%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT344^1 : 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 : n025.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 08:45:31 AM UTC 2026
% Result : Theorem 1.48s 1.47s
% Output : Refutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT344^1 : 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
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 06:15:27 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : DAT344^1 : TPTP v9.2.1. Released v9.2.0.
% 0.15/0.42 % Domain : Data Structures
% 0.15/0.42 % Problem : Nil is a right-neutral element of app polymorphic, step case
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English : Nil is a right-neutral element of app for polymorphic fixed-length
% 0.15/0.42 % lists. The proof is by induction with a separate problem file for
% 0.15/0.42 % the base and step case as well as the correct instantiation of the
% 0.15/0.42 % induction axiom for lists. The main file uses the conjectures of
% 0.15/0.42 % the other files as lemmas in order to prove the final result. To
% 0.15/0.42 % simplify proof search, the lemmas in the problem file for the
% 0.15/0.42 % induction step have been preselected.
% 0.15/0.42
% 0.15/0.42 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.15/0.42 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.15/0.42 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.15/0.42 % Source : [Rot25]
% 0.15/0.42 % Names : ListAppNil/list-app-nil-indstep.p [Rot25]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : ? v9.2.0
% 0.15/0.42 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 0 def)
% 0.15/0.42 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 2 ( 1 avg)
% 0.15/0.42 % Number of connectives : 72 ( 0 ~; 0 |; 0 &; 71 @)
% 0.15/0.42 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 7 ( 5 avg)
% 0.15/0.42 % Number of types : 1 ( 1 usr)
% 0.15/0.42 % Number of type decls : 8 ( 3 !>P; 2 !>D)
% 0.15/0.42 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 8 ( 7 usr; 1 con; 0-5 aty)
% 0.15/0.42 % Number of variables : 19 ( 0 ^; 13 !; 0 ?; 19 :)
% 0.15/0.42 % ( 6 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.42 % SPC : DH1_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments :
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(nat_type,type,
% 0.15/0.42 nat: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(zero_type,type,
% 0.15/0.42 zero: nat ).
% 0.15/0.42
% 0.15/0.42 thf(suc_type,type,
% 0.15/0.42 suc: nat > nat ).
% 0.15/0.42
% 0.15/0.42 thf(plus_type,type,
% 0.15/0.42 plus: nat > nat > nat ).
% 0.15/0.42
% 0.15/0.42 thf(list_type,type,
% 0.15/0.42 list: $tType > nat > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(nil_type,type,
% 0.15/0.42 nil:
% 0.15/0.42 !>[A: $tType] : ( list @ A @ zero ) ).
% 0.15/0.42
% 0.15/0.42 thf(cons_type,type,
% 0.15/0.42 cons:
% 0.15/0.42 !>[A: $tType,N: nat] : ( A > ( list @ A @ N ) > ( list @ A @ ( suc @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(app_type,type,
% 0.15/0.42 app:
% 0.15/0.42 !>[A: $tType,N: nat,M: nat] : ( ( list @ A @ N ) > ( list @ A @ M ) > ( list @ A @ ( plus @ N @ M ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(ax2,axiom,
% 0.15/0.42 ! [N: nat,M: nat] :
% 0.15/0.42 ( ( plus @ ( suc @ N ) @ M )
% 0.15/0.42 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(ax4,axiom,
% 0.15/0.42 ! [A: $tType,N: nat,M: nat,X: A,Y: list @ A @ N,Z: list @ A @ M] :
% 0.15/0.42 ( ( app @ A @ ( suc @ N ) @ M @ ( cons @ A @ N @ X @ Y ) @ Z )
% 0.15/0.42 = ( cons @ A @ ( plus @ N @ M ) @ X @ ( app @ A @ N @ M @ Y @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(plus_zero_r,axiom,
% 0.15/0.42 ! [M: nat] :
% 0.15/0.42 ( ( plus @ M @ zero )
% 0.15/0.42 = M ) ).
% 0.15/0.42
% 0.15/0.42 thf(list_app_nil_indstep,conjecture,
% 0.15/0.42 ! [A: $tType,N: nat,X: A,L: list @ A @ N] :
% 0.15/0.42 ( ( ( app @ A @ N @ zero @ L @ ( nil @ A ) )
% 0.15/0.42 = L )
% 0.15/0.42 => ( ( app @ A @ ( suc @ N ) @ zero @ ( cons @ A @ N @ X @ L ) @ ( nil @ A ) )
% 0.15/0.42 = ( cons @ A @ N @ X @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.39/1.17 ---- Embedded in THF ---
% 1.39/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.17 %%% Generated on Tue Feb 24 06:15:28 EST 2026
% 1.39/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.17 %%% Logic specification used:
% 1.39/1.17 %%% thf(spec, logic, $$dhol).
% 1.39/1.17
% 1.39/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2DTF29423.p
% 1.39/1.17 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.39/1.17 thf(is_per, definition, (! [A:$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)))))))))).
% 1.39/1.17 thf(nat_type, type, nat: $tType).
% 1.39/1.17 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.39/1.17 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.39/1.17 thf(zero_type, type, zero: nat).
% 1.39/1.17 thf(suc_type, type, suc: (nat > nat)).
% 1.39/1.17 thf(plus_type, type, plus: (nat > (nat > nat))).
% 1.39/1.17 thf(list_type, type, list: ($tType > $tType)).
% 1.39/1.17 thf(listStar, type, 'listStar': (!> [A:$tType]: (((A > (A > $o)) > (nat > ((list @ A) > ((list @ A) > $o))))))).
% 1.39/1.17 thf('\'listStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:nat]: (((isPer @ (list @ B)) @ (((listStar @ B) @ BStar) @ C)))))))).
% 1.39/1.17 thf(nil_type, type, nil: (!> [A:$tType]: ((list @ A)))).
% 1.39/1.17 thf(nil_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (((((listStar @ A) @ AStar) @ zero) @ (nil @ A)) @ (nil @ A)))))).
% 1.39/1.17 thf(cons_type, type, cons: (!> [A:$tType]: ((nat > (A > ((list @ A) > (list @ A))))))).
% 1.39/1.17 thf(cons_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:A,D_prime:A]: (((D = D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ (suc @ N)) @ ((((cons @ A) @ N) @ D) @ D0)) @ ((((cons @ A) @ N) @ D_prime) @ D0_prime)))))))))))))).
% 1.39/1.17 thf(app_type, type, app: (!> [A:$tType]: ((nat > (nat > ((list @ A) > ((list @ A) > (list @ A)))))))).
% 1.39/1.17 thf(app_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [D:(list @ A),D_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ D) @ D_prime) => (! [D0:(list @ A),D0_prime:(list @ A)]: (((((((listStar @ A) @ AStar) @ M) @ D0) @ D0_prime) => (((((listStar @ A) @ AStar) @ ((plus @ N) @ M)) @ (((((app @ A) @ N) @ M) @ D) @ D0)) @ (((((app @ A) @ N) @ M) @ D_prime) @ D0_prime)))))))))))))))).
% 1.39/1.17 thf(ax2, axiom, (! [N:nat]: ((! [M:nat]: ((((plus @ (suc @ N)) @ M) = (suc @ ((plus @ N) @ M)))))))).
% 1.39/1.17 thf(ax4, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [M:nat]: ((! [X:A]: ((! [Y:(list @ A),Z:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ Y) @ Y) => ((((((listStar @ A) @ AStar) @ M) @ Z) @ Z) => (((((listStar @ A) @ AStar) @ ((plus @ (suc @ N)) @ M)) @ (((((app @ A) @ (suc @ N)) @ M) @ ((((cons @ A) @ N) @ X) @ Y)) @ Z)) @ ((((cons @ A) @ ((plus @ N) @ M)) @ X) @ (((((app @ A) @ N) @ M) @ Y) @ Z))))))))))))))))).
% 1.39/1.17 thf(plus_zero_r, axiom, (! [M:nat]: ((((plus @ M) @ zero) = M)))).
% 1.39/1.17 thf(list_app_nil_indstep, conjecture, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [X:A]: ((! [L:(list @ A)]: (((((((listStar @ A) @ AStar) @ N) @ L) @ L) => ((((((listStar @ A) @ AStar) @ ((plus @ N) @ zero)) @ (((((app @ A) @ N) @ zero) @ L) @ (nil @ A))) @ L) => (((((listStar @ A) @ AStar) @ ((plus @ (suc @ N)) @ zero)) @ (((((app @ A) @ (suc @ N)) @ zero) @ ((((cons @ A) @ N) @ X) @ L)) @ (nil @ A))) @ ((((cons @ A) @ N) @ X) @ L)))))))))))))).
% 1.39/1.17 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2DTF29423.p
% 1.39/1.17 ------------------------
% 1.39/1.18 ---- Cleaned THF ---
% 1.39/1.18 thf(is_per_type,type,
% 1.39/1.18 isPer:
% 1.39/1.18 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.39/1.18
% 1.39/1.18 thf(is_per,definition,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 <=> ( ! [X: A,Y: A] :
% 1.39/1.18 ( ( AStar @ X @ Y )
% 1.39/1.18 => ( AStar @ Y @ X ) )
% 1.39/1.18 & ! [X: A,Y: A,Z: A] :
% 1.39/1.18 ( ( AStar @ X @ Y )
% 1.39/1.18 => ( ( AStar @ Y @ Z )
% 1.39/1.18 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(nat_type,type,
% 1.39/1.18 nat: $tType ).
% 1.39/1.18
% 1.39/1.18 thf(natStar,type,
% 1.39/1.18 natStar: nat > nat > $o ).
% 1.39/1.18
% 1.39/1.18 thf(natStar_is_eq,axiom,
% 1.39/1.18 ! [X: nat,Y: nat] :
% 1.39/1.18 ( ( natStar @ X @ Y )
% 1.39/1.18 <=> ( X = Y ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(zero_type,type,
% 1.39/1.18 zero: nat ).
% 1.39/1.18
% 1.39/1.18 thf(suc_type,type,
% 1.39/1.18 suc: nat > nat ).
% 1.39/1.18
% 1.39/1.18 thf(plus_type,type,
% 1.39/1.18 plus: nat > nat > nat ).
% 1.39/1.18
% 1.39/1.18 thf(list_type,type,
% 1.39/1.18 list: $tType > $tType ).
% 1.39/1.18
% 1.39/1.18 thf(listStar,type,
% 1.39/1.18 listStar:
% 1.39/1.18 !>[A: $tType] : ( ( A > A > $o ) > nat > ( list @ A ) > ( list @ A ) > $o ) ).
% 1.39/1.18
% 1.39/1.18 thf('\'listStar\'_is_per',axiom,
% 1.39/1.18 ! [B: $tType,BStar: B > B > $o] :
% 1.39/1.18 ( ( isPer @ B @ BStar )
% 1.39/1.18 => ! [C: nat] : ( isPer @ ( list @ B ) @ ( listStar @ B @ BStar @ C ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(nil_type,type,
% 1.39/1.18 nil:
% 1.39/1.18 !>[A: $tType] : ( list @ A ) ).
% 1.39/1.18
% 1.39/1.18 thf(nil_tp_ax,axiom,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 => ( listStar @ A @ AStar @ zero @ ( nil @ A ) @ ( nil @ A ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(cons_type,type,
% 1.39/1.18 cons:
% 1.39/1.18 !>[A: $tType] : ( nat > A > ( list @ A ) > ( list @ A ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(cons_tp_ax,axiom,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 => ! [N: nat,D: A,D_prime: A] :
% 1.39/1.18 ( ( D = D_prime )
% 1.39/1.18 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.39/1.18 ( ( listStar @ A @ AStar @ N @ D0 @ D0_prime )
% 1.39/1.18 => ( listStar @ A @ AStar @ ( suc @ N ) @ ( cons @ A @ N @ D @ D0 ) @ ( cons @ A @ N @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(app_type,type,
% 1.39/1.18 app:
% 1.39/1.18 !>[A: $tType] : ( nat > nat > ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(app_tp_ax,axiom,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 => ! [N: nat,M: nat,D: list @ A,D_prime: list @ A] :
% 1.39/1.18 ( ( listStar @ A @ AStar @ N @ D @ D_prime )
% 1.39/1.18 => ! [D0: list @ A,D0_prime: list @ A] :
% 1.39/1.18 ( ( listStar @ A @ AStar @ M @ D0 @ D0_prime )
% 1.39/1.18 => ( listStar @ A @ AStar @ ( plus @ N @ M ) @ ( app @ A @ N @ M @ D @ D0 ) @ ( app @ A @ N @ M @ D_prime @ D0_prime ) ) ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(ax2,axiom,
% 1.39/1.18 ! [N: nat,M: nat] :
% 1.39/1.18 ( ( plus @ ( suc @ N ) @ M )
% 1.39/1.18 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(ax4,axiom,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 => ! [N: nat,M: nat,X: A,Y: list @ A,Z: list @ A] :
% 1.39/1.18 ( ( listStar @ A @ AStar @ N @ Y @ Y )
% 1.39/1.18 => ( ( listStar @ A @ AStar @ M @ Z @ Z )
% 1.39/1.18 => ( listStar @ A @ AStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ A @ ( suc @ N ) @ M @ ( cons @ A @ N @ X @ Y ) @ Z ) @ ( cons @ A @ ( plus @ N @ M ) @ X @ ( app @ A @ N @ M @ Y @ Z ) ) ) ) ) ) ).
% 1.39/1.18
% 1.39/1.18 thf(plus_zero_r,axiom,
% 1.39/1.18 ! [M: nat] :
% 1.39/1.18 ( ( plus @ M @ zero )
% 1.39/1.18 = M ) ).
% 1.39/1.18
% 1.39/1.18 thf(list_app_nil_indstep,conjecture,
% 1.39/1.18 ! [A: $tType,AStar: A > A > $o] :
% 1.39/1.18 ( ( isPer @ A @ AStar )
% 1.39/1.18 => ! [N: nat,X: A,L: list @ A] :
% 1.39/1.18 ( ( listStar @ A @ AStar @ N @ L @ L )
% 1.39/1.18 => ( ( listStar @ A @ AStar @ ( plus @ N @ zero ) @ ( app @ A @ N @ zero @ L @ ( nil @ A ) ) @ L )
% 1.39/1.18 => ( listStar @ A @ AStar @ ( plus @ ( suc @ N ) @ zero ) @ ( app @ A @ ( suc @ N ) @ zero @ ( cons @ A @ N @ X @ L ) @ ( nil @ A ) ) @ ( cons @ A @ N @ X @ L ) ) ) ) ) ).
% 1.39/1.18 ------------------------
% 1.39/1.19 % (29522)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/183Mi)
% 1.48/1.20 % (29524)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_29423 for (2999ds/27Mi)
% 1.48/1.20 % (29525)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/2Mi)
% 1.48/1.20 % (29527)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_29423 for (2999ds/275Mi)
% 1.48/1.20 % (29526)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_29423 for (2999ds/2Mi)
% 1.48/1.20 % (29528)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/18Mi)
% 1.48/1.20 % (29525)Instruction limit reached!
% 1.48/1.20 % (29525)------------------------------
% 1.48/1.20 % (29525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.20 % (29525)Termination reason: Unknown
% 1.48/1.20 % (29525)Termination phase: shuffling
% 1.48/1.20
% 1.48/1.20 % (29526)Instruction limit reached!
% 1.48/1.20 % (29526)------------------------------
% 1.48/1.20 % (29526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.20 % (29526)Termination reason: Unknown
% 1.48/1.20 % (29526)Termination phase: shuffling
% 1.48/1.20
% 1.48/1.20 % (29526)Memory used [KB]: 1023
% 1.48/1.20 % (29526)Time elapsed: 0.002 s
% 1.48/1.20 % (29526)Instructions burned: 2 (million)
% 1.48/1.20 % (29526)------------------------------
% 1.48/1.20 % (29526)------------------------------
% 1.48/1.20 % (29525)Memory used [KB]: 1023
% 1.48/1.20 % (29525)Time elapsed: 0.002 s
% 1.48/1.20 % (29525)Instructions burned: 2 (million)
% 1.48/1.20 % (29525)------------------------------
% 1.48/1.20 % (29525)------------------------------
% 1.48/1.20 % (29523)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_29423 for (2999ds/4Mi)
% 1.48/1.20 % (29523)Instruction limit reached!
% 1.48/1.20 % (29523)------------------------------
% 1.48/1.20 % (29523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.20 % (29523)Termination reason: Unknown
% 1.48/1.20 % (29523)Termination phase: Property scanning
% 1.48/1.20
% 1.48/1.20 % (29523)Memory used [KB]: 1023
% 1.48/1.20 % (29523)Time elapsed: 0.003 s
% 1.48/1.20 % (29523)Instructions burned: 4 (million)
% 1.48/1.20 % (29523)------------------------------
% 1.48/1.20 % (29523)------------------------------
% 1.48/1.21 % (29528)Instruction limit reached!
% 1.48/1.21 % (29528)------------------------------
% 1.48/1.21 % (29528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (29528)Termination reason: Unknown
% 1.48/1.21 % (29528)Termination phase: Saturation
% 1.48/1.21
% 1.48/1.21 % (29528)Memory used [KB]: 5628
% 1.48/1.21 % (29528)Time elapsed: 0.011 s
% 1.48/1.21 % (29528)Instructions burned: 19 (million)
% 1.48/1.21 % (29528)------------------------------
% 1.48/1.21 % (29528)------------------------------
% 1.48/1.21 % (29524)Instruction limit reached!
% 1.48/1.21 % (29524)------------------------------
% 1.48/1.21 % (29524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (29524)Termination reason: Unknown
% 1.48/1.21 % (29524)Termination phase: Saturation
% 1.48/1.21
% 1.48/1.21 % (29524)Memory used [KB]: 5756
% 1.48/1.21 % (29524)Time elapsed: 0.016 s
% 1.48/1.21 % (29524)Instructions burned: 27 (million)
% 1.48/1.21 % (29524)------------------------------
% 1.48/1.21 % (29524)------------------------------
% 1.48/1.22 % (29529)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/3Mi)
% 1.48/1.22 % (29530)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_29423 for (2999ds/37Mi)
% 1.48/1.22 % (29529)Instruction limit reached!
% 1.48/1.22 % (29529)------------------------------
% 1.48/1.22 % (29529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.22 % (29529)Termination reason: Unknown
% 1.48/1.22 % (29529)Termination phase: Preprocessing 3
% 1.48/1.22
% 1.48/1.22 % (29529)Memory used [KB]: 1023
% 1.48/1.22 % (29529)Time elapsed: 0.003 s
% 1.48/1.22 % (29529)Instructions burned: 4 (million)
% 1.48/1.22 % (29529)------------------------------
% 1.48/1.22 % (29529)------------------------------
% 1.48/1.22 % Exception at run slice level
% 1.48/1.22 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.22 % (29531)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_29423 for (2999ds/15Mi)
% 1.48/1.22 % (29532)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_29423 for (2999ds/3Mi)
% 1.48/1.23 % (29532)Instruction limit reached!
% 1.48/1.23 % (29532)------------------------------
% 1.48/1.23 % (29532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (29532)Termination reason: Unknown
% 1.48/1.23 % (29532)Termination phase: Preprocessing 2
% 1.48/1.23
% 1.48/1.23 % (29532)Memory used [KB]: 1023
% 1.48/1.23 % (29532)Time elapsed: 0.003 s
% 1.48/1.23 % (29532)Instructions burned: 4 (million)
% 1.48/1.23 % (29532)------------------------------
% 1.48/1.23 % (29532)------------------------------
% 1.48/1.23 % (29531)Instruction limit reached!
% 1.48/1.23 % (29531)------------------------------
% 1.48/1.23 % (29531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (29531)Termination reason: Unknown
% 1.48/1.23 % (29531)Termination phase: Saturation
% 1.48/1.23
% 1.48/1.23 % (29531)Memory used [KB]: 5756
% 1.48/1.23 % (29531)Time elapsed: 0.009 s
% 1.48/1.23 % (29531)Instructions burned: 16 (million)
% 1.48/1.23 % (29531)------------------------------
% 1.48/1.23 % (29531)------------------------------
% 1.48/1.23 % (29533)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_29423 for (2999ds/1041Mi)
% 1.48/1.23 % Exception at run slice level
% 1.48/1.23 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.23 % (29534)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/7Mi)
% 1.48/1.23 % (29535)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/16Mi)
% 1.48/1.24 % (29534)Instruction limit reached!
% 1.48/1.24 % (29534)------------------------------
% 1.48/1.24 % (29534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (29534)Termination reason: Unknown
% 1.48/1.24 % (29534)Termination phase: Property scanning
% 1.48/1.24
% 1.48/1.24 % (29534)Memory used [KB]: 1023
% 1.48/1.24 % (29534)Time elapsed: 0.005 s
% 1.48/1.24 % (29534)Instructions burned: 7 (million)
% 1.48/1.24 % (29534)------------------------------
% 1.48/1.24 % (29534)------------------------------
% 1.48/1.24 % (29536)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_29423 for (2999ds/3Mi)
% 1.48/1.24 % (29535)Instruction limit reached!
% 1.48/1.24 % (29535)------------------------------
% 1.48/1.24 % (29535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (29535)Termination reason: Unknown
% 1.48/1.24 % (29535)Termination phase: Saturation
% 1.48/1.24
% 1.48/1.24 % (29535)Memory used [KB]: 5756
% 1.48/1.24 % (29535)Time elapsed: 0.009 s
% 1.48/1.24 % (29535)Instructions burned: 16 (million)
% 1.48/1.24 % (29535)------------------------------
% 1.48/1.24 % (29535)------------------------------
% 1.48/1.24 % (29537)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_29423 for (2999ds/3Mi)
% 1.48/1.24 % (29536)Instruction limit reached!
% 1.48/1.24 % (29536)------------------------------
% 1.48/1.24 % (29536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (29536)Termination reason: Unknown
% 1.48/1.24 % (29536)Termination phase: Preprocessing 1
% 1.48/1.24
% 1.48/1.24 % (29536)Memory used [KB]: 1023
% 1.48/1.24 % (29536)Time elapsed: 0.003 s
% 1.48/1.24 % (29536)Instructions burned: 4 (million)
% 1.48/1.24 % (29536)------------------------------
% 1.48/1.24 % (29536)------------------------------
% 1.48/1.25 % (29537)Instruction limit reached!
% 1.48/1.25 % (29537)------------------------------
% 1.48/1.25 % (29537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (29537)Termination reason: Unknown
% 1.48/1.25 % (29537)Termination phase: shuffling
% 1.48/1.25
% 1.48/1.25 % (29537)Memory used [KB]: 1023
% 1.48/1.25 % (29537)Time elapsed: 0.003 s
% 1.48/1.25 % (29537)Instructions burned: 4 (million)
% 1.48/1.25 % (29537)------------------------------
% 1.48/1.25 % (29537)------------------------------
% 1.48/1.25 % (29538)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/7Mi)
% 1.48/1.25 % (29522)Instruction limit reached!
% 1.48/1.25 % (29522)------------------------------
% 1.48/1.25 % (29522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (29522)Termination reason: Unknown
% 1.48/1.25 % (29522)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (29522)Memory used [KB]: 7036
% 1.48/1.25 % (29522)Time elapsed: 0.056 s
% 1.48/1.25 % (29522)Instructions burned: 183 (million)
% 1.48/1.25 % (29522)------------------------------
% 1.48/1.25 % (29522)------------------------------
% 1.48/1.25 % (29538)Instruction limit reached!
% 1.48/1.25 % (29538)------------------------------
% 1.48/1.25 % (29538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (29538)Termination reason: Unknown
% 1.48/1.25 % (29538)Termination phase: Equality resolution with deletion
% 1.48/1.25
% 1.48/1.25 % (29538)Memory used [KB]: 1023
% 1.48/1.25 % (29538)Time elapsed: 0.004 s
% 1.48/1.25 % (29538)Instructions burned: 7 (million)
% 1.48/1.25 % (29538)------------------------------
% 1.48/1.25 % (29538)------------------------------
% 1.48/1.25 % (29539)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/3Mi)
% 1.48/1.25 % (29539)Instruction limit reached!
% 1.48/1.25 % (29539)------------------------------
% 1.48/1.25 % (29539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (29539)Termination reason: Unknown
% 1.48/1.25 % (29539)Termination phase: shuffling
% 1.48/1.25
% 1.48/1.25 % (29539)Memory used [KB]: 1023
% 1.48/1.25 % (29539)Time elapsed: 0.003 s
% 1.48/1.25 % (29539)Instructions burned: 3 (million)
% 1.48/1.25 % (29539)------------------------------
% 1.48/1.25 % (29539)------------------------------
% 1.48/1.26 % (29543)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/6Mi)
% 1.48/1.26 % (29540)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/4Mi)
% 1.48/1.26 % (29543)Instruction limit reached!
% 1.48/1.26 % (29543)------------------------------
% 1.48/1.26 % (29543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (29543)Termination reason: Unknown
% 1.48/1.26 % (29543)Termination phase: Property scanning
% 1.48/1.26
% 1.48/1.26 % (29543)Memory used [KB]: 1023
% 1.48/1.26 % (29543)Time elapsed: 0.003 s
% 1.48/1.26 % (29543)Instructions burned: 7 (million)
% 1.48/1.26 % (29543)------------------------------
% 1.48/1.26 % (29543)------------------------------
% 1.48/1.26 % (29541)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/18Mi)
% 1.48/1.26 % (29540)Instruction limit reached!
% 1.48/1.26 % (29540)------------------------------
% 1.48/1.26 % (29540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (29540)Termination reason: Unknown
% 1.48/1.26 % (29540)Termination phase: Naming
% 1.48/1.26
% 1.48/1.26 % (29540)Memory used [KB]: 1023
% 1.48/1.26 % (29540)Time elapsed: 0.003 s
% 1.48/1.26 % (29540)Instructions burned: 4 (million)
% 1.48/1.26 % (29540)------------------------------
% 1.48/1.26 % (29540)------------------------------
% 1.48/1.26 % (29542)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/710Mi)
% 1.48/1.26 % (29544)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_29423 for (2999ds/902Mi)
% 1.48/1.27 % (29541)Instruction limit reached!
% 1.48/1.27 % (29541)------------------------------
% 1.48/1.27 % (29541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (29541)Termination reason: Unknown
% 1.48/1.27 % (29541)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (29541)Memory used [KB]: 5628
% 1.48/1.27 % (29541)Time elapsed: 0.010 s
% 1.48/1.27 % (29541)Instructions burned: 18 (million)
% 1.48/1.27 % (29541)------------------------------
% 1.48/1.27 % (29541)------------------------------
% 1.48/1.27 % (29546)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/5Mi)
% 1.48/1.27 % (29545)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_29423 for (2999ds/21Mi)
% 1.48/1.27 % Exception at run slice level
% 1.48/1.27 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.28 % (29547)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_29423 for (2999ds/6Mi)
% 1.48/1.28 % Exception at run slice level
% 1.48/1.28 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.28 % (29545)Instruction limit reached!
% 1.48/1.28 % (29545)------------------------------
% 1.48/1.28 % (29545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (29545)Termination reason: Unknown
% 1.48/1.28 % (29545)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (29545)Memory used [KB]: 5756
% 1.48/1.28 % (29545)Time elapsed: 0.013 s
% 1.48/1.28 % (29545)Instructions burned: 22 (million)
% 1.48/1.28 % (29545)------------------------------
% 1.48/1.28 % (29545)------------------------------
% 1.48/1.28 % (29548)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/377Mi)
% 1.48/1.28 % (29549)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_29423 for (2999ds/779Mi)
% 1.48/1.29 % Exception at run slice level
% 1.48/1.29 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.29 % (29550)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_29423 for (2999ds/19Mi)
% 1.48/1.29 % Exception at run slice level
% 1.48/1.29 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.30 % (29551)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29423 for (2999ds/879Mi)
% 1.48/1.30 % (29552)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29423 for (2998ds/17Mi)
% 1.48/1.31 % (29527)Instruction limit reached!
% 1.48/1.31 % (29527)------------------------------
% 1.48/1.31 % (29527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.31 % (29527)Termination reason: Unknown
% 1.48/1.31 % (29527)Termination phase: Saturation
% 1.48/1.31
% 1.48/1.31 % (29527)Memory used [KB]: 5884
% 1.48/1.31 % (29527)Time elapsed: 0.112 s
% 1.48/1.31 % (29527)Instructions burned: 276 (million)
% 1.48/1.31 % (29527)------------------------------
% 1.48/1.31 % (29527)------------------------------
% 1.48/1.31 % (29552)Instruction limit reached!
% 1.48/1.31 % (29552)------------------------------
% 1.48/1.31 % (29552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.31 % (29552)Termination reason: Unknown
% 1.48/1.31 % (29552)Termination phase: Saturation
% 1.48/1.31
% 1.48/1.31 % (29552)Memory used [KB]: 5756
% 1.48/1.31 % (29552)Time elapsed: 0.010 s
% 1.48/1.31 % (29552)Instructions burned: 17 (million)
% 1.48/1.31 % (29552)------------------------------
% 1.48/1.31 % (29552)------------------------------
% 1.48/1.31 % (29553)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29423 for (2998ds/3Mi)
% 1.48/1.31 % (29553)Instruction limit reached!
% 1.48/1.31 % (29553)------------------------------
% 1.48/1.31 % (29553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.31 % (29553)Termination reason: Unknown
% 1.48/1.31 % (29553)Termination phase: Preprocessing 1
% 1.48/1.31
% 1.48/1.31 % (29553)Memory used [KB]: 1023
% 1.48/1.31 % (29553)Time elapsed: 0.003 s
% 1.48/1.31 % (29553)Instructions burned: 4 (million)
% 1.48/1.31 % (29553)------------------------------
% 1.48/1.31 % (29553)------------------------------
% 1.48/1.33 % (29554)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29423 for (2998ds/30Mi)
% 1.48/1.33 % (29555)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29423 for (2998ds/127Mi)
% 1.48/1.33 % (29556)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29423 for (2998ds/100Mi)
% 1.48/1.34 % (29554)Instruction limit reached!
% 1.48/1.34 % (29554)------------------------------
% 1.48/1.34 % (29554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.34 % (29554)Termination reason: Unknown
% 1.48/1.34 % (29554)Termination phase: Saturation
% 1.48/1.34
% 1.48/1.34 % (29554)Memory used [KB]: 5756
% 1.48/1.34 % (29554)Time elapsed: 0.016 s
% 1.48/1.34 % (29554)Instructions burned: 30 (million)
% 1.48/1.34 % (29554)------------------------------
% 1.48/1.34 % (29554)------------------------------
% 1.48/1.36 % (29557)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_29423 for (2998ds/3Mi)
% 1.48/1.36 % Exception at run slice level
% 1.48/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.37 % (29558)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_29423 for (2998ds/20Mi)
% 1.48/1.38 % (29556)Instruction limit reached!
% 1.48/1.38 % (29556)------------------------------
% 1.48/1.38 % (29556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (29556)Termination reason: Unknown
% 1.48/1.38 % (29556)Termination phase: Saturation
% 1.48/1.38
% 1.48/1.38 % (29556)Memory used [KB]: 6140
% 1.48/1.38 % (29556)Time elapsed: 0.050 s
% 1.48/1.38 % (29556)Instructions burned: 100 (million)
% 1.48/1.38 % (29556)------------------------------
% 1.48/1.38 % (29556)------------------------------
% 1.48/1.38 % (29558)Instruction limit reached!
% 1.48/1.38 % (29558)------------------------------
% 1.48/1.38 % (29558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (29558)Termination reason: Unknown
% 1.48/1.38 % (29558)Termination phase: Saturation
% 1.48/1.38
% 1.48/1.38 % (29558)Memory used [KB]: 5628
% 1.48/1.38 % (29558)Time elapsed: 0.011 s
% 1.48/1.38 % (29558)Instructions burned: 20 (million)
% 1.48/1.38 % (29558)------------------------------
% 1.48/1.38 % (29558)------------------------------
% 1.48/1.38 % (29555)Instruction limit reached!
% 1.48/1.38 % (29555)------------------------------
% 1.48/1.38 % (29555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (29555)Termination reason: Unknown
% 1.48/1.38 % (29555)Termination phase: Saturation
% 1.48/1.38
% 1.48/1.38 % (29555)Memory used [KB]: 6140
% 1.48/1.38 % (29555)Time elapsed: 0.059 s
% 1.48/1.38 % (29555)Instructions burned: 127 (million)
% 1.48/1.38 % (29555)------------------------------
% 1.48/1.38 % (29555)------------------------------
% 1.48/1.39 % (29559)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_29423 for (2998ds/86Mi)
% 1.48/1.39 % (29561)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_29423 for (2998ds/39Mi)
% 1.48/1.40 % Exception at run slice level
% 1.48/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.40 % (29560)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_29423 for (2998ds/107Mi)
% 1.48/1.42 % (29562)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_29423 for (2997ds/448Mi)
% 1.48/1.42 % Exception at run slice level
% 1.48/1.42 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.43 % (29563)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_29423 for (2997ds/46Mi)
% 1.48/1.44 % (29559)Instruction limit reached!
% 1.48/1.44 % (29559)------------------------------
% 1.48/1.44 % (29559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.44 % (29559)Termination reason: Unknown
% 1.48/1.44 % (29559)Termination phase: Saturation
% 1.48/1.44
% 1.48/1.44 % (29559)Memory used [KB]: 6268
% 1.48/1.44 % (29559)Time elapsed: 0.043 s
% 1.48/1.44 % (29559)Instructions burned: 87 (million)
% 1.48/1.44 % (29559)------------------------------
% 1.48/1.44 % (29559)------------------------------
% 1.48/1.44 % (29560)Instruction limit reached!
% 1.48/1.44 % (29560)------------------------------
% 1.48/1.44 % (29560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.44 % (29560)Termination reason: Unknown
% 1.48/1.44 % (29560)Termination phase: Saturation
% 1.48/1.44
% 1.48/1.44 % (29560)Memory used [KB]: 6268
% 1.48/1.44 % (29560)Time elapsed: 0.058 s
% 1.48/1.44 % (29560)Instructions burned: 107 (million)
% 1.48/1.44 % (29560)------------------------------
% 1.48/1.44 % (29560)------------------------------
% 1.48/1.45 % (29564)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_29423 for (2997ds/98Mi)
% 1.48/1.45 % (29565)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_29423 for (2997ds/507Mi)
% 1.48/1.45 % Exception at run slice level
% 1.48/1.45 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.48/1.46 % (29563)Instruction limit reached!
% 1.48/1.46 % (29563)------------------------------
% 1.48/1.46 % (29563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.46 % (29563)Termination reason: Unknown
% 1.48/1.46 % (29563)Termination phase: Saturation
% 1.48/1.46
% 1.48/1.46 % (29563)Memory used [KB]: 5884
% 1.48/1.46 % (29563)Time elapsed: 0.024 s
% 1.48/1.46 % (29563)Instructions burned: 47 (million)
% 1.48/1.46 % (29563)------------------------------
% 1.48/1.46 % (29563)------------------------------
% 1.48/1.46 % (29548)Instruction limit reached!
% 1.48/1.46 % (29548)------------------------------
% 1.48/1.46 % (29548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.46 % (29548)Termination reason: Unknown
% 1.48/1.46 % (29548)Termination phase: Saturation
% 1.48/1.46
% 1.48/1.46 % (29548)Memory used [KB]: 6268
% 1.48/1.46 % (29548)Time elapsed: 0.181 s
% 1.48/1.46 % (29548)Instructions burned: 378 (million)
% 1.48/1.46 % (29548)------------------------------
% 1.48/1.46 % (29548)------------------------------
% 1.48/1.47 % (29566)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_29423 for (2997ds/149Mi)
% 1.48/1.47 % (29565)First to succeed.
% 1.48/1.47 % (29567)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29423 for (2997ds/39Mi)
% 1.48/1.47 % (29565)Refutation found. Thanks to Tanya!
% 1.48/1.47 % SZS status Theorem for DTF2THF_29423
% 1.48/1.47 % SZS output start Proof for DTF2THF_29423
% 1.48/1.47 thf(type_def_6, type, nat: $tType).
% 1.48/1.47 thf(type_def_7, type, list: ($tType) > $tType).
% 1.48/1.47 thf(type_def_8, type, sK2: $tType).
% 1.48/1.47 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.48/1.47 thf(func_def_2, type, nat: $tType).
% 1.48/1.47 thf(func_def_3, type, natStar: nat > nat > $o).
% 1.48/1.47 thf(func_def_4, type, zero: nat).
% 1.48/1.47 thf(func_def_5, type, suc: nat > nat).
% 1.48/1.47 thf(func_def_6, type, plus: nat > nat > nat).
% 1.48/1.47 thf(func_def_7, type, list: ($tType) > $tType).
% 1.48/1.47 thf(func_def_8, type, listStar: !>[X0: $tType]:((X0 > X0 > $o) > nat > list @ X0 > list @ X0 > $o)).
% 1.48/1.47 thf(func_def_9, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.48/1.47 thf(func_def_10, type, cons: !>[X0: $tType]:(nat > X0 > list @ X0 > list @ X0)).
% 1.48/1.47 thf(func_def_11, type, app: !>[X0: $tType]:(nat > nat > list @ X0 > list @ X0 > list @ X0)).
% 1.48/1.47 thf(func_def_14, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_15, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_23, type, sK3: sK2 > sK2 > $o).
% 1.48/1.47 thf(func_def_24, type, sK4: nat).
% 1.48/1.47 thf(func_def_25, type, sK5: sK2).
% 1.48/1.47 thf(func_def_26, type, sK6: list @ sK2).
% 1.48/1.47 thf(func_def_27, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_28, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_29, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_30, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_31, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.48/1.47 thf(func_def_33, type, ph13: !>[X0: $tType]:(X0)).
% 1.48/1.47 thf(f253,plain,(
% 1.48/1.47 $false),
% 1.48/1.47 inference(avatar_sat_refutation,[status(thm)],[f108,f119,f183,f191,f251])).
% 1.48/1.47 thf(f251,plain,(
% 1.48/1.47 spl12_6),
% 1.48/1.47 inference(avatar_contradiction_clause,[status(thm)],[f250])).
% 1.48/1.47 thf(f250,plain,(
% 1.48/1.47 $false | spl12_6),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f249,f73])).
% 1.48/1.47 thf(f73,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) = $true)),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f62])).
% 1.48/1.47 thf(f62,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) = $true) & (((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) = $true) & ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true) & ((listStar @ sK2 @ sK3 @ (plus @ sK4 @ zero) @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) = $true))),
% 1.48/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f54,f61,f60])).
% 1.48/1.47 thf(f60,plain,(
% 1.48/1.47 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : nat,X3 : X0,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X4 @ X4) = $true) & ($true != (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ zero) @ (app @ X0 @ (suc @ X2) @ zero @ (cons @ X0 @ X2 @ X3 @ X4) @ nil @ X0) @ (cons @ X0 @ X2 @ X3 @ X4))) & ($true = (listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X4 @ nil @ X0) @ X4)))) => (((isPer @ sK2 @ sK3) = $true) & ? [X4 : list @ sK2,X3 : sK2,X2 : nat] : (((listStar @ sK2 @ sK3 @ X2 @ X4 @ X4) = $true) & ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ X2) @ zero) @ (app @ sK2 @ (suc @ X2) @ zero @ (cons @ sK2 @ X2 @ X3 @ X4) @ nil @ sK2) @ (cons @ sK2 @ X2 @ X3 @ X4))) & ((listStar @ sK2 @ sK3 @ (plus @ X2 @ zero) @ (app @ sK2 @ X2 @ zero @ X4 @ nil @ sK2) @ X4) = $true)))),
% 1.48/1.47 introduced(definition,[],[choice_axiom])).
% 1.48/1.47 thf(f61,plain,(
% 1.48/1.47 ? [X4 : list @ sK2,X3 : sK2,X2 : nat] : (((listStar @ sK2 @ sK3 @ X2 @ X4 @ X4) = $true) & ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ X2) @ zero) @ (app @ sK2 @ (suc @ X2) @ zero @ (cons @ sK2 @ X2 @ X3 @ X4) @ nil @ sK2) @ (cons @ sK2 @ X2 @ X3 @ X4))) & ((listStar @ sK2 @ sK3 @ (plus @ X2 @ zero) @ (app @ sK2 @ X2 @ zero @ X4 @ nil @ sK2) @ X4) = $true)) => (((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) = $true) & ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true) & ((listStar @ sK2 @ sK3 @ (plus @ sK4 @ zero) @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) = $true))),
% 1.48/1.47 introduced(definition,[],[choice_axiom])).
% 1.48/1.47 thf(f54,plain,(
% 1.48/1.47 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : nat,X3 : X0,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X4 @ X4) = $true) & ($true != (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ zero) @ (app @ X0 @ (suc @ X2) @ zero @ (cons @ X0 @ X2 @ X3 @ X4) @ nil @ X0) @ (cons @ X0 @ X2 @ X3 @ X4))) & ($true = (listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X4 @ nil @ X0) @ X4))))),
% 1.48/1.47 inference(flattening,[status(thm)],[f53])).
% 1.48/1.47 thf(f53,plain,(
% 1.48/1.47 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : nat,X3 : X0,X4 : list @ X0] : ((($true != (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ zero) @ (app @ X0 @ (suc @ X2) @ zero @ (cons @ X0 @ X2 @ X3 @ X4) @ nil @ X0) @ (cons @ X0 @ X2 @ X3 @ X4))) & ($true = (listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X4 @ nil @ X0) @ X4))) & ((listStar @ X0 @ X1 @ X2 @ X4 @ X4) = $true)) & ((isPer @ X0 @ X1) = $true))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f30])).
% 1.48/1.47 thf(f30,plain,(
% 1.48/1.47 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : X0,X4 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X4 @ X4) = $true) => (($true = (listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X4 @ nil @ X0) @ X4)) => ($true = (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ zero) @ (app @ X0 @ (suc @ X2) @ zero @ (cons @ X0 @ X2 @ X3 @ X4) @ nil @ X0) @ (cons @ X0 @ X2 @ X3 @ X4))))))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f29])).
% 1.48/1.47 thf(f29,plain,(
% 1.48/1.47 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : X0,X4 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X4 @ X4) => ((listStar @ X0 @ X1 @ (plus @ X2 @ zero) @ (app @ X0 @ X2 @ zero @ X4 @ nil @ X0) @ X4) => (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ zero) @ (app @ X0 @ (suc @ X2) @ zero @ (cons @ X0 @ X2 @ X3 @ X4) @ nil @ X0) @ (cons @ X0 @ X2 @ X3 @ X4)))))),
% 1.48/1.47 inference(rectify,[status(thm)],[f11])).
% 1.48/1.47 thf(f11,negated_conjecture,(
% 1.48/1.47 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X2 : X0,X14 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X14 @ X14) => ((listStar @ X0 @ X1 @ (plus @ X8 @ zero) @ (app @ X0 @ X8 @ zero @ X14 @ nil @ X0) @ X14) => (listStar @ X0 @ X1 @ (plus @ (suc @ X8) @ zero) @ (app @ X0 @ (suc @ X8) @ zero @ (cons @ X0 @ X8 @ X2 @ X14) @ nil @ X0) @ (cons @ X0 @ X8 @ X2 @ X14)))))),
% 1.48/1.47 inference(negated_conjecture,[status(cth)],[f10])).
% 1.48/1.47 thf(f10,conjecture,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X2 : X0,X14 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X14 @ X14) => ((listStar @ X0 @ X1 @ (plus @ X8 @ zero) @ (app @ X0 @ X8 @ zero @ X14 @ nil @ X0) @ X14) => (listStar @ X0 @ X1 @ (plus @ (suc @ X8) @ zero) @ (app @ X0 @ (suc @ X8) @ zero @ (cons @ X0 @ X8 @ X2 @ X14) @ nil @ X0) @ (cons @ X0 @ X8 @ X2 @ X14)))))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',list_app_nil_indstep)).
% 1.48/1.47 thf(f249,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | spl12_6),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f246,f94])).
% 1.48/1.47 thf(f94,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ sK4 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) = $true)),
% 1.48/1.47 inference(superposition,[status(thm)],[f70,f74])).
% 1.48/1.47 thf(f74,plain,(
% 1.48/1.47 ( ! [X0 : nat] : (((plus @ X0 @ zero) = X0)) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f28])).
% 1.48/1.47 thf(f28,plain,(
% 1.48/1.47 ! [X0 : nat] : ((plus @ X0 @ zero) = X0)),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f27])).
% 1.48/1.47 thf(f27,plain,(
% 1.48/1.47 ! [X0 : nat] : ((plus @ X0 @ zero) = X0)),
% 1.48/1.47 inference(rectify,[status(thm)],[f9])).
% 1.48/1.47 thf(f9,axiom,(
% 1.48/1.47 ! [X13 : nat] : ((plus @ X13 @ zero) = X13)),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',plus_zero_r)).
% 1.48/1.47 thf(f70,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ (plus @ sK4 @ zero) @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) = $true)),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f62])).
% 1.48/1.47 thf(f246,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ sK4 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) != $true) | ((isPer @ sK2 @ sK3) != $true) | spl12_6),
% 1.48/1.47 inference(trivial_inequality_removal,[status(thm)],[f242])).
% 1.48/1.47 thf(f242,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | ($true != $true) | ((listStar @ sK2 @ sK3 @ sK4 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2) @ sK6) != $true) | spl12_6),
% 1.48/1.47 inference(superposition,[status(thm)],[f217,f92])).
% 1.48/1.47 thf(f92,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X2 : nat,X1 : X0 > X0 > $o,X6 : list @ X0,X4 : X0,X5 : list @ X0] : (((listStar @ X0 @ X1 @ (suc @ X2) @ (cons @ X0 @ X2 @ X4 @ X5) @ (cons @ X0 @ X2 @ X4 @ X6)) = $true) | ((isPer @ X0 @ X1) != $true) | ((listStar @ X0 @ X1 @ X2 @ X5 @ X6) != $true)) )),
% 1.48/1.47 inference(equality_resolution,[status(thm)],[f86])).
% 1.48/1.47 thf(f86,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X2 : nat,X3 : X0,X1 : X0 > X0 > $o,X6 : list @ X0,X4 : X0,X5 : list @ X0] : (((isPer @ X0 @ X1) != $true) | ((listStar @ X0 @ X1 @ X2 @ X5 @ X6) != $true) | ($true = (listStar @ X0 @ X1 @ (suc @ X2) @ (cons @ X0 @ X2 @ X3 @ X5) @ (cons @ X0 @ X2 @ X4 @ X6))) | (X3 != X4)) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f55])).
% 1.48/1.47 thf(f55,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat,X3 : X0,X4 : X0] : (! [X5 : list @ X0,X6 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X5 @ X6) != $true) | ($true = (listStar @ X0 @ X1 @ (suc @ X2) @ (cons @ X0 @ X2 @ X3 @ X5) @ (cons @ X0 @ X2 @ X4 @ X6)))) | (X3 != X4)))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f14])).
% 1.48/1.47 thf(f14,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : X0,X4 : X0] : ((X3 = X4) => ! [X5 : list @ X0,X6 : list @ X0] : (((listStar @ X0 @ X1 @ X2 @ X5 @ X6) = $true) => ($true = (listStar @ X0 @ X1 @ (suc @ X2) @ (cons @ X0 @ X2 @ X3 @ X5) @ (cons @ X0 @ X2 @ X4 @ X6))))))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f13])).
% 1.48/1.47 thf(f13,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : X0,X4 : X0] : ((X3 = X4) => ! [X5 : list @ X0,X6 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X5 @ X6) => (listStar @ X0 @ X1 @ (suc @ X2) @ (cons @ X0 @ X2 @ X3 @ X5) @ (cons @ X0 @ X2 @ X4 @ X6)))))),
% 1.48/1.47 inference(rectify,[status(thm)],[f5])).
% 1.48/1.47 thf(f5,axiom,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X9 : X0,X10 : X0] : ((X9 = X10) => ! [X11 : list @ X0,X12 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X11 @ X12) => (listStar @ X0 @ X1 @ (suc @ X8) @ (cons @ X0 @ X8 @ X9 @ X11) @ (cons @ X0 @ X8 @ X10 @ X12)))))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',cons_tp_ax)).
% 1.48/1.47 thf(f217,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ (suc @ sK4) @ (cons @ sK2 @ sK4 @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | spl12_6),
% 1.48/1.47 inference(superposition,[status(thm)],[f207,f74])).
% 1.48/1.47 thf(f207,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ sK4 @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | spl12_6),
% 1.48/1.47 inference(superposition,[status(thm)],[f178,f74])).
% 1.48/1.47 thf(f178,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | spl12_6),
% 1.48/1.47 inference(avatar_component_clause,[status(thm)],[f176])).
% 1.48/1.47 thf(f176,definition,(
% 1.48/1.47 spl12_6 <=> ($true = (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6)))),
% 1.48/1.47 introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition])).
% 1.48/1.47 thf(f191,plain,(
% 1.48/1.47 spl12_7),
% 1.48/1.47 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.48/1.47 thf(f190,plain,(
% 1.48/1.47 $false | spl12_7),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f188,f73])).
% 1.48/1.47 thf(f188,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | spl12_7),
% 1.48/1.47 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.48/1.47 thf(f184,plain,(
% 1.48/1.47 ($true != $true) | ((isPer @ sK2 @ sK3) != $true) | spl12_7),
% 1.48/1.47 inference(superposition,[status(thm)],[f182,f84])).
% 1.48/1.47 thf(f84,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((listStar @ X0 @ X1 @ zero @ nil @ X0 @ nil @ X0) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f58])).
% 1.48/1.47 thf(f58,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((listStar @ X0 @ X1 @ zero @ nil @ X0 @ nil @ X0) = $true) | ((isPer @ X0 @ X1) != $true))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f32])).
% 1.48/1.47 thf(f32,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ((listStar @ X0 @ X1 @ zero @ nil @ X0 @ nil @ X0) = $true))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f31])).
% 1.48/1.47 thf(f31,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (listStar @ X0 @ X1 @ zero @ nil @ X0 @ nil @ X0))),
% 1.48/1.47 inference(rectify,[status(thm)],[f4])).
% 1.48/1.47 thf(f4,axiom,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (listStar @ X0 @ X1 @ zero @ nil @ X0 @ nil @ X0))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',nil_tp_ax)).
% 1.48/1.47 thf(f182,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2)) | spl12_7),
% 1.48/1.47 inference(avatar_component_clause,[status(thm)],[f180])).
% 1.48/1.47 thf(f180,definition,(
% 1.48/1.47 spl12_7 <=> ($true = (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2))),
% 1.48/1.47 introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition])).
% 1.48/1.47 thf(f183,plain,(
% 1.48/1.47 ~spl12_6 | ~spl12_7 | ~spl12_1),
% 1.48/1.47 inference(avatar_split_clause,[status(thm)],[f174,f102,f180,f176])).
% 1.48/1.47 thf(f102,definition,(
% 1.48/1.47 spl12_1 <=> ! [X0 : list @ sK2] : (($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ X0)) | ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ X0 @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true))),
% 1.48/1.47 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.48/1.47 thf(f174,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | ($true != (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2)) | ~spl12_1),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f173,f72])).
% 1.48/1.47 thf(f72,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) = $true)),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f62])).
% 1.48/1.47 thf(f173,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) != $true) | ($true != (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2)) | ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | ~spl12_1),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f156,f73])).
% 1.48/1.47 thf(f156,plain,(
% 1.48/1.47 ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | ((isPer @ sK2 @ sK3) != $true) | ($true != (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2)) | ((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) != $true) | ~spl12_1),
% 1.48/1.47 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.48/1.47 thf(f150,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | ($true != $true) | ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (cons @ sK2 @ (plus @ sK4 @ zero) @ sK5 @ (app @ sK2 @ sK4 @ zero @ sK6 @ nil @ sK2)) @ (cons @ sK2 @ sK4 @ sK5 @ sK6))) | ((listStar @ sK2 @ sK3 @ sK4 @ sK6 @ sK6) != $true) | ($true != (listStar @ sK2 @ sK3 @ zero @ nil @ sK2 @ nil @ sK2)) | ~spl12_1),
% 1.48/1.47 inference(superposition,[status(thm)],[f103,f87])).
% 1.48/1.47 thf(f87,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : X0 > X0 > $o,X6 : list @ X0,X4 : X0,X5 : list @ X0] : (((listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ X3) @ (app @ X0 @ (suc @ X2) @ X3 @ (cons @ X0 @ X2 @ X4 @ X5) @ X6) @ (cons @ X0 @ (plus @ X2 @ X3) @ X4 @ (app @ X0 @ X2 @ X3 @ X5 @ X6))) = $true) | ((listStar @ X0 @ X1 @ X3 @ X6 @ X6) != $true) | ((isPer @ X0 @ X1) != $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X5 @ X5))) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f52])).
% 1.48/1.47 thf(f52,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : nat,X4 : X0,X5 : list @ X0,X6 : list @ X0] : (((listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ X3) @ (app @ X0 @ (suc @ X2) @ X3 @ (cons @ X0 @ X2 @ X4 @ X5) @ X6) @ (cons @ X0 @ (plus @ X2 @ X3) @ X4 @ (app @ X0 @ X2 @ X3 @ X5 @ X6))) = $true) | ($true != (listStar @ X0 @ X1 @ X2 @ X5 @ X5)) | ((listStar @ X0 @ X1 @ X3 @ X6 @ X6) != $true)) | ((isPer @ X0 @ X1) != $true))),
% 1.48/1.47 inference(flattening,[status(thm)],[f51])).
% 1.48/1.47 thf(f51,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : nat,X4 : X0,X5 : list @ X0,X6 : list @ X0] : ((((listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ X3) @ (app @ X0 @ (suc @ X2) @ X3 @ (cons @ X0 @ X2 @ X4 @ X5) @ X6) @ (cons @ X0 @ (plus @ X2 @ X3) @ X4 @ (app @ X0 @ X2 @ X3 @ X5 @ X6))) = $true) | ((listStar @ X0 @ X1 @ X3 @ X6 @ X6) != $true)) | ($true != (listStar @ X0 @ X1 @ X2 @ X5 @ X5))) | ((isPer @ X0 @ X1) != $true))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f26])).
% 1.48/1.47 thf(f26,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : nat,X4 : X0,X5 : list @ X0,X6 : list @ X0] : (($true = (listStar @ X0 @ X1 @ X2 @ X5 @ X5)) => (((listStar @ X0 @ X1 @ X3 @ X6 @ X6) = $true) => ((listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ X3) @ (app @ X0 @ (suc @ X2) @ X3 @ (cons @ X0 @ X2 @ X4 @ X5) @ X6) @ (cons @ X0 @ (plus @ X2 @ X3) @ X4 @ (app @ X0 @ X2 @ X3 @ X5 @ X6))) = $true))))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f25])).
% 1.48/1.47 thf(f25,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : nat,X4 : X0,X5 : list @ X0,X6 : list @ X0] : ((listStar @ X0 @ X1 @ X2 @ X5 @ X5) => ((listStar @ X0 @ X1 @ X3 @ X6 @ X6) => (listStar @ X0 @ X1 @ (plus @ (suc @ X2) @ X3) @ (app @ X0 @ (suc @ X2) @ X3 @ (cons @ X0 @ X2 @ X4 @ X5) @ X6) @ (cons @ X0 @ (plus @ X2 @ X3) @ X4 @ (app @ X0 @ X2 @ X3 @ X5 @ X6))))))),
% 1.48/1.47 inference(rectify,[status(thm)],[f8])).
% 1.48/1.47 thf(f8,axiom,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X8 : nat,X13 : nat,X2 : X0,X3 : list @ X0,X4 : list @ X0] : ((listStar @ X0 @ X1 @ X8 @ X3 @ X3) => ((listStar @ X0 @ X1 @ X13 @ X4 @ X4) => (listStar @ X0 @ X1 @ (plus @ (suc @ X8) @ X13) @ (app @ X0 @ (suc @ X8) @ X13 @ (cons @ X0 @ X8 @ X2 @ X3) @ X4) @ (cons @ X0 @ (plus @ X8 @ X13) @ X2 @ (app @ X0 @ X8 @ X13 @ X3 @ X4))))))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',ax4)).
% 1.48/1.47 thf(f103,plain,(
% 1.48/1.47 ( ! [X0 : list @ sK2] : (($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ X0)) | ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ X0 @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true)) ) | ~spl12_1),
% 1.48/1.47 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.48/1.47 thf(f119,plain,(
% 1.48/1.47 spl12_2),
% 1.48/1.47 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.48/1.47 thf(f118,plain,(
% 1.48/1.47 $false | spl12_2),
% 1.48/1.47 inference(subsumption_resolution,[status(thm)],[f117,f73])).
% 1.48/1.47 thf(f117,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | spl12_2),
% 1.48/1.47 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.48/1.47 thf(f116,plain,(
% 1.48/1.47 ((isPer @ sK2 @ sK3) != $true) | ($true != $true) | spl12_2),
% 1.48/1.47 inference(superposition,[status(thm)],[f107,f88])).
% 1.48/1.47 thf(f88,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X2 : nat,X1 : X0 > X0 > $o] : (((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.48/1.47 thf(f50,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f16])).
% 1.48/1.47 thf(f16,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat] : ((isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)) = $true))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f15])).
% 1.48/1.47 thf(f15,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat] : (isPer @ list @ X0 @ (listStar @ X0 @ X1 @ X2)))),
% 1.48/1.47 inference(rectify,[status(thm)],[f3])).
% 1.48/1.47 thf(f3,axiom,(
% 1.48/1.47 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : nat] : (isPer @ list @ X5 @ (listStar @ X5 @ X6 @ X7)))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p','\'listStar\'_is_per')).
% 1.48/1.47 thf(f107,plain,(
% 1.48/1.47 ($true != (isPer @ list @ sK2 @ (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero)))) | spl12_2),
% 1.48/1.47 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.48/1.47 thf(f105,definition,(
% 1.48/1.47 spl12_2 <=> ($true = (isPer @ list @ sK2 @ (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero))))),
% 1.48/1.47 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.48/1.47 thf(f108,plain,(
% 1.48/1.47 spl12_1 | ~spl12_2),
% 1.48/1.47 inference(avatar_split_clause,[status(thm)],[f100,f105,f102])).
% 1.48/1.47 thf(f100,plain,(
% 1.48/1.47 ( ! [X0 : list @ sK2] : (($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ X0)) | ($true != (isPer @ list @ sK2 @ (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero)))) | ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ X0 @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true)) )),
% 1.48/1.47 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.48/1.47 thf(f97,plain,(
% 1.48/1.47 ( ! [X0 : list @ sK2] : (((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ X0 @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true) | ($true != (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ X0)) | ($true != (isPer @ list @ sK2 @ (listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero)))) | ($true != $true)) )),
% 1.48/1.47 inference(superposition,[status(thm)],[f71,f82])).
% 1.48/1.47 thf(f82,plain,(
% 1.48/1.47 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X6 : X0,X4 : X0,X5 : X0] : (((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X4 @ X5)) | ((isPer @ X0 @ X1) != $true) | ($true != (X1 @ X5 @ X6))) )),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f68])).
% 1.48/1.47 thf(f68,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true = (X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1))) & ((X1 @ (sK8 @ X0 @ X1) @ (sK7 @ X0 @ X1)) != $true)) | (((X1 @ (sK10 @ X0 @ X1) @ (sK11 @ X0 @ X1)) = $true) & ((X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1)) = $true) & ($true != (X1 @ (sK9 @ X0 @ X1) @ (sK11 @ X0 @ X1))))))),
% 1.48/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f65,f67,f66])).
% 1.48/1.47 thf(f66,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X8 @ X7))) => (($true = (X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1))) & ((X1 @ (sK8 @ X0 @ X1) @ (sK7 @ X0 @ X1)) != $true)))),
% 1.48/1.47 introduced(definition,[],[choice_axiom])).
% 1.48/1.47 thf(f67,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X9 : X0,X10 : X0,X11 : X0] : (((X1 @ X10 @ X11) = $true) & ($true = (X1 @ X9 @ X10)) & ($true != (X1 @ X9 @ X11))) => (((X1 @ (sK10 @ X0 @ X1) @ (sK11 @ X0 @ X1)) = $true) & ((X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1)) = $true) & ($true != (X1 @ (sK9 @ X0 @ X1) @ (sK11 @ X0 @ X1)))))),
% 1.48/1.47 introduced(definition,[],[choice_axiom])).
% 1.48/1.47 thf(f65,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X8 @ X7))) | ? [X9 : X0,X10 : X0,X11 : X0] : (((X1 @ X10 @ X11) = $true) & ($true = (X1 @ X9 @ X10)) & ($true != (X1 @ X9 @ X11)))))),
% 1.48/1.47 inference(rectify,[status(thm)],[f64])).
% 1.48/1.47 thf(f64,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)) | ? [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ($true = (X1 @ X4 @ X5)) & ((X1 @ X4 @ X6) != $true))))),
% 1.48/1.47 inference(flattening,[status(thm)],[f63])).
% 1.48/1.47 thf(f63,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X3 @ X2) != $true)) | ? [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ($true = (X1 @ X4 @ X5)) & ((X1 @ X4 @ X6) != $true)))))),
% 1.48/1.47 inference(nnf_transformation,[status(thm)],[f57])).
% 1.48/1.47 thf(f57,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.48/1.47 inference(flattening,[status(thm)],[f56])).
% 1.48/1.47 thf(f56,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X4 : X0,X5 : X0,X6 : X0] : ((((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X5 @ X6))) | ($true != (X1 @ X4 @ X5))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true))))),
% 1.48/1.47 inference(ennf_transformation,[status(thm)],[f20])).
% 1.48/1.47 thf(f20,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X5)) => (($true = (X1 @ X5 @ X6)) => ((X1 @ X4 @ X6) = $true))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true))))),
% 1.48/1.47 inference(fool_elimination,[status(thm)],[f19])).
% 1.48/1.47 thf(f19,plain,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((X1 @ X4 @ X5) => ((X1 @ X5 @ X6) => (X1 @ X4 @ X6)))))),
% 1.48/1.47 inference(rectify,[status(thm)],[f1])).
% 1.48/1.47 thf(f1,axiom,(
% 1.48/1.47 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))))),
% 1.48/1.47 file('/export/starexec/sandbox2/tmp/tmp.v6P8A3U1ka/DTF2THF_29423.p',is_per)).
% 1.48/1.47 thf(f71,plain,(
% 1.48/1.47 ((listStar @ sK2 @ sK3 @ (plus @ (suc @ sK4) @ zero) @ (app @ sK2 @ (suc @ sK4) @ zero @ (cons @ sK2 @ sK4 @ sK5 @ sK6) @ nil @ sK2) @ (cons @ sK2 @ sK4 @ sK5 @ sK6)) != $true)),
% 1.48/1.47 inference(cnf_transformation,[status(thm)],[f62])).
% 1.48/1.47 % SZS output end Proof for DTF2THF_29423
% 1.48/1.47 % (29565)------------------------------
% 1.48/1.47 % (29565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.47 % (29565)Termination reason: Refutation
% 1.48/1.47
% 1.48/1.47 % (29565)Memory used [KB]: 5884
% 1.48/1.47 % (29565)Time elapsed: 0.021 s
% 1.48/1.47 % (29565)Instructions burned: 55 (million)
% 1.48/1.47 % (29565)------------------------------
% 1.48/1.47 % (29565)------------------------------
% 1.48/1.47 % (29521)Success in time 0.281 s
%------------------------------------------------------------------------------