).
% 1.55/1.77 thf(f149,plain,(
% 1.55/1.77 ((sP0 @ nat @ natStar) = $true) | ~spl11_3),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.55/1.77 thf(f326,plain,(
% 1.55/1.77 ((sP0 @ nat @ natStar) != $true) | ($true = (sP1 @ nat @ natStar)) | ($true != (natStar @ (sK2 @ nat @ natStar) @ (sK2 @ nat @ natStar))) | ~spl11_11),
% 1.55/1.77 inference(superposition,[status(thm)],[f63,f277])).
% 1.55/1.77 thf(f277,plain,(
% 1.55/1.77 ((sK2 @ nat @ natStar) = (sK3 @ nat @ natStar)) | ~spl11_11),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f276])).
% 1.55/1.77 thf(f63,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0)) != $true) | ($true != (sP0 @ X1 @ X0)) | ((sP1 @ X1 @ X0) = $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f48])).
% 1.55/1.77 thf(f325,plain,(
% 1.55/1.77 spl11_3 | ~spl11_5),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f324,f172,f148])).
% 1.55/1.77 thf(f172,definition,(
% 1.55/1.77 spl11_5 <=> ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar))),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.55/1.77 thf(f324,plain,(
% 1.55/1.77 ((sP0 @ nat @ natStar) = $true) | ~spl11_5),
% 1.55/1.77 inference(subsumption_resolution,[status(thm)],[f310,f66])).
% 1.55/1.77 thf(f66,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true) | ($true = (sP0 @ X1 @ X0))) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f52])).
% 1.55/1.77 thf(f52,plain,(
% 1.55/1.77 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP0 @ X1 @ X0)) | (((X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) & ((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true))) & (! [X5 : X1,X6 : X1,X7 : X1] : (($true != (X0 @ X5 @ X6)) | ((X0 @ X6 @ X7) != $true) | ((X0 @ X5 @ X7) = $true)) | ($true != (sP0 @ X1 @ X0))))),
% 1.55/1.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f50,f51])).
% 1.55/1.77 thf(f51,plain,(
% 1.55/1.77 ! [X1 : $tType,X0 : X1 > X1 > $o] : (? [X2 : X1,X3 : X1,X4 : X1] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X3 @ X4) = $true) & ($true != (X0 @ X2 @ X4))) => (((X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) & ((X0 @ (sK4 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true)))),
% 1.55/1.77 introduced(definition,[],[choice_axiom])).
% 1.55/1.77 thf(f50,plain,(
% 1.55/1.77 ! [X0 : X1 > X1 > $o,X1 : $tType] : ((($true = (sP0 @ X1 @ X0)) | ? [X2 : X1,X3 : X1,X4 : X1] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X3 @ X4) = $true) & ($true != (X0 @ X2 @ X4)))) & (! [X5 : X1,X6 : X1,X7 : X1] : (($true != (X0 @ X5 @ X6)) | ((X0 @ X6 @ X7) != $true) | ((X0 @ X5 @ X7) = $true)) | ($true != (sP0 @ X1 @ X0))))),
% 1.55/1.77 inference(rectify,[status(thm)],[f49])).
% 1.55/1.77 thf(f49,plain,(
% 1.55/1.77 ! [X1 : X0 > X0 > $o,X0 : $tType] : ((((sP0 @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X4) = $true) & ((X1 @ X2 @ X4) != $true))) & (! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X4) = $true)) | ((sP0 @ X0 @ X1) != $true)))),
% 1.55/1.77 inference(nnf_transformation,[status(thm)],[f40])).
% 1.55/1.77 thf(f310,plain,(
% 1.55/1.77 ((sP0 @ nat @ natStar) = $true) | ((natStar @ (sK4 @ nat @ natStar) @ (sK6 @ nat @ natStar)) = $true) | ~spl11_5),
% 1.55/1.77 inference(superposition,[status(thm)],[f67,f173])).
% 1.55/1.77 thf(f173,plain,(
% 1.55/1.77 ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar)) | ~spl11_5),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.55/1.77 thf(f67,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (X0 @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) | ($true = (sP0 @ X1 @ X0))) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f52])).
% 1.55/1.77 thf(f280,plain,(
% 1.55/1.77 spl11_11 | ~spl11_3 | spl11_10),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f260,f273,f148,f276])).
% 1.55/1.77 thf(f260,plain,(
% 1.55/1.77 ($true = (sP1 @ nat @ natStar)) | ((sK2 @ nat @ natStar) = (sK3 @ nat @ natStar)) | ((sP0 @ nat @ natStar) != $true)),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f258])).
% 1.55/1.77 thf(f258,plain,(
% 1.55/1.77 ((sK2 @ nat @ natStar) = (sK3 @ nat @ natStar)) | ($true != $true) | ((sP0 @ nat @ natStar) != $true) | ($true = (sP1 @ nat @ natStar))),
% 1.55/1.77 inference(superposition,[status(thm)],[f58,f64])).
% 1.55/1.77 thf(f64,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) = $true) | ((sP1 @ X1 @ X0) = $true) | ($true != (sP0 @ X1 @ X0))) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f48])).
% 1.55/1.77 thf(f58,plain,(
% 1.55/1.77 ( ! [X0 : nat,X1 : nat] : (((natStar @ X0 @ X1) != $true) | (X0 = X1)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f43])).
% 1.55/1.77 thf(f226,plain,(
% 1.55/1.77 ~spl11_7 | spl11_8),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f225,f217,f184])).
% 1.55/1.77 thf(f217,definition,(
% 1.55/1.77 spl11_8 <=> ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) = $true)),
% 1.55/1.77 introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition])).
% 1.55/1.77 thf(f225,plain,(
% 1.55/1.77 ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | spl11_8),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f224])).
% 1.55/1.77 thf(f224,plain,(
% 1.55/1.77 ($true != $true) | ((sP1 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | spl11_8),
% 1.55/1.77 inference(superposition,[status(thm)],[f218,f62])).
% 1.55/1.77 thf(f62,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (($true = (sP0 @ X1 @ X0)) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f48])).
% 1.55/1.77 thf(f218,plain,(
% 1.55/1.77 ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | spl11_8),
% 1.55/1.77 inference(avatar_component_clause,[status(thm)],[f217])).
% 1.55/1.77 thf(f222,plain,(
% 1.55/1.77 ~spl11_8 | spl11_9),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f215,f220,f217])).
% 1.55/1.77 thf(f215,plain,(
% 1.55/1.77 ( ! [X0 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ X0) != $true) | ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ X0 @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true)) )),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f193])).
% 1.55/1.77 thf(f193,plain,(
% 1.55/1.77 ( ! [X0 : list @ list @ list @ nat] : (((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ X0 @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true) | ($true != $true) | ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ X0) != $true) | ((sP0 @ list @ list @ list @ nat @ (listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9))) != $true)) )),
% 1.55/1.77 inference(superposition,[status(thm)],[f177,f65])).
% 1.55/1.77 thf(f65,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o,X6 : X1,X7 : X1,X5 : X1] : (((X0 @ X5 @ X7) = $true) | ($true != (X0 @ X5 @ X6)) | ((X0 @ X6 @ X7) != $true) | ($true != (sP0 @ X1 @ X0))) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f52])).
% 1.55/1.77 thf(f177,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ (app @ list @ list @ nat @ sK7 @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true)),
% 1.55/1.77 inference(forward_demodulation,[status(thm)],[f176,f75])).
% 1.55/1.77 thf(f176,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ sK7 @ sK9) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ (app @ list @ list @ nat @ (plus @ zero @ sK7) @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true)),
% 1.55/1.77 inference(forward_demodulation,[status(thm)],[f73,f75])).
% 1.55/1.77 thf(f73,plain,(
% 1.55/1.77 ((listStar @ list @ list @ nat @ (listStar @ list @ nat @ (listStar @ nat @ natStar @ (suc @ zero)) @ (suc @ zero)) @ (plus @ zero @ (plus @ sK7 @ sK9)) @ (app @ list @ list @ nat @ zero @ (plus @ sK7 @ sK9) @ nil @ list @ list @ nat @ (app @ list @ list @ nat @ sK7 @ sK9 @ sK8 @ sK10)) @ (app @ list @ list @ nat @ (plus @ zero @ sK7) @ sK9 @ (app @ list @ list @ nat @ zero @ sK7 @ nil @ list @ list @ nat @ sK8) @ sK10)) != $true)),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f55])).
% 1.55/1.77 thf(f174,plain,(
% 1.55/1.77 spl11_5 | spl11_3),
% 1.55/1.77 inference(avatar_split_clause,[status(thm)],[f168,f148,f172])).
% 1.55/1.77 thf(f168,plain,(
% 1.55/1.77 ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar)) | ((sP0 @ nat @ natStar) = $true)),
% 1.55/1.77 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.55/1.77 thf(f159,plain,(
% 1.55/1.77 ((sP0 @ nat @ natStar) = $true) | ((sK5 @ nat @ natStar) = (sK4 @ nat @ natStar)) | ($true != $true)),
% 1.55/1.77 inference(superposition,[status(thm)],[f58,f68])).
% 1.55/1.77 thf(f68,plain,(
% 1.55/1.77 ( ! [X1 : $tType,X0 : X1 > X1 > $o] : (((X0 @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) = $true) | ($true = (sP0 @ X1 @ X0))) )),
% 1.55/1.77 inference(cnf_transformation,[status(thm)],[f52])).
% 1.55/1.77 % SZS output end Proof for DTF2THF_7357
% 1.55/1.77 % (7509)------------------------------
% 1.55/1.77 % (7509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.77 % (7509)Termination reason: Refutation
% 1.55/1.77
% 1.55/1.77 % (7509)Memory used [KB]: 6268
% 1.55/1.77 % (7509)Time elapsed: 0.086 s
% 1.55/1.77 % (7509)Instructions burned: 187 (million)
% 1.55/1.77 % (7509)------------------------------
% 1.55/1.77 % (7509)------------------------------
% 1.55/1.77 % (7461)Success in time 0.509 s
%------------------------------------------------------------------------------