%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT427^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 08:45:43 AM UTC 2026
% Result : Theorem 1.96s 1.53s
% Output : Refutation 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT427^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:18:10 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : DAT427^1 : TPTP v9.2.1. Released v9.2.0.
% 0.30/0.47 % Domain : Data Structures
% 0.30/0.47 % Problem : Reversal of a red-black-tree is an involution, RT step
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.30/0.47 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.30/0.47 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.30/0.47 % Source : [Rot25]
% 0.30/0.47 % Names : RedBlackTree/rbt-rev-invol-RTStep.p [Rot25]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : ? v9.2.0
% 0.30/0.47 % Syntax : Number of formulae : 15 ( 3 unt; 11 typ; 0 def)
% 0.30/0.47 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 3 ( 1 avg)
% 0.30/0.47 % Number of connectives : 137 ( 0 ~; 0 |; 0 &; 135 @)
% 0.30/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 8 ( 6 avg)
% 0.30/0.47 % Number of types : 2 ( 2 usr)
% 0.30/0.47 % Number of type decls : 11 ( 4 !>P; 3 !>D)
% 0.30/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 10 ( 9 usr; 3 con; 0-7 aty)
% 0.30/0.47 % Number of variables : 28 ( 0 ^; 18 !; 0 ?; 28 :)
% 0.30/0.47 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : DH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments :
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(color_type,type,
% 0.30/0.47 color: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(black_type,type,
% 0.30/0.47 black: color ).
% 0.30/0.47
% 0.30/0.47 thf(red_type,type,
% 0.30/0.47 red: color ).
% 0.30/0.47
% 0.30/0.47 thf(nat_type,type,
% 0.30/0.47 nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(zero_type,type,
% 0.30/0.47 zero: nat ).
% 0.30/0.47
% 0.30/0.47 thf(suc_type,type,
% 0.30/0.47 suc: nat > nat ).
% 0.30/0.47
% 0.30/0.47 thf(tree_type,type,
% 0.30/0.47 tree: $tType > color > nat > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(leaf_type,type,
% 0.30/0.47 leaf:
% 0.30/0.47 !>[A: $tType] : ( tree @ A @ black @ zero ) ).
% 0.30/0.47
% 0.30/0.47 thf(redTree_type,type,
% 0.30/0.47 rt:
% 0.30/0.47 !>[A: $tType,N: nat] : ( ( tree @ A @ black @ N ) > A > ( tree @ A @ black @ N ) > ( tree @ A @ red @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(blackTree_type,type,
% 0.30/0.47 bt:
% 0.30/0.47 !>[A: $tType,N: nat,C1: color,C2: color] : ( ( tree @ A @ C1 @ N ) > A > ( tree @ A @ C2 @ N ) > ( tree @ A @ black @ ( suc @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(rbt_rev,type,
% 0.30/0.47 rev:
% 0.30/0.47 !>[A: $tType,C: color,N: nat] : ( ( tree @ A @ C @ N ) > ( tree @ A @ C @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(rev_leaf,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( rev @ A @ black @ zero @ ( leaf @ A ) )
% 0.30/0.47 = ( leaf @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(rev_bt,axiom,
% 0.30/0.47 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.30/0.47 ( ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) )
% 0.30/0.47 = ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(rev_rt,axiom,
% 0.30/0.47 ! [A: $tType,X: A,N: nat,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.30/0.47 ( ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) )
% 0.30/0.47 = ( rt @ A @ N @ ( rev @ A @ black @ N @ T2 ) @ X @ ( rev @ A @ black @ N @ T1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(rt_step,conjecture,
% 0.30/0.47 ! [A: $tType,X: A,N: nat,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.30/0.47 ( ( ( rev @ A @ black @ N @ ( rev @ A @ black @ N @ T1 ) )
% 0.30/0.47 = T1 )
% 0.30/0.47 => ( ( ( rev @ A @ black @ N @ ( rev @ A @ black @ N @ T2 ) )
% 0.30/0.47 = T2 )
% 0.30/0.47 => ( ( rev @ A @ red @ N @ ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) ) )
% 0.30/0.47 = ( rt @ A @ N @ T1 @ X @ T2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.71/1.39 ---- Embedded in THF ---
% 1.71/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.39 %%% Generated on Tue Feb 24 06:18:11 EST 2026
% 1.71/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.39 %%% Logic specification used:
% 1.71/1.39 %%% thf(spec, logic, $$dhol).
% 1.71/1.39
% 1.71/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2DTF23718.p
% 1.71/1.39 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.71/1.39 thf(is_per, definition, (! [A:$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)))))))))).
% 1.71/1.39 thf(color_type, type, color: $tType).
% 1.71/1.39 thf(colorStar, type, 'colorStar': (color > (color > $o))).
% 1.71/1.39 thf(colorStar_is_eq, axiom, (! [X:color,Y:color]: (((('colorStar' @ X) @ Y) <=> (X = Y))))).
% 1.71/1.39 thf(black_type, type, black: color).
% 1.71/1.39 thf(red_type, type, red: color).
% 1.71/1.39 thf(nat_type, type, nat: $tType).
% 1.71/1.39 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.71/1.39 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.71/1.39 thf(zero_type, type, zero: nat).
% 1.71/1.39 thf(suc_type, type, suc: (nat > nat)).
% 1.71/1.39 thf(tree_type, type, tree: ($tType > $tType)).
% 1.71/1.39 thf(treeStar, type, 'treeStar': (!> [A:$tType]: (((A > (A > $o)) > (color > (nat > ((tree @ A) > ((tree @ A) > $o)))))))).
% 1.71/1.39 thf('\'treeStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:color]: ((! [C0:nat]: (((isPer @ (tree @ B)) @ ((((treeStar @ B) @ BStar) @ C) @ C0)))))))))).
% 1.71/1.39 thf(leaf_type, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 1.71/1.39 thf(leaf_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ (leaf @ A)) @ (leaf @ A)))))).
% 1.71/1.39 thf(redTree_type, type, rt: (!> [A:$tType]: ((nat > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))).
% 1.71/1.39 thf(rt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ (((((rt @ A) @ N) @ D) @ D0) @ D1)) @ (((((rt @ A) @ N) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))).
% 1.71/1.39 thf(blackTree_type, type, bt: (!> [A:$tType]: ((nat > (color > (color > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))))).
% 1.71/1.39 thf(bt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C2) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D) @ D0) @ D1)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))))))).
% 1.71/1.39 thf(rbt_rev, type, rev: (!> [A:$tType]: ((color > (nat > ((tree @ A) > (tree @ A))))))).
% 1.71/1.39 thf(rev_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [C:color]: ((! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C) @ N) @ D) @ D_prime) => ((((((treeStar @ A) @ AStar) @ C) @ N) @ ((((rev @ A) @ C) @ N) @ D)) @ ((((rev @ A) @ C) @ N) @ D_prime))))))))))))).
% 1.71/1.39 thf(rev_leaf, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ (leaf @ A))) @ (leaf @ A)))))).
% 1.71/1.39 thf(rev_bt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2))) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1))))))))))))))))))).
% 1.71/1.39 thf(rev_rt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ (((((rt @ A) @ N) @ T1) @ X) @ T2))) @ (((((rt @ A) @ N) @ ((((rev @ A) @ black) @ N) @ T2)) @ X) @ ((((rev @ A) @ black) @ N) @ T1))))))))))))))).
% 1.71/1.39 thf(rt_step, conjecture, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ ((((rev @ A) @ black) @ N) @ ((((rev @ A) @ black) @ N) @ T1))) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ ((((rev @ A) @ black) @ N) @ ((((rev @ A) @ black) @ N) @ T2))) @ T2) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ (((((rt @ A) @ N) @ T1) @ X) @ T2)))) @ (((((rt @ A) @ N) @ T1) @ X) @ T2)))))))))))))))).
% 1.71/1.39 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2DTF23718.p
% 1.71/1.39 ------------------------
% 1.94/1.41 ---- Cleaned THF ---
% 1.94/1.41 thf(is_per_type,type,
% 1.94/1.41 isPer:
% 1.94/1.41 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.94/1.41
% 1.94/1.41 thf(is_per,definition,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 <=> ( ! [X: A,Y: A] :
% 1.94/1.41 ( ( AStar @ X @ Y )
% 1.94/1.41 => ( AStar @ Y @ X ) )
% 1.94/1.41 & ! [X: A,Y: A,Z: A] :
% 1.94/1.41 ( ( AStar @ X @ Y )
% 1.94/1.41 => ( ( AStar @ Y @ Z )
% 1.94/1.41 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(color_type,type,
% 1.94/1.41 color: $tType ).
% 1.94/1.41
% 1.94/1.41 thf(colorStar,type,
% 1.94/1.41 colorStar: color > color > $o ).
% 1.94/1.41
% 1.94/1.41 thf(colorStar_is_eq,axiom,
% 1.94/1.41 ! [X: color,Y: color] :
% 1.94/1.41 ( ( colorStar @ X @ Y )
% 1.94/1.41 <=> ( X = Y ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(black_type,type,
% 1.94/1.41 black: color ).
% 1.94/1.41
% 1.94/1.41 thf(red_type,type,
% 1.94/1.41 red: color ).
% 1.94/1.41
% 1.94/1.41 thf(nat_type,type,
% 1.94/1.41 nat: $tType ).
% 1.94/1.41
% 1.94/1.41 thf(natStar,type,
% 1.94/1.41 natStar: nat > nat > $o ).
% 1.94/1.41
% 1.94/1.41 thf(natStar_is_eq,axiom,
% 1.94/1.41 ! [X: nat,Y: nat] :
% 1.94/1.41 ( ( natStar @ X @ Y )
% 1.94/1.41 <=> ( X = Y ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(zero_type,type,
% 1.94/1.41 zero: nat ).
% 1.94/1.41
% 1.94/1.41 thf(suc_type,type,
% 1.94/1.41 suc: nat > nat ).
% 1.94/1.41
% 1.94/1.41 thf(tree_type,type,
% 1.94/1.41 tree: $tType > $tType ).
% 1.94/1.41
% 1.94/1.41 thf(treeStar,type,
% 1.94/1.41 treeStar:
% 1.94/1.41 !>[A: $tType] : ( ( A > A > $o ) > color > nat > ( tree @ A ) > ( tree @ A ) > $o ) ).
% 1.94/1.41
% 1.94/1.41 thf('\'treeStar\'_is_per',axiom,
% 1.94/1.41 ! [B: $tType,BStar: B > B > $o] :
% 1.94/1.41 ( ( isPer @ B @ BStar )
% 1.94/1.41 => ! [C: color,C0: nat] : ( isPer @ ( tree @ B ) @ ( treeStar @ B @ BStar @ C @ C0 ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(leaf_type,type,
% 1.94/1.41 leaf:
% 1.94/1.41 !>[A: $tType] : ( tree @ A ) ).
% 1.94/1.41
% 1.94/1.41 thf(leaf_tp_ax,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ( treeStar @ A @ AStar @ black @ zero @ ( leaf @ A ) @ ( leaf @ A ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(redTree_type,type,
% 1.94/1.41 rt:
% 1.94/1.41 !>[A: $tType] : ( nat > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rt_tp_ax,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ black @ N @ D @ D_prime )
% 1.94/1.41 => ! [D0: A,D0_prime: A] :
% 1.94/1.41 ( ( D0 = D0_prime )
% 1.94/1.41 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ black @ N @ D1 @ D1_prime )
% 1.94/1.41 => ( treeStar @ A @ AStar @ red @ N @ ( rt @ A @ N @ D @ D0 @ D1 ) @ ( rt @ A @ N @ D_prime @ D0_prime @ D1_prime ) ) ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(blackTree_type,type,
% 1.94/1.41 bt:
% 1.94/1.41 !>[A: $tType] : ( nat > color > color > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(bt_tp_ax,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [N: nat,C1: color,C2: color,D: tree @ A,D_prime: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ C1 @ N @ D @ D_prime )
% 1.94/1.41 => ! [D0: A,D0_prime: A] :
% 1.94/1.41 ( ( D0 = D0_prime )
% 1.94/1.41 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ C2 @ N @ D1 @ D1_prime )
% 1.94/1.41 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ D @ D0 @ D1 ) @ ( bt @ A @ N @ C1 @ C2 @ D_prime @ D0_prime @ D1_prime ) ) ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rbt_rev,type,
% 1.94/1.41 rev:
% 1.94/1.41 !>[A: $tType] : ( color > nat > ( tree @ A ) > ( tree @ A ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rev_tp_ax,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [C: color,N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ C @ N @ D @ D_prime )
% 1.94/1.41 => ( treeStar @ A @ AStar @ C @ N @ ( rev @ A @ C @ N @ D ) @ ( rev @ A @ C @ N @ D_prime ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rev_leaf,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ( treeStar @ A @ AStar @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) @ ( leaf @ A ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rev_bt,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 1.94/1.41 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 1.94/1.41 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rev_rt,axiom,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [X: A,N: nat,T1: tree @ A,T2: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 1.94/1.41 => ( ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 1.94/1.41 => ( treeStar @ A @ AStar @ red @ N @ ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) ) @ ( rt @ A @ N @ ( rev @ A @ black @ N @ T2 ) @ X @ ( rev @ A @ black @ N @ T1 ) ) ) ) ) ) ).
% 1.94/1.41
% 1.94/1.41 thf(rt_step,conjecture,
% 1.94/1.41 ! [A: $tType,AStar: A > A > $o] :
% 1.94/1.41 ( ( isPer @ A @ AStar )
% 1.94/1.41 => ! [X: A,N: nat,T1: tree @ A,T2: tree @ A] :
% 1.94/1.41 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 1.94/1.41 => ( ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 1.94/1.41 => ( ( treeStar @ A @ AStar @ black @ N @ ( rev @ A @ black @ N @ ( rev @ A @ black @ N @ T1 ) ) @ T1 )
% 1.94/1.41 => ( ( treeStar @ A @ AStar @ black @ N @ ( rev @ A @ black @ N @ ( rev @ A @ black @ N @ T2 ) ) @ T2 )
% 1.94/1.41 => ( treeStar @ A @ AStar @ red @ N @ ( rev @ A @ red @ N @ ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) ) ) @ ( rt @ A @ N @ T1 @ X @ T2 ) ) ) ) ) ) ) ).
% 1.94/1.41 ------------------------
% 1.94/1.43 % (24046)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/183Mi)
% 1.94/1.43 % (24048)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_23718 for (2999ds/27Mi)
% 1.94/1.43 % (24049)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/2Mi)
% 1.94/1.43 % (24049)Instruction limit reached!
% 1.94/1.43 % (24049)------------------------------
% 1.94/1.43 % (24049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.43 % (24049)Termination reason: Unknown
% 1.94/1.43 % (24049)Termination phase: shuffling
% 1.94/1.43
% 1.94/1.43 % (24049)Memory used [KB]: 1023
% 1.94/1.43 % (24049)Time elapsed: 0.002 s
% 1.94/1.43 % (24049)Instructions burned: 3 (million)
% 1.94/1.43 % (24049)------------------------------
% 1.94/1.43 % (24049)------------------------------
% 1.94/1.43 % (24047)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_23718 for (2999ds/4Mi)
% 1.94/1.43 % (24050)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_23718 for (2999ds/2Mi)
% 1.94/1.43 % (24051)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_23718 for (2999ds/275Mi)
% 1.94/1.43 % (24052)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/18Mi)
% 1.94/1.43 % (24050)Instruction limit reached!
% 1.94/1.43 % (24050)------------------------------
% 1.94/1.43 % (24050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.43 % (24050)Termination reason: Unknown
% 1.94/1.43 % (24050)Termination phase: shuffling
% 1.94/1.43
% 1.94/1.43 % (24050)Memory used [KB]: 1023
% 1.94/1.43 % (24050)Time elapsed: 0.003 s
% 1.94/1.43 % (24050)Instructions burned: 2 (million)
% 1.94/1.43 % (24050)------------------------------
% 1.94/1.43 % (24050)------------------------------
% 1.94/1.44 % (24047)Instruction limit reached!
% 1.94/1.44 % (24047)------------------------------
% 1.94/1.44 % (24047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.44 % (24047)Termination reason: Unknown
% 1.94/1.44 % (24047)Termination phase: shuffling
% 1.94/1.44
% 1.94/1.44 % (24047)Memory used [KB]: 1023
% 1.94/1.44 % (24047)Time elapsed: 0.004 s
% 1.94/1.44 % (24047)Instructions burned: 4 (million)
% 1.94/1.44 % (24047)------------------------------
% 1.94/1.44 % (24047)------------------------------
% 1.94/1.44 % (24048)Instruction limit reached!
% 1.94/1.44 % (24048)------------------------------
% 1.94/1.44 % (24048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.44 % (24048)Termination reason: Unknown
% 1.94/1.44 % (24048)Termination phase: Saturation
% 1.94/1.44
% 1.94/1.44 % (24048)Memory used [KB]: 5756
% 1.94/1.44 % (24048)Time elapsed: 0.011 s
% 1.94/1.44 % (24048)Instructions burned: 28 (million)
% 1.94/1.44 % (24048)------------------------------
% 1.94/1.44 % (24048)------------------------------
% 1.94/1.44 % (24053)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/3Mi)
% 1.94/1.44 % (24053)Instruction limit reached!
% 1.94/1.44 % (24053)------------------------------
% 1.94/1.44 % (24053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.44 % (24053)Termination reason: Unknown
% 1.94/1.44 % (24053)Termination phase: shuffling
% 1.94/1.44
% 1.94/1.44 % (24053)Memory used [KB]: 1023
% 1.94/1.44 % (24053)Time elapsed: 0.003 s
% 1.94/1.44 % (24053)Instructions burned: 4 (million)
% 1.94/1.44 % (24053)------------------------------
% 1.94/1.44 % (24053)------------------------------
% 1.94/1.44 % (24052)Instruction limit reached!
% 1.94/1.44 % (24052)------------------------------
% 1.94/1.44 % (24052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.44 % (24052)Termination reason: Unknown
% 1.94/1.44 % (24052)Termination phase: Saturation
% 1.94/1.44
% 1.94/1.44 % (24052)Memory used [KB]: 5628
% 1.94/1.44 % (24052)Time elapsed: 0.013 s
% 1.94/1.44 % (24052)Instructions burned: 19 (million)
% 1.94/1.44 % (24052)------------------------------
% 1.94/1.44 % (24052)------------------------------
% 1.94/1.45 % (24056)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_23718 for (2999ds/3Mi)
% 1.94/1.45 % (24056)Instruction limit reached!
% 1.94/1.45 % (24056)------------------------------
% 1.94/1.45 % (24056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.45 % (24056)Termination reason: Unknown
% 1.94/1.45 % (24056)Termination phase: shuffling
% 1.94/1.45
% 1.94/1.45 % (24056)Memory used [KB]: 1023
% 1.94/1.45 % (24056)Time elapsed: 0.003 s
% 1.94/1.45 % (24056)Instructions burned: 4 (million)
% 1.94/1.45 % (24056)------------------------------
% 1.94/1.45 % (24056)------------------------------
% 1.94/1.45 % (24057)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_23718 for (2999ds/1041Mi)
% 1.94/1.45 % Exception at run slice level
% 1.94/1.45 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
% 1.94/1.45 % (24054)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_23718 for (2999ds/37Mi)
% 1.94/1.45 % (24055)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_23718 for (2999ds/15Mi)
% 1.94/1.45 % Exception at run slice level
% 1.94/1.45 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
% 1.94/1.46 % (24060)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/16Mi)
% 1.94/1.46 % (24061)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_23718 for (2999ds/3Mi)
% 1.94/1.46 % (24055)Instruction limit reached!
% 1.94/1.46 % (24055)------------------------------
% 1.94/1.46 % (24055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.46 % (24055)Termination reason: Unknown
% 1.94/1.46 % (24055)Termination phase: Saturation
% 1.94/1.46
% 1.94/1.46 % (24055)Memory used [KB]: 1151
% 1.94/1.46 % (24055)Time elapsed: 0.010 s
% 1.94/1.46 % (24055)Instructions burned: 15 (million)
% 1.94/1.46 % (24061)Instruction limit reached!
% 1.94/1.46 % (24061)------------------------------
% 1.94/1.46 % (24061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.46 % (24055)------------------------------
% 1.94/1.46 % (24055)------------------------------
% 1.94/1.46 % (24061)Termination reason: Unknown
% 1.94/1.46 % (24061)Termination phase: shuffling
% 1.94/1.46
% 1.94/1.46 % (24061)Memory used [KB]: 1023
% 1.94/1.46 % (24061)Time elapsed: 0.003 s
% 1.94/1.46 % (24061)Instructions burned: 4 (million)
% 1.94/1.46 % (24061)------------------------------
% 1.94/1.46 % (24061)------------------------------
% 1.94/1.46 % (24058)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/7Mi)
% 1.94/1.46 % (24060)Instruction limit reached!
% 1.94/1.46 % (24060)------------------------------
% 1.94/1.46 % (24060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.46 % (24060)Termination reason: Unknown
% 1.94/1.46 % (24060)Termination phase: Saturation
% 1.94/1.46
% 1.94/1.46 % (24060)Memory used [KB]: 5628
% 1.94/1.46 % (24060)Time elapsed: 0.007 s
% 1.94/1.46 % (24060)Instructions burned: 16 (million)
% 1.94/1.46 % (24060)------------------------------
% 1.94/1.46 % (24060)------------------------------
% 1.94/1.47 % (24058)Instruction limit reached!
% 1.94/1.47 % (24058)------------------------------
% 1.94/1.47 % (24058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.47 % (24058)Termination reason: Unknown
% 1.94/1.47 % (24058)Termination phase: Preprocessing 3
% 1.94/1.47
% 1.94/1.47 % (24058)Memory used [KB]: 1023
% 1.94/1.47 % (24058)Time elapsed: 0.006 s
% 1.94/1.47 % (24058)Instructions burned: 7 (million)
% 1.94/1.47 % (24058)------------------------------
% 1.94/1.47 % (24058)------------------------------
% 1.94/1.47 % (24062)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_23718 for (2999ds/3Mi)
% 1.94/1.47 % (24063)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/7Mi)
% 1.94/1.47 % (24062)Instruction limit reached!
% 1.94/1.47 % (24062)------------------------------
% 1.94/1.47 % (24062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.47 % (24062)Termination reason: Unknown
% 1.94/1.47 % (24062)Termination phase: shuffling
% 1.94/1.47
% 1.94/1.47 % (24062)Memory used [KB]: 1023
% 1.94/1.47 % (24062)Time elapsed: 0.003 s
% 1.94/1.47 % (24062)Instructions burned: 3 (million)
% 1.94/1.47 % (24062)------------------------------
% 1.94/1.47 % (24062)------------------------------
% 1.94/1.47 % (24063)Instruction limit reached!
% 1.94/1.47 % (24063)------------------------------
% 1.94/1.47 % (24063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.47 % (24063)Termination reason: Unknown
% 1.94/1.47 % (24063)Termination phase: Preprocessing 3
% 1.94/1.47
% 1.94/1.47 % (24063)Memory used [KB]: 1023
% 1.94/1.47 % (24063)Time elapsed: 0.004 s
% 1.94/1.47 % (24063)Instructions burned: 7 (million)
% 1.94/1.47 % (24063)------------------------------
% 1.94/1.47 % (24063)------------------------------
% 1.94/1.47 % (24065)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/4Mi)
% 1.94/1.47 % (24065)Instruction limit reached!
% 1.94/1.47 % (24065)------------------------------
% 1.94/1.47 % (24065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.47 % (24065)Termination reason: Unknown
% 1.94/1.47 % (24065)Termination phase: shuffling
% 1.94/1.47
% 1.94/1.47 % (24065)Memory used [KB]: 1023
% 1.94/1.47 % (24065)Time elapsed: 0.003 s
% 1.94/1.47 % (24065)Instructions burned: 4 (million)
% 1.94/1.47 % (24065)------------------------------
% 1.94/1.47 % (24065)------------------------------
% 1.94/1.48 % (24064)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/3Mi)
% 1.94/1.48 % (24064)Instruction limit reached!
% 1.94/1.48 % (24064)------------------------------
% 1.94/1.48 % (24064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.48 % (24064)Termination reason: Unknown
% 1.94/1.48 % (24064)Termination phase: shuffling
% 1.94/1.48
% 1.94/1.48 % (24064)Memory used [KB]: 1023
% 1.94/1.48 % (24064)Time elapsed: 0.003 s
% 1.94/1.48 % (24064)Instructions burned: 3 (million)
% 1.94/1.48 % (24064)------------------------------
% 1.94/1.48 % (24064)------------------------------
% 1.94/1.48 % (24068)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/6Mi)
% 1.94/1.48 % (24066)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/18Mi)
% 1.94/1.48 % (24046)Instruction limit reached!
% 1.94/1.48 % (24046)------------------------------
% 1.94/1.48 % (24046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.48 % (24046)Termination reason: Unknown
% 1.94/1.48 % (24046)Termination phase: Saturation
% 1.94/1.48
% 1.94/1.48 % (24046)Memory used [KB]: 7164
% 1.94/1.48 % (24046)Time elapsed: 0.059 s
% 1.94/1.48 % (24046)Instructions burned: 185 (million)
% 1.94/1.48 % (24046)------------------------------
% 1.94/1.48 % (24046)------------------------------
% 1.94/1.48 % (24070)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_23718 for (2999ds/902Mi)
% 1.94/1.49 % (24067)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/710Mi)
% 1.94/1.49 % (24068)Instruction limit reached!
% 1.94/1.49 % (24068)------------------------------
% 1.94/1.49 % (24068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.49 % (24068)Termination reason: Unknown
% 1.94/1.49 % (24068)Termination phase: Preprocessing 3
% 1.94/1.49
% 1.94/1.49 % (24068)Memory used [KB]: 1023
% 1.94/1.49 % (24068)Time elapsed: 0.004 s
% 1.94/1.49 % (24068)Instructions burned: 7 (million)
% 1.94/1.49 % (24068)------------------------------
% 1.94/1.49 % (24068)------------------------------
% 1.94/1.49 % (24066)Instruction limit reached!
% 1.94/1.49 % (24066)------------------------------
% 1.94/1.49 % (24066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.49 % (24066)Termination reason: Unknown
% 1.94/1.49 % (24066)Termination phase: Saturation
% 1.94/1.49
% 1.94/1.49 % (24066)Memory used [KB]: 5628
% 1.94/1.49 % (24066)Time elapsed: 0.012 s
% 1.94/1.49 % (24066)Instructions burned: 18 (million)
% 1.94/1.49 % (24066)------------------------------
% 1.94/1.49 % (24066)------------------------------
% 1.94/1.49 % (24072)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/5Mi)
% 1.94/1.50 % Exception at run slice level
% 1.94/1.50 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
% 1.94/1.50 % (24073)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_23718 for (2999ds/6Mi)
% 1.96/1.50 % (24071)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_23718 for (2999ds/21Mi)
% 1.96/1.50 % Exception at run slice level
% 1.96/1.50 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
% 1.96/1.51 % (24075)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_23718 for (2999ds/779Mi)
% 1.96/1.51 % Exception at run slice level
% 1.96/1.51 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
% 1.96/1.51 % (24076)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_23718 for (2999ds/19Mi)
% 1.96/1.51 % Exception at run slice level
% 1.96/1.51 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
% 1.96/1.51 % (24071)Instruction limit reached!
% 1.96/1.51 % (24071)------------------------------
% 1.96/1.51 % (24071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.51 % (24071)Termination reason: Unknown
% 1.96/1.51 % (24071)Termination phase: Saturation
% 1.96/1.51
% 1.96/1.51 % (24071)Memory used [KB]: 5628
% 1.96/1.51 % (24071)Time elapsed: 0.014 s
% 1.96/1.51 % (24071)Instructions burned: 21 (million)
% 1.96/1.51 % (24071)------------------------------
% 1.96/1.51 % (24071)------------------------------
% 1.96/1.51 % (24074)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/377Mi)
% 1.96/1.52 % (24077)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/879Mi)
% 1.96/1.52 % (24078)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/17Mi)
% 1.96/1.52 % (24051)First to succeed.
% 1.96/1.52 % (24078)Instruction limit reached!
% 1.96/1.52 % (24078)------------------------------
% 1.96/1.52 % (24078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.52 % (24078)Termination reason: Unknown
% 1.96/1.52 % (24078)Termination phase: Saturation
% 1.96/1.52
% 1.96/1.52 % (24078)Memory used [KB]: 5756
% 1.96/1.52 % (24078)Time elapsed: 0.008 s
% 1.96/1.52 % (24078)Instructions burned: 18 (million)
% 1.96/1.52 % (24078)------------------------------
% 1.96/1.52 % (24078)------------------------------
% 1.96/1.53 % (24079)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23718 for (2999ds/3Mi)
% 1.96/1.53 % (24051)Refutation found. Thanks to Tanya!
% 1.96/1.53 % SZS status Theorem for DTF2THF_23718
% 1.96/1.53 % SZS output start Proof for DTF2THF_23718
% 1.96/1.53 thf(type_def_6, type, color: $tType).
% 1.96/1.53 thf(type_def_7, type, nat: $tType).
% 1.96/1.53 thf(type_def_8, type, tree: ($tType) > $tType).
% 1.96/1.53 thf(type_def_9, type, sK5: $tType).
% 1.96/1.53 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.96/1.53 thf(func_def_2, type, color: $tType).
% 1.96/1.53 thf(func_def_3, type, colorStar: color > color > $o).
% 1.96/1.53 thf(func_def_4, type, black: color).
% 1.96/1.53 thf(func_def_5, type, red: color).
% 1.96/1.53 thf(func_def_6, type, nat: $tType).
% 1.96/1.53 thf(func_def_7, type, natStar: nat > nat > $o).
% 1.96/1.53 thf(func_def_8, type, zero: nat).
% 1.96/1.53 thf(func_def_9, type, suc: nat > nat).
% 1.96/1.53 thf(func_def_10, type, tree: ($tType) > $tType).
% 1.96/1.53 thf(func_def_11, type, treeStar: !>[X0: $tType]:((X0 > X0 > $o) > color > nat > tree @ X0 > tree @ X0 > $o)).
% 1.96/1.53 thf(func_def_12, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 1.96/1.53 thf(func_def_13, type, rt: !>[X0: $tType]:(nat > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.96/1.53 thf(func_def_14, type, bt: !>[X0: $tType]:(nat > color > color > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.96/1.53 thf(func_def_15, type, rev: !>[X0: $tType]:(color > nat > tree @ X0 > tree @ X0)).
% 1.96/1.53 thf(func_def_18, type, sK0: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.96/1.53 thf(func_def_19, type, sK1: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.96/1.53 thf(func_def_20, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.96/1.53 thf(func_def_21, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.96/1.53 thf(func_def_22, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.96/1.53 thf(func_def_23, type, sK6: sK5 > sK5 > $o).
% 1.96/1.53 thf(func_def_24, type, sK7: sK5).
% 1.96/1.53 thf(func_def_25, type, sK8: nat).
% 1.96/1.53 thf(func_def_26, type, sK9: tree @ sK5).
% 1.96/1.53 thf(func_def_27, type, sK10: tree @ sK5).
% 1.96/1.53 thf(func_def_29, type, ph12: !>[X0: $tType]:(X0)).
% 1.96/1.53 thf(f365,plain,(
% 1.96/1.53 $false),
% 1.96/1.53 inference(avatar_sat_refutation,[status(thm)],[f92,f96,f277,f293,f329,f364])).
% 1.96/1.53 thf(f364,plain,(
% 1.96/1.53 spl11_6),
% 1.96/1.53 inference(avatar_contradiction_clause,[status(thm)],[f363])).
% 1.96/1.53 thf(f363,plain,(
% 1.96/1.53 $false | spl11_6),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f362,f73])).
% 1.96/1.53 thf(f73,plain,(
% 1.96/1.53 ($true = (isPer @ sK5 @ sK6))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 thf(f56,plain,(
% 1.96/1.53 ($true = (isPer @ sK5 @ sK6)) & (($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9)) & ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10)) @ sK10)) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)))),
% 1.96/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10])],[f40,f55,f54])).
% 1.96/1.53 thf(f54,plain,(
% 1.96/1.53 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) = $true) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X4)) @ X4)) & ($true != (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X5)) @ X5)) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5)))) => (($true = (isPer @ sK5 @ sK6)) & ? [X5 : tree @ sK5,X4 : tree @ sK5,X3 : nat,X2 : sK5] : (($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ X4 @ X4)) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ X4)) @ X4)) & ($true != (treeStar @ sK5 @ sK6 @ red @ X3 @ (rev @ sK5 @ red @ X3 @ (rev @ sK5 @ red @ X3 @ (rt @ sK5 @ X3 @ X4 @ X2 @ X5))) @ (rt @ sK5 @ X3 @ X4 @ X2 @ X5))) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ X5)) @ X5)) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ X5 @ X5))))),
% 1.96/1.53 introduced(definition,[],[choice_axiom])).
% 1.96/1.53 thf(f55,plain,(
% 1.96/1.53 ? [X5 : tree @ sK5,X4 : tree @ sK5,X3 : nat,X2 : sK5] : (($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ X4 @ X4)) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ X4)) @ X4)) & ($true != (treeStar @ sK5 @ sK6 @ red @ X3 @ (rev @ sK5 @ red @ X3 @ (rev @ sK5 @ red @ X3 @ (rt @ sK5 @ X3 @ X4 @ X2 @ X5))) @ (rt @ sK5 @ X3 @ X4 @ X2 @ X5))) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ (rev @ sK5 @ black @ X3 @ X5)) @ X5)) & ($true = (treeStar @ sK5 @ sK6 @ black @ X3 @ X5 @ X5))) => (($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9)) & ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10)) @ sK10)) & ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)))),
% 1.96/1.53 introduced(definition,[],[choice_axiom])).
% 1.96/1.53 thf(f40,plain,(
% 1.96/1.53 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) = $true) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X4)) @ X4)) & ($true != (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X5)) @ X5)) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5))))),
% 1.96/1.53 inference(flattening,[status(thm)],[f39])).
% 1.96/1.53 thf(f39,plain,(
% 1.96/1.53 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : ((((($true != (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X5)) @ X5))) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X4)) @ X4))) & ($true = (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5))) & ((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) = $true)) & ((isPer @ X0 @ X1) = $true))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f16])).
% 1.96/1.53 thf(f16,plain,(
% 1.96/1.53 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) = $true) => (($true = (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5)) => (($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X4)) @ X4)) => (($true = (treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X5)) @ X5)) => ($true = (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))))))))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f15])).
% 1.96/1.53 thf(f15,plain,(
% 1.96/1.53 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) => ((treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5) => ((treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X4)) @ X4) => ((treeStar @ X0 @ X1 @ black @ X3 @ (rev @ X0 @ black @ X3 @ (rev @ X0 @ black @ X3 @ X5)) @ X5) => (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5))) @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)))))))),
% 1.96/1.53 inference(rectify,[status(thm)],[f13])).
% 1.96/1.53 thf(f13,negated_conjecture,(
% 1.96/1.53 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ black @ X9 @ X19 @ X19) => ((treeStar @ X0 @ X1 @ black @ X9 @ (rev @ X0 @ black @ X9 @ (rev @ X0 @ black @ X9 @ X18)) @ X18) => ((treeStar @ X0 @ X1 @ black @ X9 @ (rev @ X0 @ black @ X9 @ (rev @ X0 @ black @ X9 @ X19)) @ X19) => (treeStar @ X0 @ X1 @ red @ X9 @ (rev @ X0 @ red @ X9 @ (rev @ X0 @ red @ X9 @ (rt @ X0 @ X9 @ X18 @ X2 @ X19))) @ (rt @ X0 @ X9 @ X18 @ X2 @ X19)))))))),
% 1.96/1.53 inference(negated_conjecture,[status(cth)],[f12])).
% 1.96/1.53 thf(f12,conjecture,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ black @ X9 @ X19 @ X19) => ((treeStar @ X0 @ X1 @ black @ X9 @ (rev @ X0 @ black @ X9 @ (rev @ X0 @ black @ X9 @ X18)) @ X18) => ((treeStar @ X0 @ X1 @ black @ X9 @ (rev @ X0 @ black @ X9 @ (rev @ X0 @ black @ X9 @ X19)) @ X19) => (treeStar @ X0 @ X1 @ red @ X9 @ (rev @ X0 @ red @ X9 @ (rev @ X0 @ red @ X9 @ (rt @ X0 @ X9 @ X18 @ X2 @ X19))) @ (rt @ X0 @ X9 @ X18 @ X2 @ X19)))))))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p',rt_step)).
% 1.96/1.53 thf(f362,plain,(
% 1.96/1.53 ($true != (isPer @ sK5 @ sK6)) | spl11_6),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f361,f71])).
% 1.96/1.53 thf(f71,plain,(
% 1.96/1.53 ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 thf(f361,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9)) | ($true != (isPer @ sK5 @ sK6)) | spl11_6),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f356,f69])).
% 1.96/1.53 thf(f69,plain,(
% 1.96/1.53 ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10)) @ sK10))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 thf(f356,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10)) @ sK10)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9)) | ($true != (isPer @ sK5 @ sK6)) | spl11_6),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.96/1.53 thf(f353,plain,(
% 1.96/1.53 ($true != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10)) @ sK10)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK9)) | ($true != (isPer @ sK5 @ sK6)) | spl11_6),
% 1.96/1.53 inference(superposition,[status(thm)],[f276,f75])).
% 1.96/1.53 thf(f75,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : nat,X3 : tree @ X0,X1 : X0 > X0 > $o,X8 : tree @ X0,X6 : X0,X7 : tree @ X0,X4 : tree @ X0] : (((treeStar @ X0 @ X1 @ red @ X2 @ (rt @ X0 @ X2 @ X3 @ X6 @ X7) @ (rt @ X0 @ X2 @ X4 @ X6 @ X8)) = $true) | ($true != (treeStar @ X0 @ X1 @ black @ X2 @ X7 @ X8)) | ((isPer @ X0 @ X1) != $true) | ($true != (treeStar @ X0 @ X1 @ black @ X2 @ X3 @ X4))) )),
% 1.96/1.53 inference(equality_resolution,[status(thm)],[f67])).
% 1.96/1.53 thf(f67,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : nat,X3 : tree @ X0,X1 : X0 > X0 > $o,X8 : tree @ X0,X6 : X0,X7 : tree @ X0,X4 : tree @ X0,X5 : X0] : (($true != (treeStar @ X0 @ X1 @ black @ X2 @ X3 @ X4)) | (X5 != X6) | ($true = (treeStar @ X0 @ X1 @ red @ X2 @ (rt @ X0 @ X2 @ X3 @ X5 @ X7) @ (rt @ X0 @ X2 @ X4 @ X6 @ X8))) | ($true != (treeStar @ X0 @ X1 @ black @ X2 @ X7 @ X8)) | ((isPer @ X0 @ X1) != $true)) )),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f43])).
% 1.96/1.53 thf(f43,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : nat,X3 : tree @ X0,X4 : tree @ X0] : (($true != (treeStar @ X0 @ X1 @ black @ X2 @ X3 @ X4)) | ! [X5 : X0,X6 : X0] : ((X5 != X6) | ! [X7 : tree @ X0,X8 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ red @ X2 @ (rt @ X0 @ X2 @ X3 @ X5 @ X7) @ (rt @ X0 @ X2 @ X4 @ X6 @ X8))) | ($true != (treeStar @ X0 @ X1 @ black @ X2 @ X7 @ X8))))) | ((isPer @ X0 @ X1) != $true))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f24])).
% 1.96/1.53 thf(f24,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : tree @ X0,X4 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ black @ X2 @ X3 @ X4)) => ! [X5 : X0,X6 : X0] : ((X5 = X6) => ! [X7 : tree @ X0,X8 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ black @ X2 @ X7 @ X8)) => ($true = (treeStar @ X0 @ X1 @ red @ X2 @ (rt @ X0 @ X2 @ X3 @ X5 @ X7) @ (rt @ X0 @ X2 @ X4 @ X6 @ X8)))))))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f23])).
% 1.96/1.53 thf(f23,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : tree @ X0,X4 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X2 @ X3 @ X4) => ! [X5 : X0,X6 : X0] : ((X5 = X6) => ! [X7 : tree @ X0,X8 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X2 @ X7 @ X8) => (treeStar @ X0 @ X1 @ red @ X2 @ (rt @ X0 @ X2 @ X3 @ X5 @ X7) @ (rt @ X0 @ X2 @ X4 @ X6 @ X8))))))),
% 1.96/1.53 inference(rectify,[status(thm)],[f6])).
% 1.96/1.53 thf(f6,axiom,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X9 : nat,X10 : tree @ X0,X11 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X9 @ X10 @ X11) => ! [X12 : X0,X13 : X0] : ((X12 = X13) => ! [X14 : tree @ X0,X15 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X9 @ X14 @ X15) => (treeStar @ X0 @ X1 @ red @ X9 @ (rt @ X0 @ X9 @ X10 @ X12 @ X14) @ (rt @ X0 @ X9 @ X11 @ X13 @ X15))))))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p',rt_tp_ax)).
% 1.96/1.53 thf(f276,plain,(
% 1.96/1.53 ((treeStar @ sK5 @ sK6 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK7 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | spl11_6),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f274])).
% 1.96/1.53 thf(f274,definition,(
% 1.96/1.53 spl11_6 <=> ((treeStar @ sK5 @ sK6 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK7 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) = $true)),
% 1.96/1.53 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.96/1.53 thf(f329,plain,(
% 1.96/1.53 spl11_5),
% 1.96/1.53 inference(avatar_contradiction_clause,[status(thm)],[f328])).
% 1.96/1.53 thf(f328,plain,(
% 1.96/1.53 $false | spl11_5),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f327,f72])).
% 1.96/1.53 thf(f72,plain,(
% 1.96/1.53 ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 thf(f327,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | spl11_5),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f326,f73])).
% 1.96/1.53 thf(f326,plain,(
% 1.96/1.53 ($true != (isPer @ sK5 @ sK6)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | spl11_5),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f321])).
% 1.96/1.53 thf(f321,plain,(
% 1.96/1.53 ($true != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | ($true != (isPer @ sK5 @ sK6)) | spl11_5),
% 1.96/1.53 inference(superposition,[status(thm)],[f272,f57])).
% 1.96/1.53 thf(f57,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : color,X3 : nat,X1 : X0 > X0 > $o,X4 : tree @ X0,X5 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5))) | ((isPer @ X0 @ X1) != $true) | ($true != (treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5))) )),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f41])).
% 1.96/1.53 thf(f41,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5))) | ($true != (treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5))) | ((isPer @ X0 @ X1) != $true))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f26])).
% 1.96/1.53 thf(f26,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) => ($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)))))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f25])).
% 1.96/1.53 thf(f25,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : ((treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5) => (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5))))),
% 1.96/1.53 inference(rectify,[status(thm)],[f8])).
% 1.96/1.53 thf(f8,axiom,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X7 : color,X9 : nat,X10 : tree @ X0,X11 : tree @ X0] : ((treeStar @ X0 @ X1 @ X7 @ X9 @ X10 @ X11) => (treeStar @ X0 @ X1 @ X7 @ X9 @ (rev @ X0 @ X7 @ X9 @ X10) @ (rev @ X0 @ X7 @ X9 @ X11))))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p',rev_tp_ax)).
% 1.96/1.53 thf(f272,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9) @ (rev @ sK5 @ black @ sK8 @ sK9))) | spl11_5),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f270])).
% 1.96/1.53 thf(f270,definition,(
% 1.96/1.53 spl11_5 <=> ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9) @ (rev @ sK5 @ black @ sK8 @ sK9)))),
% 1.96/1.53 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.96/1.53 thf(f293,plain,(
% 1.96/1.53 spl11_4),
% 1.96/1.53 inference(avatar_contradiction_clause,[status(thm)],[f292])).
% 1.96/1.53 thf(f292,plain,(
% 1.96/1.53 $false | spl11_4),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f291,f73])).
% 1.96/1.53 thf(f291,plain,(
% 1.96/1.53 ($true != (isPer @ sK5 @ sK6)) | spl11_4),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f290,f68])).
% 1.96/1.53 thf(f68,plain,(
% 1.96/1.53 ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 thf(f290,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)) | ($true != (isPer @ sK5 @ sK6)) | spl11_4),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 1.96/1.53 thf(f285,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)) | ($true != (isPer @ sK5 @ sK6)) | ($true != $true) | spl11_4),
% 1.96/1.53 inference(superposition,[status(thm)],[f268,f57])).
% 1.96/1.53 thf(f268,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ (rev @ sK5 @ black @ sK8 @ sK10))) | spl11_4),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f266])).
% 1.96/1.53 thf(f266,definition,(
% 1.96/1.53 spl11_4 <=> ($true = (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ (rev @ sK5 @ black @ sK8 @ sK10)))),
% 1.96/1.53 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.96/1.53 thf(f277,plain,(
% 1.96/1.53 ~spl11_4 | ~spl11_5 | ~spl11_6 | ~spl11_2 | ~spl11_3),
% 1.96/1.53 inference(avatar_split_clause,[status(thm)],[f264,f90,f85,f274,f270,f266])).
% 1.96/1.53 thf(f85,definition,(
% 1.96/1.53 spl11_2 <=> ($true = (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8)))),
% 1.96/1.53 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.96/1.53 thf(f90,definition,(
% 1.96/1.53 spl11_3 <=> ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ X0)) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true))),
% 1.96/1.53 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.96/1.53 thf(f264,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9) @ (rev @ sK5 @ black @ sK8 @ sK9))) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK7 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ (rev @ sK5 @ black @ sK8 @ sK10))) | (~spl11_2 | ~spl11_3)),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f258,f73])).
% 1.96/1.53 thf(f258,plain,(
% 1.96/1.53 ($true != (isPer @ sK5 @ sK6)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9) @ (rev @ sK5 @ black @ sK8 @ sK9))) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK7 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ (rev @ sK5 @ black @ sK8 @ sK10))) | (~spl11_2 | ~spl11_3)),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f254])).
% 1.96/1.53 thf(f254,plain,(
% 1.96/1.53 ($true != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9) @ (rev @ sK5 @ black @ sK8 @ sK9))) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK9)) @ sK7 @ (rev @ sK5 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (isPer @ sK5 @ sK6)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ (rev @ sK5 @ black @ sK8 @ sK10))) | (~spl11_2 | ~spl11_3)),
% 1.96/1.53 inference(superposition,[status(thm)],[f139,f74])).
% 1.96/1.53 thf(f74,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : X0,X3 : nat,X1 : X0 > X0 > $o,X4 : tree @ X0,X5 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)) @ (rt @ X0 @ X3 @ (rev @ X0 @ black @ X3 @ X5) @ X2 @ (rev @ X0 @ black @ X3 @ X4)))) | ((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) != $true) | ((isPer @ X0 @ X1) != $true) | ($true != (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5))) )),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f47])).
% 1.96/1.53 thf(f47,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) != $true) | ($true != (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5)) | ($true = (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)) @ (rt @ X0 @ X3 @ (rev @ X0 @ black @ X3 @ X5) @ X2 @ (rev @ X0 @ black @ X3 @ X4))))))),
% 1.96/1.53 inference(flattening,[status(thm)],[f46])).
% 1.96/1.53 thf(f46,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : ((($true = (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)) @ (rt @ X0 @ X3 @ (rev @ X0 @ black @ X3 @ X5) @ X2 @ (rev @ X0 @ black @ X3 @ X4)))) | ($true != (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5))) | ((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) != $true)) | ((isPer @ X0 @ X1) != $true))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f38])).
% 1.96/1.53 thf(f38,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) = $true) => (($true = (treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5)) => ($true = (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)) @ (rt @ X0 @ X3 @ (rev @ X0 @ black @ X3 @ X5) @ X2 @ (rev @ X0 @ black @ X3 @ X4)))))))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f37])).
% 1.96/1.53 thf(f37,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X3 @ X4 @ X4) => ((treeStar @ X0 @ X1 @ black @ X3 @ X5 @ X5) => (treeStar @ X0 @ X1 @ red @ X3 @ (rev @ X0 @ red @ X3 @ (rt @ X0 @ X3 @ X4 @ X2 @ X5)) @ (rt @ X0 @ X3 @ (rev @ X0 @ black @ X3 @ X5) @ X2 @ (rev @ X0 @ black @ X3 @ X4))))))),
% 1.96/1.53 inference(rectify,[status(thm)],[f11])).
% 1.96/1.53 thf(f11,axiom,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ black @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ black @ X9 @ X19 @ X19) => (treeStar @ X0 @ X1 @ red @ X9 @ (rev @ X0 @ red @ X9 @ (rt @ X0 @ X9 @ X18 @ X2 @ X19)) @ (rt @ X0 @ X9 @ (rev @ X0 @ black @ X9 @ X19) @ X2 @ (rev @ X0 @ black @ X9 @ X18))))))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p',rev_rt)).
% 1.96/1.53 thf(f139,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ X0)) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true)) ) | (~spl11_2 | ~spl11_3)),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f136,f86])).
% 1.96/1.53 thf(f86,plain,(
% 1.96/1.53 ($true = (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8))) | ~spl11_2),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.96/1.53 thf(f136,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8))) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ X0))) ) | ~spl11_3),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.96/1.53 thf(f135,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ X0)) | ($true != (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8))) | ($true != $true)) ) | ~spl11_3),
% 1.96/1.53 inference(superposition,[status(thm)],[f130,f65])).
% 1.96/1.53 thf(f65,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((X1 @ X2 @ X3) != $true) | ((isPer @ X0 @ X1) != $true) | ((X1 @ X3 @ X4) != $true)) )),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f53])).
% 1.96/1.53 thf(f53,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (($true = (X1 @ X6 @ X5)) | ($true != (X1 @ X5 @ X6)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true != (X1 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1))) & ($true = (X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) & ($true = (X1 @ (sK1 @ X0 @ X1) @ (sK2 @ X0 @ X1)))) | (($true != (X1 @ (sK4 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1))))))),
% 1.96/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f50,f52,f51])).
% 1.96/1.53 thf(f51,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X9) != $true) & ($true = (X1 @ X7 @ X8)) & ($true = (X1 @ X8 @ X9))) => (($true != (X1 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1))) & ($true = (X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) & ($true = (X1 @ (sK1 @ X0 @ X1) @ (sK2 @ X0 @ X1)))))),
% 1.96/1.53 introduced(definition,[],[choice_axiom])).
% 1.96/1.53 thf(f52,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X10 : X0,X11 : X0] : (($true != (X1 @ X11 @ X10)) & ($true = (X1 @ X10 @ X11))) => (($true != (X1 @ (sK4 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)))))),
% 1.96/1.53 introduced(definition,[],[choice_axiom])).
% 1.96/1.53 thf(f50,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (($true = (X1 @ X6 @ X5)) | ($true != (X1 @ X5 @ X6)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X9) != $true) & ($true = (X1 @ X7 @ X8)) & ($true = (X1 @ X8 @ X9))) | ? [X10 : X0,X11 : X0] : (($true != (X1 @ X11 @ X10)) & ($true = (X1 @ X10 @ X11)))))),
% 1.96/1.53 inference(rectify,[status(thm)],[f49])).
% 1.96/1.53 thf(f49,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X4 @ X5)) | ($true != (X1 @ X5 @ X6))) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X6)) & ($true = (X1 @ X4 @ X5)) & ($true = (X1 @ X5 @ X6))) | ? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true))))),
% 1.96/1.53 inference(flattening,[status(thm)],[f48])).
% 1.96/1.53 thf(f48,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X4 @ X5)) | ($true != (X1 @ X5 @ X6))) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X6)) & ($true = (X1 @ X4 @ X5)) & ($true = (X1 @ X5 @ X6))) | ? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true)))))),
% 1.96/1.53 inference(nnf_transformation,[status(thm)],[f45])).
% 1.96/1.53 thf(f45,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X4 @ X5)) | ($true != (X1 @ X5 @ X6))) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.96/1.53 inference(flattening,[status(thm)],[f44])).
% 1.96/1.53 thf(f44,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : ((($true = (X1 @ X4 @ X6)) | ($true != (X1 @ X5 @ X6))) | ($true != (X1 @ X4 @ X5))) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f20])).
% 1.96/1.53 thf(f20,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (($true = (X1 @ X4 @ X5)) => (($true = (X1 @ X5 @ X6)) => ($true = (X1 @ X4 @ X6)))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f19])).
% 1.96/1.53 thf(f19,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((X1 @ X4 @ X5) => ((X1 @ X5 @ X6) => (X1 @ X4 @ X6)))) <=> (isPer @ X0 @ X1))),
% 1.96/1.53 inference(rectify,[status(thm)],[f1])).
% 1.96/1.53 thf(f1,axiom,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))) <=> (isPer @ X0 @ X1))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p',is_per)).
% 1.96/1.53 thf(f130,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ~spl11_3),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f129,f72])).
% 1.96/1.53 thf(f129,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ~spl11_3),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f128,f73])).
% 1.96/1.53 thf(f128,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ($true != (isPer @ sK5 @ sK6)) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | ~spl11_3),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f127,f68])).
% 1.96/1.53 thf(f127,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)) | ($true != (isPer @ sK5 @ sK6)) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | ~spl11_3),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.96/1.53 thf(f120,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ (rev @ sK5 @ black @ sK8 @ sK10) @ sK7 @ (rev @ sK5 @ black @ sK8 @ sK9))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK10 @ sK10)) | ($true != (isPer @ sK5 @ sK6)) | ($true != $true) | ($true != (treeStar @ sK5 @ sK6 @ black @ sK8 @ sK9 @ sK9)) | ~spl11_3),
% 1.96/1.53 inference(superposition,[status(thm)],[f108,f74])).
% 1.96/1.53 thf(f108,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) @ X0)) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ X0) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)))) ) | ~spl11_3),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f107,f73])).
% 1.96/1.53 thf(f107,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ X0) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) @ X0)) | ($true != (isPer @ sK5 @ sK6))) ) | ~spl11_3),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.96/1.53 thf(f102,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != $true) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) @ X0)) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ X0) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) | ($true != (isPer @ sK5 @ sK6))) ) | ~spl11_3),
% 1.96/1.53 inference(superposition,[status(thm)],[f91,f57])).
% 1.96/1.53 thf(f91,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ X0)) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true)) ) | ~spl11_3),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.96/1.53 thf(f96,plain,(
% 1.96/1.53 spl11_2),
% 1.96/1.53 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.96/1.53 thf(f95,plain,(
% 1.96/1.53 $false | spl11_2),
% 1.96/1.53 inference(subsumption_resolution,[status(thm)],[f94,f73])).
% 1.96/1.53 thf(f94,plain,(
% 1.96/1.53 ($true != (isPer @ sK5 @ sK6)) | spl11_2),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.96/1.53 thf(f93,plain,(
% 1.96/1.53 ($true != $true) | ($true != (isPer @ sK5 @ sK6)) | spl11_2),
% 1.96/1.53 inference(superposition,[status(thm)],[f87,f66])).
% 1.96/1.53 thf(f66,plain,(
% 1.96/1.53 ( ! [X0 : $tType,X2 : color,X3 : nat,X1 : X0 > X0 > $o] : (($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))) | ((isPer @ X0 @ X1) != $true)) )),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f42])).
% 1.96/1.53 thf(f42,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : color,X3 : nat] : ($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))))),
% 1.96/1.53 inference(ennf_transformation,[status(thm)],[f30])).
% 1.96/1.53 thf(f30,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : color,X3 : nat] : ($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))))),
% 1.96/1.53 inference(fool_elimination,[status(thm)],[f29])).
% 1.96/1.53 thf(f29,plain,(
% 1.96/1.53 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : color,X3 : nat] : (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3)))),
% 1.96/1.53 inference(rectify,[status(thm)],[f4])).
% 1.96/1.53 thf(f4,axiom,(
% 1.96/1.53 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : color,X8 : nat] : (isPer @ tree @ X5 @ (treeStar @ X5 @ X6 @ X7 @ X8)))),
% 1.96/1.53 file('/export/starexec/sandbox/tmp/tmp.cVGPrNYEYW/DTF2THF_23718.p','\'treeStar\'_is_per')).
% 1.96/1.53 thf(f87,plain,(
% 1.96/1.53 ($true != (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8))) | spl11_2),
% 1.96/1.53 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.96/1.53 thf(f92,plain,(
% 1.96/1.53 ~spl11_2 | spl11_3),
% 1.96/1.53 inference(avatar_split_clause,[status(thm)],[f78,f90,f85])).
% 1.96/1.53 thf(f78,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ X0)) | ((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8)))) )),
% 1.96/1.53 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.96/1.53 thf(f77,plain,(
% 1.96/1.53 ( ! [X0 : tree @ sK5] : (((treeStar @ sK5 @ sK6 @ red @ sK8 @ X0 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)) != $true) | ($true != $true) | ($true != (isPer @ tree @ sK5 @ (treeStar @ sK5 @ sK6 @ red @ sK8))) | ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ X0))) )),
% 1.96/1.53 inference(superposition,[status(thm)],[f70,f65])).
% 1.96/1.53 thf(f70,plain,(
% 1.96/1.53 ($true != (treeStar @ sK5 @ sK6 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rev @ sK5 @ red @ sK8 @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10))) @ (rt @ sK5 @ sK8 @ sK9 @ sK7 @ sK10)))),
% 1.96/1.53 inference(cnf_transformation,[status(thm)],[f56])).
% 1.96/1.53 % SZS output end Proof for DTF2THF_23718
% 1.96/1.53 % (24051)------------------------------
% 1.96/1.53 % (24051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.53 % (24051)Termination reason: Refutation
% 1.96/1.53
% 1.96/1.53 % (24051)Memory used [KB]: 6012
% 1.96/1.53 % (24051)Time elapsed: 0.093 s
% 1.96/1.53 % (24051)Instructions burned: 153 (million)
% 1.96/1.53 % (24051)------------------------------
% 1.96/1.53 % (24051)------------------------------
% 1.96/1.53 % (24045)Success in time 0.097 s
%------------------------------------------------------------------------------