%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT423^1 : 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 : n004.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 2.25s 1.52s
% Output : Refutation 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT423^1 : 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
% 0.16/0.34 % Computer : n004.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:16:41 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : DAT423^1 : TPTP v9.2.1. Released v9.2.0.
% 0.31/0.47 % Domain : Data Structures
% 0.31/0.47 % Problem : Reversal of a red-black-tree is an involution, RT substep 3
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.31/0.47 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.31/0.47 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.31/0.47 % Source : [Rot25]
% 0.31/0.47 % Names : RedBlackTree/rbt-rev-invol-subBTStep3.p [Rot25]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : ? v9.2.0
% 0.31/0.47 % Syntax : Number of formulae : 17 ( 3 unt; 11 typ; 0 def)
% 0.31/0.47 % Number of atoms : 12 ( 12 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 3 ( 2 avg)
% 0.31/0.47 % Number of connectives : 277 ( 0 ~; 0 |; 0 &; 271 @)
% 0.31/0.47 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 10 ( 8 avg)
% 0.31/0.47 % Number of types : 2 ( 2 usr)
% 0.31/0.47 % Number of type decls : 11 ( 4 !>P; 3 !>D)
% 0.31/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 10 ( 9 usr; 3 con; 0-7 aty)
% 0.31/0.47 % Number of variables : 44 ( 0 ^; 34 !; 0 ?; 44 :)
% 0.31/0.47 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.47 % SPC : DH1_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments :
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(color_type,type,
% 0.31/0.47 color: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(black_type,type,
% 0.31/0.47 black: color ).
% 0.31/0.47
% 0.31/0.47 thf(red_type,type,
% 0.31/0.47 red: color ).
% 0.31/0.47
% 0.31/0.47 thf(nat_type,type,
% 0.31/0.47 nat: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(zero_type,type,
% 0.31/0.47 zero: nat ).
% 0.31/0.47
% 0.31/0.47 thf(suc_type,type,
% 0.31/0.47 suc: nat > nat ).
% 0.31/0.47
% 0.31/0.47 thf(tree_type,type,
% 0.31/0.47 tree: $tType > color > nat > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(leaf_type,type,
% 0.31/0.47 leaf:
% 0.31/0.47 !>[A: $tType] : ( tree @ A @ black @ zero ) ).
% 0.31/0.47
% 0.31/0.47 thf(redTree_type,type,
% 0.31/0.47 rt:
% 0.31/0.47 !>[A: $tType,N: nat] : ( ( tree @ A @ black @ N ) > A > ( tree @ A @ black @ N ) > ( tree @ A @ red @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(blackTree_type,type,
% 0.31/0.47 bt:
% 0.31/0.47 !>[A: $tType,N: nat,C1: color,C2: color] : ( ( tree @ A @ C1 @ N ) > A > ( tree @ A @ C2 @ N ) > ( tree @ A @ black @ ( suc @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(rbt_rev,type,
% 0.31/0.47 rev:
% 0.31/0.47 !>[A: $tType,C: color,N: nat] : ( ( tree @ A @ C @ N ) > ( tree @ A @ C @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(rev_leaf,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( rev @ A @ black @ zero @ ( leaf @ A ) )
% 0.31/0.47 = ( leaf @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(rev_bt,axiom,
% 0.31/0.47 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.31/0.47 ( ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) )
% 0.31/0.47 = ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(rev_rt,axiom,
% 0.31/0.47 ! [A: $tType,X: A,N: nat,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.31/0.47 ( ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) )
% 0.31/0.47 = ( rt @ A @ N @ ( rev @ A @ black @ N @ T2 ) @ X @ ( rev @ A @ black @ N @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(first_step,axiom,
% 0.31/0.47 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.31/0.47 ( ( ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) )
% 0.31/0.47 = T1 )
% 0.31/0.47 => ( ( ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) )
% 0.31/0.47 = T2 )
% 0.31/0.47 => ( ( rev @ A @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) )
% 0.31/0.47 = ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(second_step,axiom,
% 0.31/0.47 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.31/0.47 ( ( ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) )
% 0.31/0.47 = T1 )
% 0.31/0.47 => ( ( ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) )
% 0.31/0.47 = T2 )
% 0.31/0.47 => ( ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) )
% 0.31/0.47 = ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ X @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(third_step,conjecture,
% 0.31/0.47 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.31/0.47 ( ( ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) )
% 0.31/0.47 = T1 )
% 0.31/0.47 => ( ( ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) )
% 0.31/0.47 = T2 )
% 0.31/0.47 => ( ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ X @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) )
% 0.31/0.47 = ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.01/1.48 ---- Embedded in THF ---
% 2.01/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.01/1.48 %%% Generated on Tue Feb 24 06:16:42 EST 2026
% 2.01/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.01/1.48 %%% Logic specification used:
% 2.01/1.48 %%% thf(spec, logic, $$dhol).
% 2.01/1.48
% 2.01/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.To87vZeRvk/DTF2DTF26358.p
% 2.01/1.48 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 2.01/1.48 thf(is_per, definition, (! [A:$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)))))))))).
% 2.01/1.48 thf(color_type, type, color: $tType).
% 2.01/1.48 thf(colorStar, type, 'colorStar': (color > (color > $o))).
% 2.01/1.48 thf(colorStar_is_eq, axiom, (! [X:color,Y:color]: (((('colorStar' @ X) @ Y) <=> (X = Y))))).
% 2.01/1.48 thf(black_type, type, black: color).
% 2.01/1.48 thf(red_type, type, red: color).
% 2.01/1.48 thf(nat_type, type, nat: $tType).
% 2.01/1.48 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 2.01/1.48 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 2.01/1.48 thf(zero_type, type, zero: nat).
% 2.01/1.48 thf(suc_type, type, suc: (nat > nat)).
% 2.01/1.48 thf(tree_type, type, tree: ($tType > $tType)).
% 2.01/1.48 thf(treeStar, type, 'treeStar': (!> [A:$tType]: (((A > (A > $o)) > (color > (nat > ((tree @ A) > ((tree @ A) > $o)))))))).
% 2.01/1.48 thf('\'treeStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:color]: ((! [C0:nat]: (((isPer @ (tree @ B)) @ ((((treeStar @ B) @ BStar) @ C) @ C0)))))))))).
% 2.01/1.48 thf(leaf_type, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 2.01/1.48 thf(leaf_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ (leaf @ A)) @ (leaf @ A)))))).
% 2.01/1.48 thf(redTree_type, type, rt: (!> [A:$tType]: ((nat > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))).
% 2.01/1.48 thf(rt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ (((((rt @ A) @ N) @ D) @ D0) @ D1)) @ (((((rt @ A) @ N) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))).
% 2.01/1.48 thf(blackTree_type, type, bt: (!> [A:$tType]: ((nat > (color > (color > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))))).
% 2.01/1.48 thf(bt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C2) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D) @ D0) @ D1)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))))))).
% 2.01/1.48 thf(rbt_rev, type, rev: (!> [A:$tType]: ((color > (nat > ((tree @ A) > (tree @ A))))))).
% 2.01/1.48 thf(rev_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [C:color]: ((! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C) @ N) @ D) @ D_prime) => ((((((treeStar @ A) @ AStar) @ C) @ N) @ ((((rev @ A) @ C) @ N) @ D)) @ ((((rev @ A) @ C) @ N) @ D_prime))))))))))))).
% 2.01/1.48 thf(rev_leaf, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ (leaf @ A))) @ (leaf @ A)))))).
% 2.01/1.48 thf(rev_bt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2))) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1))))))))))))))))))).
% 2.01/1.48 thf(rev_rt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ (((((rt @ A) @ N) @ T1) @ X) @ T2))) @ (((((rt @ A) @ N) @ ((((rev @ A) @ black) @ N) @ T2)) @ X) @ ((((rev @ A) @ black) @ N) @ T2))))))))))))))).
% 2.01/1.48 thf(first_step, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => (((((((treeStar @ A) @ AStar) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ T1))) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ T2))) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2)))) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1)))))))))))))))))))))).
% 2.01/1.48 thf(second_step, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => (((((((treeStar @ A) @ AStar) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ T1))) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ T2))) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C2) @ C1) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1)))) @ (((((((bt @ A) @ N) @ C1) @ C2) @ ((((rev @ A) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ T1))) @ X) @ ((((rev @ A) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ T2)))))))))))))))))))))).
% 2.01/1.48 thf(third_step, conjecture, (! [A:$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)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ ((((rev @ A) @ C1) @ N) @ ((((rev @ A) @ C1) @ N) @ T1))) @ X) @ ((((rev @ A) @ C2) @ N) @ ((((rev @ A) @ C2) @ N) @ T2)))) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2)))))))))))))))))))).
% 2.01/1.48 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.To87vZeRvk/DTF2DTF26358.p
% 2.01/1.48 ------------------------
% 2.01/1.50 ---- Cleaned THF ---
% 2.01/1.50 thf(is_per_type,type,
% 2.01/1.50 isPer:
% 2.01/1.50 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 2.01/1.50
% 2.01/1.50 thf(is_per,definition,
% 2.01/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.01/1.50 ( ( isPer @ A @ AStar )
% 2.01/1.50 <=> ( ! [X: A,Y: A] :
% 2.01/1.50 ( ( AStar @ X @ Y )
% 2.01/1.50 => ( AStar @ Y @ X ) )
% 2.01/1.50 & ! [X: A,Y: A,Z: A] :
% 2.01/1.50 ( ( AStar @ X @ Y )
% 2.01/1.50 => ( ( AStar @ Y @ Z )
% 2.01/1.50 => ( AStar @ X @ Z ) ) ) ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(color_type,type,
% 2.01/1.50 color: $tType ).
% 2.01/1.50
% 2.01/1.50 thf(colorStar,type,
% 2.01/1.50 colorStar: color > color > $o ).
% 2.01/1.50
% 2.01/1.50 thf(colorStar_is_eq,axiom,
% 2.01/1.50 ! [X: color,Y: color] :
% 2.01/1.50 ( ( colorStar @ X @ Y )
% 2.01/1.50 <=> ( X = Y ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(black_type,type,
% 2.01/1.50 black: color ).
% 2.01/1.50
% 2.01/1.50 thf(red_type,type,
% 2.01/1.50 red: color ).
% 2.01/1.50
% 2.01/1.50 thf(nat_type,type,
% 2.01/1.50 nat: $tType ).
% 2.01/1.50
% 2.01/1.50 thf(natStar,type,
% 2.01/1.50 natStar: nat > nat > $o ).
% 2.01/1.50
% 2.01/1.50 thf(natStar_is_eq,axiom,
% 2.01/1.50 ! [X: nat,Y: nat] :
% 2.01/1.50 ( ( natStar @ X @ Y )
% 2.01/1.50 <=> ( X = Y ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(zero_type,type,
% 2.01/1.50 zero: nat ).
% 2.01/1.50
% 2.01/1.50 thf(suc_type,type,
% 2.01/1.50 suc: nat > nat ).
% 2.01/1.50
% 2.01/1.50 thf(tree_type,type,
% 2.01/1.50 tree: $tType > $tType ).
% 2.01/1.50
% 2.01/1.50 thf(treeStar,type,
% 2.01/1.50 treeStar:
% 2.01/1.50 !>[A: $tType] : ( ( A > A > $o ) > color > nat > ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.01/1.50
% 2.01/1.50 thf('\'treeStar\'_is_per',axiom,
% 2.01/1.50 ! [B: $tType,BStar: B > B > $o] :
% 2.01/1.50 ( ( isPer @ B @ BStar )
% 2.01/1.50 => ! [C: color,C0: nat] : ( isPer @ ( tree @ B ) @ ( treeStar @ B @ BStar @ C @ C0 ) ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(leaf_type,type,
% 2.01/1.50 leaf:
% 2.01/1.50 !>[A: $tType] : ( tree @ A ) ).
% 2.01/1.50
% 2.01/1.50 thf(leaf_tp_ax,axiom,
% 2.01/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.01/1.50 ( ( isPer @ A @ AStar )
% 2.01/1.50 => ( treeStar @ A @ AStar @ black @ zero @ ( leaf @ A ) @ ( leaf @ A ) ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(redTree_type,type,
% 2.01/1.50 rt:
% 2.01/1.50 !>[A: $tType] : ( nat > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.01/1.50
% 2.01/1.50 thf(rt_tp_ax,axiom,
% 2.01/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.01/1.50 ( ( isPer @ A @ AStar )
% 2.01/1.50 => ! [N: nat,D: tree @ A,D_prime: tree @ A] :
% 2.01/1.50 ( ( treeStar @ A @ AStar @ black @ N @ D @ D_prime )
% 2.01/1.50 => ! [D0: A,D0_prime: A] :
% 2.01/1.50 ( ( D0 = D0_prime )
% 2.01/1.50 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 2.01/1.50 ( ( treeStar @ A @ AStar @ black @ N @ D1 @ D1_prime )
% 2.25/1.50 => ( treeStar @ A @ AStar @ red @ N @ ( rt @ A @ N @ D @ D0 @ D1 ) @ ( rt @ A @ N @ D_prime @ D0_prime @ D1_prime ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(blackTree_type,type,
% 2.25/1.50 bt:
% 2.25/1.50 !>[A: $tType] : ( nat > color > color > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(bt_tp_ax,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [N: nat,C1: color,C2: color,D: tree @ A,D_prime: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C1 @ N @ D @ D_prime )
% 2.25/1.50 => ! [D0: A,D0_prime: A] :
% 2.25/1.50 ( ( D0 = D0_prime )
% 2.25/1.50 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C2 @ N @ D1 @ D1_prime )
% 2.25/1.50 => ( 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 ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(rbt_rev,type,
% 2.25/1.50 rev:
% 2.25/1.50 !>[A: $tType] : ( color > nat > ( tree @ A ) > ( tree @ A ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(rev_tp_ax,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [C: color,N: nat,D: tree @ A,D_prime: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C @ N @ D @ D_prime )
% 2.25/1.50 => ( treeStar @ A @ AStar @ C @ N @ ( rev @ A @ C @ N @ D ) @ ( rev @ A @ C @ N @ D_prime ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(rev_leaf,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ( treeStar @ A @ AStar @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) @ ( leaf @ A ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(rev_bt,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 2.25/1.50 => ( 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 ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(rev_rt,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [X: A,N: nat,T1: tree @ A,T2: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 2.25/1.50 => ( 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 ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(first_step,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C1 @ N @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) @ T2 )
% 2.25/1.50 => ( 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 ) ) ) ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(second_step,axiom,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C1 @ N @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) @ T2 )
% 2.25/1.50 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C2 @ C1 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) @ ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ X @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) ) ) ) ) ) ) ) ).
% 2.25/1.50
% 2.25/1.50 thf(third_step,conjecture,
% 2.25/1.50 ! [A: $tType,AStar: A > A > $o] :
% 2.25/1.50 ( ( isPer @ A @ AStar )
% 2.25/1.50 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 2.25/1.50 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C1 @ N @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ T1 )
% 2.25/1.50 => ( ( treeStar @ A @ AStar @ C2 @ N @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) @ T2 )
% 2.25/1.50 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C1 @ N @ ( rev @ A @ C1 @ N @ T1 ) ) @ X @ ( rev @ A @ C2 @ N @ ( rev @ A @ C2 @ N @ T2 ) ) ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) ) ) ) ) ) ).
% 2.25/1.50 ------------------------
% 2.25/1.51 % (26571)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26358 for (2999ds/2Mi)
% 2.25/1.51 % (26574)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26358 for (2999ds/18Mi)
% 2.25/1.51 % (26572)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_26358 for (2999ds/2Mi)
% 2.25/1.51 % (26573)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_26358 for (2999ds/275Mi)
% 2.25/1.51 % Exception at run slice level
% 2.25/1.51 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
% 2.25/1.51 % (26571)Instruction limit reached!
% 2.25/1.51 % (26571)------------------------------
% 2.25/1.51 % (26571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.51 % (26571)Termination reason: Unknown
% 2.25/1.51 % (26571)Termination phase: shuffling
% 2.25/1.51
% 2.25/1.51 % (26571)Memory used [KB]: 1023
% 2.25/1.51 % (26571)Time elapsed: 0.003 s
% 2.25/1.51 % (26571)Instructions burned: 4 (million)
% 2.25/1.51 % (26571)------------------------------
% 2.25/1.51 % (26571)------------------------------
% 2.25/1.51 % (26568)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26358 for (2999ds/183Mi)
% 2.25/1.52 % (26574)Instruction limit reached!
% 2.25/1.52 % (26574)------------------------------
% 2.25/1.52 % (26574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.52 % (26574)Termination reason: Unknown
% 2.25/1.52 % (26574)Termination phase: Saturation
% 2.25/1.52
% 2.25/1.52 % (26574)Memory used [KB]: 1151
% 2.25/1.52 % (26574)Time elapsed: 0.007 s
% 2.25/1.52 % (26574)Instructions burned: 18 (million)
% 2.25/1.52 % (26574)------------------------------
% 2.25/1.52 % (26574)------------------------------
% 2.25/1.52 % (26569)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_26358 for (2999ds/4Mi)
% 2.25/1.52 % (26570)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_26358 for (2999ds/27Mi)
% 2.25/1.52 % (26569)Instruction limit reached!
% 2.25/1.52 % (26569)------------------------------
% 2.25/1.52 % (26569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.52 % (26569)Termination reason: Unknown
% 2.25/1.52 % (26569)Termination phase: shuffling
% 2.25/1.52
% 2.25/1.52 % (26569)Memory used [KB]: 1023
% 2.25/1.52 % (26569)Time elapsed: 0.004 s
% 2.25/1.52 % (26569)Instructions burned: 4 (million)
% 2.25/1.52 % (26569)------------------------------
% 2.25/1.52 % (26569)------------------------------
% 2.25/1.52 % (26576)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_26358 for (2999ds/37Mi)
% 2.25/1.52 % (26573)First to succeed.
% 2.25/1.52 % Exception at run slice level
% 2.25/1.52 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
% 2.25/1.52 % (26575)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26358 for (2999ds/3Mi)
% 2.25/1.52 % (26575)Instruction limit reached!
% 2.25/1.52 % (26575)------------------------------
% 2.25/1.52 % (26575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.52 % (26575)Termination reason: Unknown
% 2.25/1.52 % (26575)Termination phase: shuffling
% 2.25/1.52
% 2.25/1.52 % (26575)Memory used [KB]: 1023
% 2.25/1.52 % (26575)Time elapsed: 0.003 s
% 2.25/1.52 % (26575)Instructions burned: 4 (million)
% 2.25/1.52 % (26575)------------------------------
% 2.25/1.52 % (26575)------------------------------
% 2.25/1.52 % (26573)Refutation found. Thanks to Tanya!
% 2.25/1.52 % SZS status Theorem for DTF2THF_26358
% 2.25/1.52 % SZS output start Proof for DTF2THF_26358
% 2.25/1.52 thf(type_def_6, type, color: $tType).
% 2.25/1.52 thf(type_def_7, type, nat: $tType).
% 2.25/1.52 thf(type_def_8, type, tree: ($tType) > $tType).
% 2.25/1.52 thf(type_def_9, type, sK0: $tType).
% 2.25/1.52 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 2.25/1.52 thf(func_def_2, type, color: $tType).
% 2.25/1.52 thf(func_def_3, type, colorStar: color > color > $o).
% 2.25/1.52 thf(func_def_4, type, black: color).
% 2.25/1.52 thf(func_def_5, type, red: color).
% 2.25/1.52 thf(func_def_6, type, nat: $tType).
% 2.25/1.52 thf(func_def_7, type, natStar: nat > nat > $o).
% 2.25/1.52 thf(func_def_8, type, zero: nat).
% 2.25/1.52 thf(func_def_9, type, suc: nat > nat).
% 2.25/1.52 thf(func_def_10, type, tree: ($tType) > $tType).
% 2.25/1.52 thf(func_def_11, type, treeStar: !>[X0: $tType]:((X0 > X0 > $o) > color > nat > tree @ X0 > tree @ X0 > $o)).
% 2.25/1.52 thf(func_def_12, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 2.25/1.52 thf(func_def_13, type, rt: !>[X0: $tType]:(nat > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 2.25/1.52 thf(func_def_14, type, bt: !>[X0: $tType]:(nat > color > color > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 2.25/1.52 thf(func_def_15, type, rev: !>[X0: $tType]:(color > nat > tree @ X0 > tree @ X0)).
% 2.25/1.52 thf(func_def_18, type, sK1: sK0 > sK0 > $o).
% 2.25/1.52 thf(func_def_19, type, sK2: sK0).
% 2.25/1.52 thf(func_def_20, type, sK3: nat).
% 2.25/1.52 thf(func_def_21, type, sK4: color).
% 2.25/1.52 thf(func_def_22, type, sK5: color).
% 2.25/1.52 thf(func_def_23, type, sK6: tree @ sK0).
% 2.25/1.52 thf(func_def_24, type, sK7: tree @ sK0).
% 2.25/1.52 thf(func_def_25, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.25/1.52 thf(func_def_26, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.25/1.52 thf(func_def_27, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.25/1.52 thf(func_def_28, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.25/1.52 thf(func_def_29, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.25/1.52 thf(func_def_31, type, ph14: !>[X0: $tType]:(X0)).
% 2.25/1.52 thf(f109,plain,(
% 2.25/1.52 $false),
% 2.25/1.52 inference(subsumption_resolution,[status(thm)],[f108,f73])).
% 2.25/1.52 thf(f73,plain,(
% 2.25/1.52 ($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6))),
% 2.25/1.52 inference(cnf_transformation,[status(thm)],[f60])).
% 2.25/1.52 thf(f60,plain,(
% 2.25/1.52 (($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) & ($true = (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7)) & ($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6)) & ($true = (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7)) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK2 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7))) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7)))) & ($true = (isPer @ sK0 @ sK1))),
% 2.25/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f57,f59,f58])).
% 2.25/1.52 thf(f58,plain,(
% 2.25/1.52 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($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 @ X4 @ X3 @ X6 @ X6)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) & ($true != (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7))) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)))) & ((isPer @ X0 @ X1) = $true)) => (? [X7 : tree @ sK0,X6 : tree @ sK0,X5 : color,X4 : color,X3 : nat,X2 : sK0] : (($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 @ X4 @ X3 @ X6 @ X6) = $true) & ($true = (treeStar @ sK0 @ sK1 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7)) @ X7)) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X4 @ X5 @ (rev @ sK0 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7))) @ (bt @ sK0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)))) & ($true = (isPer @ sK0 @ sK1)))),
% 2.25/1.52 introduced(definition,[],[choice_axiom])).
% 2.25/1.52 thf(f59,plain,(
% 2.25/1.52 ? [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 @ X4 @ X3 @ X6 @ X6) = $true) & ($true = (treeStar @ sK0 @ sK1 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7)) @ X7)) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ X3) @ (bt @ sK0 @ X3 @ X4 @ X5 @ (rev @ sK0 @ X4 @ X3 @ (rev @ sK0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ sK0 @ X5 @ X3 @ (rev @ sK0 @ X5 @ X3 @ X7))) @ (bt @ sK0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)))) => (($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) & ($true = (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ sK7 @ sK7)) & ($true = (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ sK6 @ sK6)) & ($true = (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7)) & ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK2 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7))) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7))))),
% 2.25/1.52 introduced(definition,[],[choice_axiom])).
% 2.25/1.52 thf(f57,plain,(
% 2.25/1.52 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : (($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 @ X4 @ X3 @ X6 @ X6)) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) & ($true != (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7))) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)))) & ((isPer @ X0 @ X1) = $true))),
% 2.25/1.52 inference(flattening,[status(thm)],[f56])).
% 2.25/1.52 thf(f56,plain,(
% 2.25/1.52 ? [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : nat,X4 : color,X5 : color,X6 : tree @ X0,X7 : tree @ X0] : ((((($true != (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7))) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))) & ($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7))) & ($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))),
% 2.25/1.52 inference(ennf_transformation,[status(thm)],[f42])).
% 2.25/1.52 thf(f42,plain,(
% 2.25/1.52 ~! [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)) => (($true = (treeStar @ X0 @ X1 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7)) @ X7)) => ($true = (treeStar @ X0 @ X1 @ black @ (suc @ X3) @ (bt @ X0 @ X3 @ X4 @ X5 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7))) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7))))))))),
% 2.25/1.52 inference(fool_elimination,[status(thm)],[f41])).
% 2.25/1.52 thf(f41,plain,(
% 2.25/1.52 ~! [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) @ (bt @ X0 @ X3 @ X4 @ X5 @ (rev @ X0 @ X4 @ X3 @ (rev @ X0 @ X4 @ X3 @ X6)) @ X2 @ (rev @ X0 @ X5 @ X3 @ (rev @ X0 @ X5 @ X3 @ X7))) @ (bt @ X0 @ X3 @ X4 @ X5 @ X6 @ X2 @ X7)))))))),
% 2.25/1.52 inference(rectify,[status(thm)],[f15])).
% 2.25/1.52 thf(f15,negated_conjecture,(
% 2.25/1.52 ~! [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) @ (bt @ X0 @ X9 @ X16 @ X17 @ (rev @ X0 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ X18)) @ X2 @ (rev @ X0 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ X19))) @ (bt @ X0 @ X9 @ X16 @ X17 @ X18 @ X2 @ X19)))))))),
% 2.25/1.52 inference(negated_conjecture,[status(cth)],[f14])).
% 2.25/1.52 thf(f14,conjecture,(
% 2.25/1.52 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : X0,X9 : nat,X16 : color,X17 : color,X18 : tree @ X0,X19 : tree @ X0] : ((treeStar @ X0 @ X1 @ X16 @ X9 @ X18 @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ X19 @ X19) => ((treeStar @ X0 @ X1 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ X18)) @ X18) => ((treeStar @ X0 @ X1 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ X19)) @ X19) => (treeStar @ X0 @ X1 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X16 @ X17 @ (rev @ X0 @ X16 @ X9 @ (rev @ X0 @ X16 @ X9 @ X18)) @ X2 @ (rev @ X0 @ X17 @ X9 @ (rev @ X0 @ X17 @ X9 @ X19))) @ (bt @ X0 @ X9 @ X16 @ X17 @ X18 @ X2 @ X19)))))))),
% 2.25/1.52 file('/export/starexec/sandbox/tmp/tmp.To87vZeRvk/DTF2THF_26358.p',third_step)).
% 2.25/1.52 thf(f108,plain,(
% 2.25/1.52 ($true != (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6))),
% 2.25/1.52 inference(subsumption_resolution,[status(thm)],[f107,f70])).
% 2.25/1.52 thf(f70,plain,(
% 2.25/1.52 ($true = (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7))),
% 2.25/1.52 inference(cnf_transformation,[status(thm)],[f60])).
% 2.25/1.52 thf(f107,plain,(
% 2.25/1.52 ($true != (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7)) | ($true != (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6))),
% 2.25/1.52 inference(subsumption_resolution,[status(thm)],[f91,f68])).
% 2.25/1.52 thf(f68,plain,(
% 2.25/1.52 ($true = (isPer @ sK0 @ sK1))),
% 2.25/1.52 inference(cnf_transformation,[status(thm)],[f60])).
% 2.25/1.52 thf(f91,plain,(
% 2.25/1.52 ($true != (isPer @ sK0 @ sK1)) | ($true != (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) | ($true != (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7))),
% 2.25/1.52 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 2.25/1.52 thf(f88,plain,(
% 2.25/1.52 ($true != (isPer @ sK0 @ sK1)) | ($true != (treeStar @ sK0 @ sK1 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK6)) | ($true != (treeStar @ sK0 @ sK1 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7)) @ sK7)) | ($true != $true)),
% 2.25/1.52 inference(superposition,[status(thm)],[f69,f87])).
% 2.25/1.52 thf(f87,plain,(
% 2.25/1.52 ( ! [X0 : $tType,X2 : nat,X3 : color,X10 : tree @ X0,X1 : X0 > X0 > $o,X8 : X0,X6 : tree @ X0,X9 : tree @ X0,X4 : color,X5 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ black @ (suc @ X2) @ (bt @ X0 @ X2 @ X3 @ X4 @ X5 @ X8 @ X9) @ (bt @ X0 @ X2 @ X3 @ X4 @ X6 @ X8 @ X10))) | ($true != (treeStar @ X0 @ X1 @ X4 @ X2 @ X9 @ X10)) | ((isPer @ X0 @ X1) != $true) | ((treeStar @ X0 @ X1 @ X3 @ X2 @ X5 @ X6) != $true)) )),
% 2.25/1.52 inference(equality_resolution,[status(thm)],[f67])).
% 2.25/1.52 thf(f67,plain,(
% 2.25/1.52 ( ! [X0 : $tType,X2 : nat,X3 : color,X10 : tree @ X0,X1 : X0 > X0 > $o,X8 : X0,X6 : tree @ X0,X9 : tree @ X0,X7 : X0,X4 : color,X5 : tree @ X0] : (((isPer @ X0 @ X1) != $true) | (X7 != X8) | ($true = (treeStar @ X0 @ X1 @ black @ (suc @ X2) @ (bt @ X0 @ X2 @ X3 @ X4 @ X5 @ X7 @ X9) @ (bt @ X0 @ X2 @ X3 @ X4 @ X6 @ X8 @ X10))) | ($true != (treeStar @ X0 @ X1 @ X4 @ X2 @ X9 @ X10)) | ((treeStar @ X0 @ X1 @ X3 @ X2 @ X5 @ X6) != $true)) )),
% 2.25/1.52 inference(cnf_transformation,[status(thm)],[f45])).
% 2.25/1.52 thf(f45,plain,(
% 2.25/1.52 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : nat,X3 : color,X4 : color,X5 : tree @ X0,X6 : tree @ X0] : (! [X7 : X0,X8 : X0] : ((X7 != X8) | ! [X9 : tree @ X0,X10 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ black @ (suc @ X2) @ (bt @ X0 @ X2 @ X3 @ X4 @ X5 @ X7 @ X9) @ (bt @ X0 @ X2 @ X3 @ X4 @ X6 @ X8 @ X10))) | ($true != (treeStar @ X0 @ X1 @ X4 @ X2 @ X9 @ X10)))) | ((treeStar @ X0 @ X1 @ X3 @ X2 @ X5 @ X6) != $true)))),
% 2.25/1.52 inference(ennf_transformation,[status(thm)],[f18])).
% 2.25/1.52 thf(f18,plain,(
% 2.25/1.52 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : nat,X3 : color,X4 : color,X5 : tree @ X0,X6 : tree @ X0] : (((treeStar @ X0 @ X1 @ X3 @ X2 @ X5 @ X6) = $true) => ! [X7 : X0,X8 : X0] : ((X7 = X8) => ! [X9 : tree @ X0,X10 : tree @ X0] : (($true = (treeStar @ X0 @ X1 @ X4 @ X2 @ X9 @ X10)) => ($true = (treeStar @ X0 @ X1 @ black @ (suc @ X2) @ (bt @ X0 @ X2 @ X3 @ X4 @ X5 @ X7 @ X9) @ (bt @ X0 @ X2 @ X3 @ X4 @ X6 @ X8 @ X10)))))))),
% 2.25/1.52 inference(fool_elimination,[status(thm)],[f17])).
% 2.25/1.52 thf(f17,plain,(
% 2.25/1.52 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : nat,X3 : color,X4 : color,X5 : tree @ X0,X6 : tree @ X0] : ((treeStar @ X0 @ X1 @ X3 @ X2 @ X5 @ X6) => ! [X7 : X0,X8 : X0] : ((X7 = X8) => ! [X9 : tree @ X0,X10 : tree @ X0] : ((treeStar @ X0 @ X1 @ X4 @ X2 @ X9 @ X10) => (treeStar @ X0 @ X1 @ black @ (suc @ X2) @ (bt @ X0 @ X2 @ X3 @ X4 @ X5 @ X7 @ X9) @ (bt @ X0 @ X2 @ X3 @ X4 @ X6 @ X8 @ X10))))))),
% 2.25/1.52 inference(rectify,[status(thm)],[f7])).
% 2.25/1.52 thf(f7,axiom,(
% 2.25/1.52 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X9 : nat,X16 : color,X17 : color,X10 : tree @ X0,X11 : tree @ X0] : ((treeStar @ X0 @ X1 @ X16 @ X9 @ X10 @ X11) => ! [X12 : X0,X13 : X0] : ((X12 = X13) => ! [X14 : tree @ X0,X15 : tree @ X0] : ((treeStar @ X0 @ X1 @ X17 @ X9 @ X14 @ X15) => (treeStar @ X0 @ X1 @ black @ (suc @ X9) @ (bt @ X0 @ X9 @ X16 @ X17 @ X10 @ X12 @ X14) @ (bt @ X0 @ X9 @ X16 @ X17 @ X11 @ X13 @ X15))))))),
% 2.25/1.52 file('/export/starexec/sandbox/tmp/tmp.To87vZeRvk/DTF2THF_26358.p',bt_tp_ax)).
% 2.25/1.52 thf(f69,plain,(
% 2.25/1.52 ($true != (treeStar @ sK0 @ sK1 @ black @ (suc @ sK3) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ (rev @ sK0 @ sK4 @ sK3 @ (rev @ sK0 @ sK4 @ sK3 @ sK6)) @ sK2 @ (rev @ sK0 @ sK5 @ sK3 @ (rev @ sK0 @ sK5 @ sK3 @ sK7))) @ (bt @ sK0 @ sK3 @ sK4 @ sK5 @ sK6 @ sK2 @ sK7)))),
% 2.25/1.52 inference(cnf_transformation,[status(thm)],[f60])).
% 2.25/1.52 % SZS output end Proof for DTF2THF_26358
% 2.25/1.52 % (26573)------------------------------
% 2.25/1.52 % (26573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.52 % (26573)Termination reason: Refutation
% 2.25/1.52
% 2.25/1.52 % (26573)Memory used [KB]: 5756
% 2.25/1.52 % (26573)Time elapsed: 0.014 s
% 2.25/1.52 % (26573)Instructions burned: 31 (million)
% 2.25/1.52 % (26573)------------------------------
% 2.25/1.52 % (26573)------------------------------
% 2.25/1.52 % (26567)Success in time 0.023 s
%------------------------------------------------------------------------------