%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT421^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:42 AM UTC 2026
% Result : Theorem 1.67s 1.30s
% Output : Refutation 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT421^1 : 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
% 0.14/0.32 % Computer : n023.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 06:17:34 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : DAT421^1 : TPTP v9.2.1. Released v9.2.0.
% 0.18/0.41 % Domain : Data Structures
% 0.18/0.41 % Problem : Reversal of a red-black-tree is an involution, RT substep 1
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English :
% 0.18/0.41
% 0.18/0.41 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.18/0.41 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.18/0.41 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.18/0.41 % Source : [Rot25]
% 0.18/0.41 % Names : RedBlackTree/rbt-rev-invol-subBTStep1.p [Rot25]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : ? v9.2.0
% 0.18/0.41 % Syntax : Number of formulae : 15 ( 3 unt; 11 typ; 0 def)
% 0.18/0.41 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.18/0.41 % Maximal formula atoms : 3 ( 1 avg)
% 0.18/0.41 % Number of connectives : 156 ( 0 ~; 0 |; 0 &; 154 @)
% 0.18/0.41 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 10 ( 7 avg)
% 0.18/0.41 % Number of types : 2 ( 2 usr)
% 0.18/0.41 % Number of type decls : 11 ( 4 !>P; 3 !>D)
% 0.18/0.41 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 10 ( 9 usr; 3 con; 0-7 aty)
% 0.18/0.41 % Number of variables : 30 ( 0 ^; 20 !; 0 ?; 30 :)
% 0.18/0.41 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.41 % SPC : DH1_THM_EQU_NAR
% 0.18/0.41
% 0.18/0.41 % Comments :
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 thf(color_type,type,
% 0.18/0.41 color: $tType ).
% 0.18/0.41
% 0.18/0.41 thf(black_type,type,
% 0.18/0.41 black: color ).
% 0.18/0.41
% 0.18/0.41 thf(red_type,type,
% 0.18/0.41 red: color ).
% 0.18/0.41
% 0.18/0.41 thf(nat_type,type,
% 0.18/0.41 nat: $tType ).
% 0.18/0.41
% 0.18/0.41 thf(zero_type,type,
% 0.18/0.41 zero: nat ).
% 0.18/0.41
% 0.18/0.41 thf(suc_type,type,
% 0.18/0.41 suc: nat > nat ).
% 0.18/0.41
% 0.18/0.41 thf(tree_type,type,
% 0.18/0.41 tree: $tType > color > nat > $tType ).
% 0.18/0.41
% 0.18/0.41 thf(leaf_type,type,
% 0.18/0.41 leaf:
% 0.18/0.41 !>[A: $tType] : ( tree @ A @ black @ zero ) ).
% 0.18/0.41
% 0.18/0.41 thf(redTree_type,type,
% 0.18/0.41 rt:
% 0.18/0.41 !>[A: $tType,N: nat] : ( ( tree @ A @ black @ N ) > A > ( tree @ A @ black @ N ) > ( tree @ A @ red @ N ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(blackTree_type,type,
% 0.18/0.41 bt:
% 0.18/0.41 !>[A: $tType,N: nat,C1: color,C2: color] : ( ( tree @ A @ C1 @ N ) > A > ( tree @ A @ C2 @ N ) > ( tree @ A @ black @ ( suc @ N ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(rbt_rev,type,
% 0.18/0.41 rev:
% 0.18/0.41 !>[A: $tType,C: color,N: nat] : ( ( tree @ A @ C @ N ) > ( tree @ A @ C @ N ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(rev_leaf,axiom,
% 0.18/0.41 ! [A: $tType] :
% 0.18/0.41 ( ( rev @ A @ black @ zero @ ( leaf @ A ) )
% 0.18/0.41 = ( leaf @ A ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(rev_bt,axiom,
% 0.18/0.41 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.18/0.41 ( ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) )
% 0.18/0.41 = ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(rev_rt,axiom,
% 0.18/0.41 ! [A: $tType,X: A,N: nat,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.18/0.41 ( ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) )
% 0.18/0.41 = ( rt @ A @ N @ ( rev @ A @ black @ N @ T2 ) @ X @ ( rev @ A @ black @ N @ T2 ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf(first_step,conjecture,
% 0.18/0.41 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.18/0.41 ( ( ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) )
% 0.18/0.41 = T1 )
% 0.18/0.41 => ( ( ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) )
% 0.18/0.41 = T2 )
% 0.18/0.41 => ( ( rev @ A @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) )
% 0.18/0.41 = ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ) ) ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.55/1.25 ---- Embedded in THF ---
% 1.55/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.25 %%% Generated on Tue Feb 24 06:17:35 EST 2026
% 1.55/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.25 %%% Logic specification used:
% 1.55/1.25 %%% thf(spec, logic, $$dhol).
% 1.55/1.25
% 1.55/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.qOURtYqgLD/DTF2DTF10968.p
% 1.55/1.25 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.55/1.25 thf(is_per, definition, (! [A:$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)))))))))).
% 1.55/1.25 thf(color_type, type, color: $tType).
% 1.55/1.25 thf(colorStar, type, 'colorStar': (color > (color > $o))).
% 1.55/1.25 thf(colorStar_is_eq, axiom, (! [X:color,Y:color]: (((('colorStar' @ X) @ Y) <=> (X = Y))))).
% 1.55/1.25 thf(black_type, type, black: color).
% 1.55/1.25 thf(red_type, type, red: color).
% 1.55/1.25 thf(nat_type, type, nat: $tType).
% 1.55/1.25 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.55/1.25 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.55/1.25 thf(zero_type, type, zero: nat).
% 1.55/1.25 thf(suc_type, type, suc: (nat > nat)).
% 1.55/1.25 thf(tree_type, type, tree: ($tType > $tType)).
% 1.55/1.25 thf(treeStar, type, 'treeStar': (!> [A:$tType]: (((A > (A > $o)) > (color > (nat > ((tree @ A) > ((tree @ A) > $o)))))))).
% 1.55/1.25 thf('\'treeStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:color]: ((! [C0:nat]: (((isPer @ (tree @ B)) @ ((((treeStar @ B) @ BStar) @ C) @ C0)))))))))).
% 1.55/1.25 thf(leaf_type, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 1.55/1.25 thf(leaf_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ (leaf @ A)) @ (leaf @ A)))))).
% 1.55/1.25 thf(redTree_type, type, rt: (!> [A:$tType]: ((nat > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))).
% 1.55/1.25 thf(rt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ (((((rt @ A) @ N) @ D) @ D0) @ D1)) @ (((((rt @ A) @ N) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))).
% 1.55/1.25 thf(blackTree_type, type, bt: (!> [A:$tType]: ((nat > (color > (color > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))))).
% 1.55/1.25 thf(bt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C2) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D) @ D0) @ D1)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))))))).
% 1.55/1.25 thf(rbt_rev, type, rev: (!> [A:$tType]: ((color > (nat > ((tree @ A) > (tree @ A))))))).
% 1.55/1.25 thf(rev_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [C:color]: ((! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C) @ N) @ D) @ D_prime) => ((((((treeStar @ A) @ AStar) @ C) @ N) @ ((((rev @ A) @ C) @ N) @ D)) @ ((((rev @ A) @ C) @ N) @ D_prime))))))))))))).
% 1.55/1.25 thf(rev_leaf, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ (leaf @ A))) @ (leaf @ A)))))).
% 1.55/1.25 thf(rev_bt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2))) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1))))))))))))))))))).
% 1.55/1.25 thf(rev_rt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ (((((rt @ A) @ N) @ T1) @ X) @ T2))) @ (((((rt @ A) @ N) @ ((((rev @ A) @ black) @ N) @ T2)) @ X) @ ((((rev @ A) @ black) @ N) @ T2))))))))))))))).
% 1.55/1.25 thf(first_step, conjecture, (! [A:$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) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ T1))) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ T2))) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2)))) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1)))))))))))))))))))))).
% 1.55/1.25 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.qOURtYqgLD/DTF2DTF10968.p
% 1.55/1.25 ------------------------
% 1.55/1.26 ---- Cleaned THF ---
% 1.55/1.26 thf(is_per_type,type,
% 1.55/1.26 isPer:
% 1.55/1.26 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.55/1.26
% 1.55/1.26 thf(is_per,definition,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 <=> ( ! [X: A,Y: A] :
% 1.55/1.26 ( ( AStar @ X @ Y )
% 1.55/1.26 => ( AStar @ Y @ X ) )
% 1.55/1.26 & ! [X: A,Y: A,Z: A] :
% 1.55/1.26 ( ( AStar @ X @ Y )
% 1.55/1.26 => ( ( AStar @ Y @ Z )
% 1.55/1.26 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(color_type,type,
% 1.55/1.26 color: $tType ).
% 1.55/1.26
% 1.55/1.26 thf(colorStar,type,
% 1.55/1.26 colorStar: color > color > $o ).
% 1.55/1.26
% 1.55/1.26 thf(colorStar_is_eq,axiom,
% 1.55/1.26 ! [X: color,Y: color] :
% 1.55/1.26 ( ( colorStar @ X @ Y )
% 1.55/1.26 <=> ( X = Y ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(black_type,type,
% 1.55/1.26 black: color ).
% 1.55/1.26
% 1.55/1.26 thf(red_type,type,
% 1.55/1.26 red: color ).
% 1.55/1.26
% 1.55/1.26 thf(nat_type,type,
% 1.55/1.26 nat: $tType ).
% 1.55/1.26
% 1.55/1.26 thf(natStar,type,
% 1.55/1.26 natStar: nat > nat > $o ).
% 1.55/1.26
% 1.55/1.26 thf(natStar_is_eq,axiom,
% 1.55/1.26 ! [X: nat,Y: nat] :
% 1.55/1.26 ( ( natStar @ X @ Y )
% 1.55/1.26 <=> ( X = Y ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(zero_type,type,
% 1.55/1.26 zero: nat ).
% 1.55/1.26
% 1.55/1.26 thf(suc_type,type,
% 1.55/1.26 suc: nat > nat ).
% 1.55/1.26
% 1.55/1.26 thf(tree_type,type,
% 1.55/1.26 tree: $tType > $tType ).
% 1.55/1.26
% 1.55/1.26 thf(treeStar,type,
% 1.55/1.26 treeStar:
% 1.55/1.26 !>[A: $tType] : ( ( A > A > $o ) > color > nat > ( tree @ A ) > ( tree @ A ) > $o ) ).
% 1.55/1.26
% 1.55/1.26 thf('\'treeStar\'_is_per',axiom,
% 1.55/1.26 ! [B: $tType,BStar: B > B > $o] :
% 1.55/1.26 ( ( isPer @ B @ BStar )
% 1.55/1.26 => ! [C: color,C0: nat] : ( isPer @ ( tree @ B ) @ ( treeStar @ B @ BStar @ C @ C0 ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(leaf_type,type,
% 1.55/1.26 leaf:
% 1.55/1.26 !>[A: $tType] : ( tree @ A ) ).
% 1.55/1.26
% 1.55/1.26 thf(leaf_tp_ax,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ( treeStar @ A @ AStar @ black @ zero @ ( leaf @ A ) @ ( leaf @ A ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(redTree_type,type,
% 1.55/1.26 rt:
% 1.55/1.26 !>[A: $tType] : ( nat > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rt_tp_ax,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ black @ N @ D @ D_prime )
% 1.55/1.26 => ! [D0: A,D0_prime: A] :
% 1.55/1.26 ( ( D0 = D0_prime )
% 1.55/1.26 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ black @ N @ D1 @ D1_prime )
% 1.55/1.26 => ( treeStar @ A @ AStar @ red @ N @ ( rt @ A @ N @ D @ D0 @ D1 ) @ ( rt @ A @ N @ D_prime @ D0_prime @ D1_prime ) ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(blackTree_type,type,
% 1.55/1.26 bt:
% 1.55/1.26 !>[A: $tType] : ( nat > color > color > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(bt_tp_ax,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [N: nat,C1: color,C2: color,D: tree @ A,D_prime: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ C1 @ N @ D @ D_prime )
% 1.55/1.26 => ! [D0: A,D0_prime: A] :
% 1.55/1.26 ( ( D0 = D0_prime )
% 1.55/1.26 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ C2 @ N @ D1 @ D1_prime )
% 1.55/1.26 => ( 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 ) ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rbt_rev,type,
% 1.55/1.26 rev:
% 1.55/1.26 !>[A: $tType] : ( color > nat > ( tree @ A ) > ( tree @ A ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rev_tp_ax,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [C: color,N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ C @ N @ D @ D_prime )
% 1.55/1.26 => ( treeStar @ A @ AStar @ C @ N @ ( rev @ A @ C @ N @ D ) @ ( rev @ A @ C @ N @ D_prime ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rev_leaf,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ( treeStar @ A @ AStar @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) @ ( leaf @ A ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rev_bt,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 1.55/1.26 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 1.55/1.26 => ( 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 ) ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(rev_rt,axiom,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [X: A,N: nat,T1: tree @ A,T2: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 1.55/1.26 => ( ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 1.55/1.26 => ( 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 @ T2 ) ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(first_step,conjecture,
% 1.55/1.26 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.26 ( ( isPer @ A @ AStar )
% 1.55/1.26 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.55/1.26 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 1.55/1.26 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 1.55/1.26 => ( ( treeStar @ A @ AStar @ C1 @ N @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ T1 )
% 1.55/1.26 => ( ( treeStar @ A @ AStar @ C2 @ N @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) @ T2 )
% 1.55/1.26 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ) ) ) ) ) ) ).
% 1.55/1.26 ------------------------
% 1.55/1.27 % (11071)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_10968 for (2999ds/27Mi)
% 1.55/1.28 % (11070)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_10968 for (2999ds/4Mi)
% 1.55/1.28 % (11069)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10968 for (2999ds/183Mi)
% 1.55/1.28 % (11072)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10968 for (2999ds/2Mi)
% 1.55/1.28 % (11073)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_10968 for (2999ds/2Mi)
% 1.55/1.28 % (11075)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10968 for (2999ds/18Mi)
% 1.55/1.28 % (11074)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_10968 for (2999ds/275Mi)
% 1.55/1.28 % (11072)Instruction limit reached!
% 1.55/1.28 % (11072)------------------------------
% 1.55/1.28 % (11072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (11072)Termination reason: Unknown
% 1.55/1.28 % (11073)Instruction limit reached!
% 1.55/1.28 % (11073)------------------------------
% 1.55/1.28 % (11073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (11073)Termination reason: Unknown
% 1.55/1.28 % (11073)Termination phase: shuffling
% 1.55/1.28
% 1.55/1.28 % (11073)Memory used [KB]: 1023
% 1.55/1.28 % (11073)Time elapsed: 0.002 s
% 1.55/1.28 % (11073)Instructions burned: 2 (million)
% 1.55/1.28 % (11073)------------------------------
% 1.55/1.28 % (11073)------------------------------
% 1.55/1.28 % (11072)Termination phase: shuffling
% 1.55/1.28
% 1.55/1.28 % (11072)Memory used [KB]: 1023
% 1.55/1.28 % (11072)Time elapsed: 0.002 s
% 1.55/1.28 % (11072)Instructions burned: 2 (million)
% 1.55/1.28 % (11072)------------------------------
% 1.55/1.28 % (11072)------------------------------
% 1.55/1.28 % (11070)Instruction limit reached!
% 1.55/1.28 % (11070)------------------------------
% 1.55/1.28 % (11070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (11070)Termination reason: Unknown
% 1.55/1.28 % (11070)Termination phase: shuffling
% 1.55/1.28
% 1.55/1.28 % (11070)Memory used [KB]: 1023
% 1.55/1.28 % (11070)Time elapsed: 0.003 s
% 1.55/1.28 % (11070)Instructions burned: 4 (million)
% 1.55/1.28 % (11070)------------------------------
% 1.55/1.28 % (11070)------------------------------
% 1.55/1.28 % (11071)Instruction limit reached!
% 1.55/1.28 % (11071)------------------------------
% 1.55/1.28 % (11071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (11071)Termination reason: Unknown
% 1.55/1.28 % (11071)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (11071)Memory used [KB]: 5756
% 1.55/1.28 % (11071)Time elapsed: 0.011 s
% 1.55/1.28 % (11071)Instructions burned: 28 (million)
% 1.55/1.28 % (11071)------------------------------
% 1.55/1.28 % (11071)------------------------------
% 1.55/1.29 % (11075)Instruction limit reached!
% 1.55/1.29 % (11075)------------------------------
% 1.55/1.29 % (11075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (11075)Termination reason: Unknown
% 1.55/1.29 % (11075)Termination phase: Saturation
% 1.55/1.29
% 1.55/1.29 % (11075)Memory used [KB]: 5628
% 1.55/1.29 % (11075)Time elapsed: 0.010 s
% 1.55/1.29 % (11075)Instructions burned: 18 (million)
% 1.55/1.29 % (11075)------------------------------
% 1.55/1.29 % (11075)------------------------------
% 1.55/1.29 % (11079)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_10968 for (2999ds/3Mi)
% 1.55/1.29 % (11079)Instruction limit reached!
% 1.55/1.29 % (11079)------------------------------
% 1.55/1.29 % (11079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (11079)Termination reason: Unknown
% 1.55/1.29 % (11079)Termination phase: shuffling
% 1.55/1.29
% 1.55/1.29 % (11079)Memory used [KB]: 1023
% 1.55/1.29 % (11079)Time elapsed: 0.002 s
% 1.55/1.29 % (11079)Instructions burned: 4 (million)
% 1.55/1.29 % (11079)------------------------------
% 1.55/1.29 % (11079)------------------------------
% 1.55/1.29 % (11074)First to succeed.
% 1.55/1.29 % (11076)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10968 for (2999ds/3Mi)
% 1.55/1.29 % (11077)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_10968 for (2999ds/37Mi)
% 1.55/1.29 % (11078)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_10968 for (2999ds/15Mi)
% 1.55/1.29 % Exception at run slice level
% 1.55/1.29 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
% 1.55/1.30 % (11076)Instruction limit reached!
% 1.55/1.30 % (11076)------------------------------
% 1.55/1.30 % (11076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (11076)Termination reason: Unknown
% 1.55/1.30 % (11076)Termination phase: shuffling
% 1.55/1.30
% 1.55/1.30 % (11076)Memory used [KB]: 1023
% 1.55/1.30 % (11076)Time elapsed: 0.003 s
% 1.55/1.30 % (11076)Instructions burned: 4 (million)
% 1.55/1.30 % (11076)------------------------------
% 1.55/1.30 % (11076)------------------------------
% 1.67/1.30 % (11074)Refutation found. Thanks to Tanya!
% 1.67/1.30 % SZS status Theorem for DTF2THF_10968
% 1.67/1.30 % SZS output start Proof for DTF2THF_10968
% 1.67/1.30 thf(type_def_6, type, color: $tType).
% 1.67/1.30 thf(type_def_7, type, nat: $tType).
% 1.67/1.30 thf(type_def_8, type, tree: ($tType) > $tType).
% 1.67/1.30 thf(type_def_9, type, sK0: $tType).
% 1.67/1.30 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.67/1.30 thf(func_def_2, type, color: $tType).
% 1.67/1.30 thf(func_def_3, type, colorStar: color > color > $o).
% 1.67/1.30 thf(func_def_4, type, black: color).
% 1.67/1.30 thf(func_def_5, type, red: color).
% 1.67/1.30 thf(func_def_6, type, nat: $tType).
% 1.67/1.30 thf(func_def_7, type, natStar: nat > nat > $o).
% 1.67/1.30 thf(func_def_8, type, zero: nat).
% 1.67/1.30 thf(func_def_9, type, suc: nat > nat).
% 1.67/1.30 thf(func_def_10, type, tree: ($tType) > $tType).
% 1.67/1.30 thf(func_def_11, type, treeStar: !>[X0: $tType]:((X0 > X0 > $o) > color > nat > tree @ X0 > tree @ X0 > $o)).
% 1.67/1.30 thf(func_def_12, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 1.67/1.30 thf(func_def_13, type, rt: !>[X0: $tType]:(nat > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.67/1.30 thf(func_def_14, type, bt: !>[X0: $tType]:(nat > color > color > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.67/1.30 thf(func_def_15, type, rev: !>[X0: $tType]:(color > nat > tree @ X0 > tree @ X0)).
% 1.67/1.30 thf(func_def_18, type, sK1: sK0 > sK0 > $o).
% 1.67/1.30 thf(func_def_19, type, sK2: sK0).
% 1.67/1.30 thf(func_def_20, type, sK3: nat).
% 1.67/1.30 thf(func_def_21, type, sK4: color).
% 1.67/1.30 thf(func_def_22, type, sK5: color).
% 1.67/1.30 thf(func_def_23, type, sK6: tree @ sK0).
% 1.67/1.30 thf(func_def_24, type, sK7: tree @ sK0).
% 1.67/1.30 thf(func_def_25, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.30 thf(func_def_26, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.30 thf(func_def_27, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.30 thf(func_def_28, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.30 thf(func_def_29, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.30 thf(func_def_31, type, ph14: !>[X0: $tType]:(X0)).
% 1.67/1.30 thf(f108,plain,(
% 1.67/1.30 $false),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f107,f63])).
% 1.67/1.30 thf(f63,plain,(
% 1.67/1.30 ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f50])).
% 1.67/1.30 thf(f50,plain,(
% 1.67/1.30 ($true = (isPer @ sK0 @ sK1)) & (($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) & ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) = $true) & ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7) = $true) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7))) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6))))) & ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) = $true))),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f41,f49,f48])).
% 1.67/1.30 thf(f48,plain,(
% 1.67/1.30 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X6)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) & ((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6)))) != $true) & ($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6)))) => (($true = (isPer @ sK0 @ sK1)) & ? [X7 : tree @ sK0,X6 : tree @ sK0,X5 : color,X4 : color,X3 : nat,X2 : sK0] : (($true = (treeStar @ sK0 @ sK1 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ X6)) @ X6)) & ($true = (treeStar @ sK0 @ sK1 @ X5 @ X3 @ X7 @ X7)) & ((treeStar @ sK0 @ sK1 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7)) @ X7) = $true) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ X3) @ (rev @ sK0 @ black @ (suc @ X3) @ (rev @ sK0 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ sK0 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X5 @ X4 @ (rev @ sK0 @ X5 @ X3 @ X7) @ X2 @ (rev @ sK0 @ X4 @ X3 @ X6))))) & ($true = (treeStar @ sK0 @ sK1 @ X4 @ X3 @ X6 @ X6))))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f49,plain,(
% 1.67/1.30 ? [X7 : tree @ sK0,X6 : tree @ sK0,X5 : color,X4 : color,X3 : nat,X2 : sK0] : (($true = (treeStar @ sK0 @ sK1 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ X6)) @ X6)) & ($true = (treeStar @ sK0 @ sK1 @ X5 @ X3 @ X7 @ X7)) & ((treeStar @ sK0 @ sK1 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7)) @ X7) = $true) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ X3) @ (rev @ sK0 @ black @ (suc @ X3) @ (rev @ sK0 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ sK0 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X5 @ X4 @ (rev @ sK0 @ X5 @ X3 @ X7) @ X2 @ (rev @ sK0 @ X4 @ X3 @ X6))))) & ($true = (treeStar @ sK0 @ sK1 @ X4 @ X3 @ X6 @ X6))) => (($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) & ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) = $true) & ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7) = $true) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7))) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6))))) & ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) = $true))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f41,plain,(
% 1.67/1.30 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) & ? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X6)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) & ((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6)))) != $true) & ($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6))))),
% 1.67/1.30 inference(flattening,[status(thm)],[f40])).
% 1.67/1.30 thf(f40,plain,(
% 1.67/1.30 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : ((((((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6)))) != $true) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7))) & ($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X6))) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7))) & ($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6))) & ((isPer @ X0 @ X1) = $true))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f20])).
% 1.67/1.30 thf(f20,plain,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6)) => (($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) => (($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X6)) => (($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) => ((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6)))) = $true))))))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f19])).
% 1.67/1.30 thf(f19,plain,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : ((treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6) => ((treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7) => ((treeStar @ X0 @ X1 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X6) => ((treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7) => (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6)))))))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f13])).
% 1.67/1.30 thf(f13,negated_conjecture,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X16 : color,X17 : color,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ X16 @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ X19 @ X19) => ((treeStar @ X0 @ X1 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ X18)) @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ X19)) @ X19) => (treeStar @ X0 @ X1 @ black @ (suc @ X9) @ (rev @ X0 @ black @ (suc @ X9) @ (rev @ X0 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X16 @ X17 @ X18 @ X2 @ X19))) @ (rev @ X0 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X17 @ X16 @ (rev @ X0 @ X17 @ X9 @ X19) @ X2 @ (rev @ X0 @ X16 @ X9 @ X18)))))))))),
% 1.67/1.30 inference(negated_conjecture,[status(cth)],[f12])).
% 1.67/1.30 thf(f12,conjecture,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X16 : color,X17 : color,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ X16 @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ X19 @ X19) => ((treeStar @ X0 @ X1 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ X18)) @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ X19)) @ X19) => (treeStar @ X0 @ X1 @ black @ (suc @ X9) @ (rev @ X0 @ black @ (suc @ X9) @ (rev @ X0 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X16 @ X17 @ X18 @ X2 @ X19))) @ (rev @ X0 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X17 @ X16 @ (rev @ X0 @ X17 @ X9 @ X19) @ X2 @ (rev @ X0 @ X16 @ X9 @ X18)))))))))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.qOURtYqgLD/DTF2THF_10968.p',first_step)).
% 1.67/1.30 thf(f107,plain,(
% 1.67/1.30 ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) != $true)),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f106,f60])).
% 1.67/1.30 thf(f60,plain,(
% 1.67/1.30 ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f50])).
% 1.67/1.30 thf(f106,plain,(
% 1.67/1.30 ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) != $true) | ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) != $true)),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f105,f65])).
% 1.67/1.30 thf(f65,plain,(
% 1.67/1.30 ($true = (isPer @ sK0 @ sK1))),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f50])).
% 1.67/1.30 thf(f105,plain,(
% 1.67/1.30 ($true != (isPer @ sK0 @ sK1)) | ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) != $true) | ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) != $true)),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.67/1.30 thf(f100,plain,(
% 1.67/1.30 ($true != (isPer @ sK0 @ sK1)) | ($true != $true) | ((treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7) != $true) | ((treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6) != $true)),
% 1.67/1.30 inference(superposition,[status(thm)],[f95,f59])).
% 1.67/1.30 thf(f59,plain,(
% 1.67/1.30 ( ! [X0 : $tType,X2 : X0,X3 : nat,X1 : X0 > X0 > $o,X6 : tree @ X0,X7 : tree @ X0,X4 : color,X5 : color] : (((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6))) = $true) | ($true != (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6)) | ($true != (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) | ((isPer @ X0 @ X1) != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f43])).
% 1.67/1.30 thf(f43,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6))) = $true) | ($true != (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) | ($true != (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6))))),
% 1.67/1.30 inference(flattening,[status(thm)],[f42])).
% 1.67/1.30 thf(f42,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : ((((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6))) = $true) | ($true != (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7))) | ($true != (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6))) | ((isPer @ X0 @ X1) != $true))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f24])).
% 1.67/1.30 thf(f24,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6)) => (($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7)) => ((treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6))) = $true))))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f23])).
% 1.67/1.30 thf(f23,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : ((treeStar @ X0 @ X1 @ X4 @ X3 @ X6 @ X6) => ((treeStar @ X0 @ X1 @ X5 @ X3 @ X7 @ X7) => (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (rev @ X0 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)) @ (bt @ X0 @ X3 @ X5 @ X4 @ (rev @ X0 @ X5 @ X3 @ X7) @ X2 @ (rev @ X0 @ X4 @ X3 @ X6))))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f10])).
% 1.67/1.30 thf(f10,axiom,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X16 : color,X17 : color,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ X16 @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ X19 @ X19) => (treeStar @ X0 @ X1 @ black @ (suc @ X9) @ (rev @ X0 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X16 @ X17 @ X18 @ X2 @ X19)) @ (bt @ X0 @ X9 @ X17 @ X16 @ (rev @ X0 @ X17 @ X9 @ X19) @ X2 @ (rev @ X0 @ X16 @ X9 @ X18))))))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.qOURtYqgLD/DTF2THF_10968.p',rev_bt)).
% 1.67/1.30 thf(f95,plain,(
% 1.67/1.30 ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7)) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6))))),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f79,f65])).
% 1.67/1.30 thf(f79,plain,(
% 1.67/1.30 ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7)) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)))) | ($true != (isPer @ sK0 @ sK1))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.67/1.30 thf(f76,plain,(
% 1.67/1.30 ($true != (isPer @ sK0 @ sK1)) | ($true != $true) | ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7)) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6))))),
% 1.67/1.30 inference(superposition,[status(thm)],[f61,f57])).
% 1.67/1.30 thf(f57,plain,(
% 1.67/1.30 ( ! [X0 : $tType,X2 : color,X3 : nat,X1 : X0 > X0 > $o,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)) = $true) | ((isPer @ X0 @ X1) != $true) | ($true != (treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5))) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f46])).
% 1.67/1.30 thf(f46,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (($true != (treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) | ((treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)) = $true)) | ((isPer @ X0 @ X1) != $true))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f34])).
% 1.67/1.30 thf(f34,plain,(
% 1.67/1.30 ! [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)) => ((treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)) = $true)))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f33])).
% 1.67/1.30 thf(f33,plain,(
% 1.67/1.30 ! [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))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f8])).
% 1.67/1.30 thf(f8,axiom,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X7 : color,X9 : nat,X10 : tree @ X0,X11 : tree @ X0] : ((treeStar @ X0 @ X1 @ X7 @ X9 @ X10 @ X11) => (treeStar @ X0 @ X1 @ X7 @ X9 @ (rev @ X0 @ X7 @ X9 @ X10) @ (rev @ X0 @ X7 @ X9 @ X11))))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.qOURtYqgLD/DTF2THF_10968.p',rev_tp_ax)).
% 1.67/1.30 thf(f61,plain,(
% 1.67/1.30 ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7))) @ (rev @ sK0 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK5 @ sK4 @ (rev @ sK0 @ sK5 @ sK3 @ sK7) @ sK2 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)))))),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f50])).
% 1.67/1.30 % SZS output end Proof for DTF2THF_10968
% 1.67/1.30 % (11074)------------------------------
% 1.67/1.30 % (11074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (11074)Termination reason: Refutation
% 1.67/1.30
% 1.67/1.30 % (11074)Memory used [KB]: 5756
% 1.67/1.30 % (11074)Time elapsed: 0.019 s
% 1.67/1.30 % (11074)Instructions burned: 30 (million)
% 1.67/1.30 % (11074)------------------------------
% 1.67/1.30 % (11074)------------------------------
% 1.67/1.30 % (11068)Success in time 0.031 s
%------------------------------------------------------------------------------