%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT424^1 : 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 : n018.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 1.68s 1.27s
% Output : Refutation 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT424^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 06:16:46 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : DAT424^1 : TPTP v9.2.1. Released v9.2.0.
% 0.15/0.41 % Domain : Data Structures
% 0.15/0.41 % Problem : Reversal of a red-black-tree is an involution, BT leaf base case
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.15/0.41 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.15/0.41 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.15/0.41 % Source : [Rot25]
% 0.15/0.41 % Names : RedBlackTree/rbt-rev-invol-base-BTLeaf.p [Rot25]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : ? v9.2.0
% 0.15/0.41 % Syntax : Number of formulae : 21 ( 6 unt; 11 typ; 0 def)
% 0.15/0.41 % Number of atoms : 18 ( 18 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 6 ( 1 avg)
% 0.15/0.41 % Number of connectives : 179 ( 7 ~; 2 |; 6 &; 160 @)
% 0.15/0.41 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 14 ( 6 avg)
% 0.15/0.41 % Number of types : 3 ( 2 usr)
% 0.15/0.41 % Number of type decls : 11 ( 4 !>P; 3 !>D)
% 0.15/0.41 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 10 ( 9 usr; 3 con; 0-7 aty)
% 0.15/0.41 % Number of variables : 52 ( 0 ^; 27 !; 15 ?; 52 :)
% 0.15/0.41 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.41 % SPC : DH1_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments :
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(color_type,type,
% 0.15/0.41 color: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(black_type,type,
% 0.15/0.41 black: color ).
% 0.15/0.41
% 0.15/0.41 thf(red_type,type,
% 0.15/0.41 red: color ).
% 0.15/0.41
% 0.15/0.41 thf(red_black,axiom,
% 0.15/0.41 ! [C: color] :
% 0.15/0.41 ( ( ( C = red )
% 0.15/0.41 & ( C != black ) )
% 0.15/0.41 | ( ( C != red )
% 0.15/0.41 & ( C = black ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(nat_type,type,
% 0.15/0.41 nat: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(zero_type,type,
% 0.15/0.41 zero: nat ).
% 0.15/0.41
% 0.15/0.41 thf(suc_type,type,
% 0.15/0.41 suc: nat > nat ).
% 0.15/0.41
% 0.15/0.41 thf(peano1,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ( ( suc @ N )
% 0.15/0.41 != zero ) ).
% 0.15/0.41
% 0.15/0.41 thf(peano2,axiom,
% 0.15/0.41 ! [N: nat,M: nat] :
% 0.15/0.41 ( ( N != M )
% 0.15/0.41 => ( ( suc @ N )
% 0.15/0.41 != ( suc @ M ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(peano3,axiom,
% 0.15/0.41 ! [P: nat > $o] :
% 0.15/0.41 ( ( P @ zero )
% 0.15/0.41 => ( ! [M: nat] :
% 0.15/0.41 ( ( P @ M )
% 0.15/0.41 => ( P @ ( suc @ M ) ) )
% 0.15/0.41 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(tree_type,type,
% 0.15/0.41 tree: $tType > color > nat > $tType ).
% 0.15/0.41
% 0.15/0.41 thf(leaf_type,type,
% 0.15/0.41 leaf:
% 0.15/0.41 !>[A: $tType] : ( tree @ A @ black @ zero ) ).
% 0.15/0.41
% 0.15/0.41 thf(redTree_type,type,
% 0.15/0.41 rt:
% 0.15/0.41 !>[A: $tType,N: nat] : ( ( tree @ A @ black @ N ) > A > ( tree @ A @ black @ N ) > ( tree @ A @ red @ N ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(rt_cons,axiom,
% 0.15/0.41 ! [A: $tType,N: nat,T: tree @ A @ red @ N] :
% 0.15/0.41 ? [X: A,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.15/0.41 ( T
% 0.15/0.41 = ( rt @ A @ N @ T1 @ X @ T2 ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(blackTree_type,type,
% 0.15/0.41 bt:
% 0.15/0.41 !>[A: $tType,N: nat,C1: color,C2: color] : ( ( tree @ A @ C1 @ N ) > A > ( tree @ A @ C2 @ N ) > ( tree @ A @ black @ ( suc @ N ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(bt_cons,axiom,
% 0.15/0.41 ! [A: $tType,N: nat,T: tree @ A @ black @ N] :
% 0.15/0.41 ( ( ( T
% 0.15/0.41 != ( leaf @ A ) )
% 0.15/0.41 & ? [X: A,M: nat,C1: color,C2: color,T1: tree @ A @ C1 @ M,T2: tree @ A @ C2 @ M] :
% 0.15/0.41 ( ( N
% 0.15/0.41 = ( suc @ M ) )
% 0.15/0.41 & ( T
% 0.15/0.41 = ( bt @ A @ M @ C1 @ C2 @ T1 @ X @ T2 ) ) ) )
% 0.15/0.41 | ( ( T
% 0.15/0.41 = ( leaf @ A ) )
% 0.15/0.41 & ~ ? [X: A,M: nat,C1: color,C2: color,T1: tree @ A @ C1 @ M,T2: tree @ A @ C2 @ M] :
% 0.15/0.41 ( ( N
% 0.15/0.41 = ( suc @ M ) )
% 0.15/0.41 & ( T
% 0.15/0.41 = ( bt @ A @ M @ C1 @ C2 @ T1 @ X @ T2 ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(rbt_rev,type,
% 0.15/0.41 rev:
% 0.15/0.41 !>[A: $tType,C: color,N: nat] : ( ( tree @ A @ C @ N ) > ( tree @ A @ C @ N ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(rev_leaf,axiom,
% 0.15/0.41 ! [A: $tType] :
% 0.15/0.41 ( ( rev @ A @ black @ zero @ ( leaf @ A ) )
% 0.15/0.41 = ( leaf @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(rev_bt,axiom,
% 0.15/0.41 ! [A: $tType,X: A,N: nat,C1: color,C2: color,T1: tree @ A @ C1 @ N,T2: tree @ A @ C2 @ N] :
% 0.15/0.41 ( ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) )
% 0.15/0.41 = ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(rev_rt,axiom,
% 0.15/0.41 ! [A: $tType,X: A,N: nat,T1: tree @ A @ black @ N,T2: tree @ A @ black @ N] :
% 0.15/0.41 ( ( rev @ A @ red @ N @ ( rt @ A @ N @ T1 @ X @ T2 ) )
% 0.15/0.41 = ( rt @ A @ N @ ( rev @ A @ black @ N @ T2 ) @ X @ ( rev @ A @ black @ N @ T1 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(bt_base,conjecture,
% 0.15/0.41 ! [A: $tType] :
% 0.15/0.41 ( ( rev @ A @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) )
% 0.15/0.41 = ( leaf @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.68/1.22 ---- Embedded in THF ---
% 1.68/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.22 %%% Generated on Tue Feb 24 06:16:46 EST 2026
% 1.68/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.22 %%% Logic specification used:
% 1.68/1.22 %%% thf(spec, logic, $$dhol).
% 1.68/1.22
% 1.68/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2DTF625.p
% 1.68/1.22 thf(is_per_type, type, isPer: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 1.68/1.22 thf(is_per, definition, (! [A:$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)))))))))).
% 1.68/1.22 thf(color_type, type, color: $tType).
% 1.68/1.22 thf(colorStar, type, 'colorStar': (color > (color > $o))).
% 1.68/1.22 thf(colorStar_is_eq, axiom, (! [X:color,Y:color]: (((('colorStar' @ X) @ Y) <=> (X = Y))))).
% 1.68/1.22 thf(black_type, type, black: color).
% 1.68/1.22 thf(red_type, type, red: color).
% 1.68/1.22 thf(nat_type, type, nat: $tType).
% 1.68/1.22 thf(natStar, type, 'natStar': (nat > (nat > $o))).
% 1.68/1.22 thf(natStar_is_eq, axiom, (! [X:nat,Y:nat]: (((('natStar' @ X) @ Y) <=> (X = Y))))).
% 1.68/1.22 thf(zero_type, type, zero: nat).
% 1.68/1.22 thf(suc_type, type, suc: (nat > nat)).
% 1.68/1.22 thf(tree_type, type, tree: ($tType > $tType)).
% 1.68/1.22 thf(treeStar, type, 'treeStar': (!> [A:$tType]: (((A > (A > $o)) > (color > (nat > ((tree @ A) > ((tree @ A) > $o)))))))).
% 1.68/1.22 thf('\'treeStar\'_is_per', axiom, (! [B:$tType,BStar:(B > (B > $o))]: ((((isPer @ B) @ BStar) => (! [C:color]: ((! [C0:nat]: (((isPer @ (tree @ B)) @ ((((treeStar @ B) @ BStar) @ C) @ C0)))))))))).
% 1.68/1.22 thf(leaf_type, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 1.68/1.22 thf(leaf_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ (leaf @ A)) @ (leaf @ A)))))).
% 1.68/1.22 thf(redTree_type, type, rt: (!> [A:$tType]: ((nat > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))).
% 1.68/1.22 thf(rt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ (((((rt @ A) @ N) @ D) @ D0) @ D1)) @ (((((rt @ A) @ N) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))).
% 1.68/1.22 thf(blackTree_type, type, bt: (!> [A:$tType]: ((nat > (color > (color > ((tree @ A) > (A > ((tree @ A) > (tree @ A)))))))))).
% 1.68/1.22 thf(bt_tp_ax, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [D:(tree @ A),D_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ D) @ D_prime) => (! [D0:A,D0_prime:A]: (((D0 = D0_prime) => (! [D1:(tree @ A),D1_prime:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C2) @ N) @ D1) @ D1_prime) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D) @ D0) @ D1)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ D_prime) @ D0_prime) @ D1_prime))))))))))))))))))))).
% 1.68/1.22 thf(rbt_rev, type, rev: (!> [A:$tType]: ((color > (nat > ((tree @ A) > (tree @ A))))))).
% 1.68/1.22 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))))))))))))).
% 1.68/1.22 thf(red_black, axiom, (! [C:color]: ((((C = red) & (C != black)) | ((C != red) & (C = black)))))).
% 1.68/1.22 thf(peano1, axiom, (! [N:nat]: (((suc @ N) != zero)))).
% 1.68/1.22 thf(peano2, axiom, (! [N:nat]: ((! [M:nat]: (((N != M) => ((suc @ N) != (suc @ M)))))))).
% 1.68/1.22 thf(peano3, axiom, (! [P:(nat > $o)]: (((P @ zero) => ((! [M:nat]: (((P @ M) => (P @ (suc @ M))))) => (! [N:nat]: ((P @ N)))))))).
% 1.68/1.22 thf(rt_cons, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [T:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ red) @ N) @ T) @ T) => (? [X:A]: ((? [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) & (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) & ((((((treeStar @ A) @ AStar) @ red) @ N) @ T) @ (((((rt @ A) @ N) @ T1) @ X) @ T2))))))))))))))))).
% 1.68/1.22 thf(bt_cons, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [N:nat]: ((! [T:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T) @ T) => (((~ (((((((treeStar @ A) @ AStar) @ black) @ N) @ T) @ (leaf @ A)))) & (? [X:A]: ((? [M:nat]: ((? [C1:color]: ((? [C2:color]: ((? [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ M) @ T1) @ T1) & (((((((treeStar @ A) @ AStar) @ C2) @ M) @ T2) @ T2) & ((N = (suc @ M)) & ((((((treeStar @ A) @ AStar) @ black) @ N) @ T) @ (((((((bt @ A) @ M) @ C1) @ C2) @ T1) @ X) @ T2)))))))))))))))) | (((((((treeStar @ A) @ AStar) @ black) @ N) @ T) @ (leaf @ A)) & (~ ((? [X:A]: ((? [M:nat]: ((? [C1:color]: ((? [C2:color]: ((? [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ M) @ T1) @ T1) & (((((((treeStar @ A) @ AStar) @ C2) @ M) @ T2) @ T2) & ((N = (suc @ M)) & ((((((treeStar @ A) @ AStar) @ black) @ N) @ T) @ (((((((bt @ A) @ M) @ C1) @ C2) @ T1) @ X) @ T2)))))))))))))))))))))))))))).
% 1.68/1.22 thf(rev_leaf, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ (leaf @ A))) @ (leaf @ A)))))).
% 1.68/1.22 thf(rev_bt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [C1:color]: ((! [C2:color]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ C1) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ C2) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ black) @ (suc @ N)) @ ((((rev @ A) @ black) @ (suc @ N)) @ (((((((bt @ A) @ N) @ C1) @ C2) @ T1) @ X) @ T2))) @ (((((((bt @ A) @ N) @ C1) @ C2) @ ((((rev @ A) @ C2) @ N) @ T2)) @ X) @ ((((rev @ A) @ C1) @ N) @ T1))))))))))))))))))).
% 1.68/1.22 thf(rev_rt, axiom, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => (! [X:A]: ((! [N:nat]: ((! [T1:(tree @ A),T2:(tree @ A)]: ((((((((treeStar @ A) @ AStar) @ black) @ N) @ T1) @ T1) => (((((((treeStar @ A) @ AStar) @ black) @ N) @ T2) @ T2) => ((((((treeStar @ A) @ AStar) @ red) @ N) @ ((((rev @ A) @ red) @ N) @ (((((rt @ A) @ N) @ T1) @ X) @ T2))) @ (((((rt @ A) @ N) @ ((((rev @ A) @ black) @ N) @ T2)) @ X) @ ((((rev @ A) @ black) @ N) @ T1))))))))))))))).
% 1.68/1.22 thf(bt_base, conjecture, (! [A:$tType,AStar:(A > (A > $o))]: ((((isPer @ A) @ AStar) => ((((((treeStar @ A) @ AStar) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ ((((rev @ A) @ black) @ zero) @ (leaf @ A)))) @ (leaf @ A)))))).
% 1.68/1.22 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2DTF625.p
% 1.68/1.22 ------------------------
% 1.68/1.23 ---- Cleaned THF ---
% 1.68/1.23 thf(is_per_type,type,
% 1.68/1.23 isPer:
% 1.68/1.23 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.68/1.23
% 1.68/1.23 thf(is_per,definition,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 <=> ( ! [X: A,Y: A] :
% 1.68/1.23 ( ( AStar @ X @ Y )
% 1.68/1.23 => ( AStar @ Y @ X ) )
% 1.68/1.23 & ! [X: A,Y: A,Z: A] :
% 1.68/1.23 ( ( AStar @ X @ Y )
% 1.68/1.23 => ( ( AStar @ Y @ Z )
% 1.68/1.23 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(color_type,type,
% 1.68/1.23 color: $tType ).
% 1.68/1.23
% 1.68/1.23 thf(colorStar,type,
% 1.68/1.23 colorStar: color > color > $o ).
% 1.68/1.23
% 1.68/1.23 thf(colorStar_is_eq,axiom,
% 1.68/1.23 ! [X: color,Y: color] :
% 1.68/1.23 ( ( colorStar @ X @ Y )
% 1.68/1.23 <=> ( X = Y ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(black_type,type,
% 1.68/1.23 black: color ).
% 1.68/1.23
% 1.68/1.23 thf(red_type,type,
% 1.68/1.23 red: color ).
% 1.68/1.23
% 1.68/1.23 thf(nat_type,type,
% 1.68/1.23 nat: $tType ).
% 1.68/1.23
% 1.68/1.23 thf(natStar,type,
% 1.68/1.23 natStar: nat > nat > $o ).
% 1.68/1.23
% 1.68/1.23 thf(natStar_is_eq,axiom,
% 1.68/1.23 ! [X: nat,Y: nat] :
% 1.68/1.23 ( ( natStar @ X @ Y )
% 1.68/1.23 <=> ( X = Y ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(zero_type,type,
% 1.68/1.23 zero: nat ).
% 1.68/1.23
% 1.68/1.23 thf(suc_type,type,
% 1.68/1.23 suc: nat > nat ).
% 1.68/1.23
% 1.68/1.23 thf(tree_type,type,
% 1.68/1.23 tree: $tType > $tType ).
% 1.68/1.23
% 1.68/1.23 thf(treeStar,type,
% 1.68/1.23 treeStar:
% 1.68/1.23 !>[A: $tType] : ( ( A > A > $o ) > color > nat > ( tree @ A ) > ( tree @ A ) > $o ) ).
% 1.68/1.23
% 1.68/1.23 thf('\'treeStar\'_is_per',axiom,
% 1.68/1.23 ! [B: $tType,BStar: B > B > $o] :
% 1.68/1.23 ( ( isPer @ B @ BStar )
% 1.68/1.23 => ! [C: color,C0: nat] : ( isPer @ ( tree @ B ) @ ( treeStar @ B @ BStar @ C @ C0 ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(leaf_type,type,
% 1.68/1.23 leaf:
% 1.68/1.23 !>[A: $tType] : ( tree @ A ) ).
% 1.68/1.23
% 1.68/1.23 thf(leaf_tp_ax,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ( treeStar @ A @ AStar @ black @ zero @ ( leaf @ A ) @ ( leaf @ A ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(redTree_type,type,
% 1.68/1.23 rt:
% 1.68/1.23 !>[A: $tType] : ( nat > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rt_tp_ax,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ black @ N @ D @ D_prime )
% 1.68/1.23 => ! [D0: A,D0_prime: A] :
% 1.68/1.23 ( ( D0 = D0_prime )
% 1.68/1.23 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ black @ N @ D1 @ D1_prime )
% 1.68/1.23 => ( treeStar @ A @ AStar @ red @ N @ ( rt @ A @ N @ D @ D0 @ D1 ) @ ( rt @ A @ N @ D_prime @ D0_prime @ D1_prime ) ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(blackTree_type,type,
% 1.68/1.23 bt:
% 1.68/1.23 !>[A: $tType] : ( nat > color > color > ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(bt_tp_ax,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [N: nat,C1: color,C2: color,D: tree @ A,D_prime: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C1 @ N @ D @ D_prime )
% 1.68/1.23 => ! [D0: A,D0_prime: A] :
% 1.68/1.23 ( ( D0 = D0_prime )
% 1.68/1.23 => ! [D1: tree @ A,D1_prime: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C2 @ N @ D1 @ D1_prime )
% 1.68/1.23 => ( 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 ) ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rbt_rev,type,
% 1.68/1.23 rev:
% 1.68/1.23 !>[A: $tType] : ( color > nat > ( tree @ A ) > ( tree @ A ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rev_tp_ax,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [C: color,N: nat,D: tree @ A,D_prime: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C @ N @ D @ D_prime )
% 1.68/1.23 => ( treeStar @ A @ AStar @ C @ N @ ( rev @ A @ C @ N @ D ) @ ( rev @ A @ C @ N @ D_prime ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(red_black,axiom,
% 1.68/1.23 ! [C: color] :
% 1.68/1.23 ( ( ( C = red )
% 1.68/1.23 & ( C != black ) )
% 1.68/1.23 | ( ( C != red )
% 1.68/1.23 & ( C = black ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(peano1,axiom,
% 1.68/1.23 ! [N: nat] :
% 1.68/1.23 ( ( suc @ N )
% 1.68/1.23 != zero ) ).
% 1.68/1.23
% 1.68/1.23 thf(peano2,axiom,
% 1.68/1.23 ! [N: nat,M: nat] :
% 1.68/1.23 ( ( N != M )
% 1.68/1.23 => ( ( suc @ N )
% 1.68/1.23 != ( suc @ M ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(peano3,axiom,
% 1.68/1.23 ! [P: nat > $o] :
% 1.68/1.23 ( ( P @ zero )
% 1.68/1.23 => ( ! [M: nat] :
% 1.68/1.23 ( ( P @ M )
% 1.68/1.23 => ( P @ ( suc @ M ) ) )
% 1.68/1.23 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rt_cons,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [N: nat,T: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ red @ N @ T @ T )
% 1.68/1.23 => ? [X: A,T1: tree @ A,T2: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 1.68/1.23 & ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 1.68/1.23 & ( treeStar @ A @ AStar @ red @ N @ T @ ( rt @ A @ N @ T1 @ X @ T2 ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(bt_cons,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [N: nat,T: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ black @ N @ T @ T )
% 1.68/1.23 => ( ( ~ ( treeStar @ A @ AStar @ black @ N @ T @ ( leaf @ A ) )
% 1.68/1.23 & ? [X: A,M: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C1 @ M @ T1 @ T1 )
% 1.68/1.23 & ( treeStar @ A @ AStar @ C2 @ M @ T2 @ T2 )
% 1.68/1.23 & ( N
% 1.68/1.23 = ( suc @ M ) )
% 1.68/1.23 & ( treeStar @ A @ AStar @ black @ N @ T @ ( bt @ A @ M @ C1 @ C2 @ T1 @ X @ T2 ) ) ) )
% 1.68/1.23 | ( ( treeStar @ A @ AStar @ black @ N @ T @ ( leaf @ A ) )
% 1.68/1.23 & ~ ? [X: A,M: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C1 @ M @ T1 @ T1 )
% 1.68/1.23 & ( treeStar @ A @ AStar @ C2 @ M @ T2 @ T2 )
% 1.68/1.23 & ( N
% 1.68/1.23 = ( suc @ M ) )
% 1.68/1.23 & ( treeStar @ A @ AStar @ black @ N @ T @ ( bt @ A @ M @ C1 @ C2 @ T1 @ X @ T2 ) ) ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rev_leaf,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ( treeStar @ A @ AStar @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) @ ( leaf @ A ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rev_bt,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [X: A,N: nat,C1: color,C2: color,T1: tree @ A,T2: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ C1 @ N @ T1 @ T1 )
% 1.68/1.23 => ( ( treeStar @ A @ AStar @ C2 @ N @ T2 @ T2 )
% 1.68/1.23 => ( treeStar @ A @ AStar @ black @ ( suc @ N ) @ ( rev @ A @ black @ ( suc @ N ) @ ( bt @ A @ N @ C1 @ C2 @ T1 @ X @ T2 ) ) @ ( bt @ A @ N @ C1 @ C2 @ ( rev @ A @ C2 @ N @ T2 ) @ X @ ( rev @ A @ C1 @ N @ T1 ) ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(rev_rt,axiom,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ! [X: A,N: nat,T1: tree @ A,T2: tree @ A] :
% 1.68/1.23 ( ( treeStar @ A @ AStar @ black @ N @ T1 @ T1 )
% 1.68/1.23 => ( ( treeStar @ A @ AStar @ black @ N @ T2 @ T2 )
% 1.68/1.23 => ( 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 ) ) ) ) ) ) ).
% 1.68/1.23
% 1.68/1.23 thf(bt_base,conjecture,
% 1.68/1.23 ! [A: $tType,AStar: A > A > $o] :
% 1.68/1.23 ( ( isPer @ A @ AStar )
% 1.68/1.23 => ( treeStar @ A @ AStar @ black @ zero @ ( rev @ A @ black @ zero @ ( rev @ A @ black @ zero @ ( leaf @ A ) ) ) @ ( leaf @ A ) ) ) ).
% 1.68/1.23 ------------------------
% 1.68/1.24 % (750)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_625 for (2999ds/183Mi)
% 1.68/1.25 % (754)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_625 for (2999ds/2Mi)
% 1.68/1.25 % (751)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_625 for (2999ds/4Mi)
% 1.68/1.25 % (753)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_625 for (2999ds/2Mi)
% 1.68/1.25 % (752)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_625 for (2999ds/27Mi)
% 1.68/1.25 % (755)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_625 for (2999ds/275Mi)
% 1.68/1.25 % (756)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_625 for (2999ds/18Mi)
% 1.68/1.25 % (753)Instruction limit reached!
% 1.68/1.25 % (753)------------------------------
% 1.68/1.25 % (753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.25 % (753)Termination reason: Unknown
% 1.68/1.25 % (754)Instruction limit reached!
% 1.68/1.25 % (754)------------------------------
% 1.68/1.25 % (754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.25 % (753)Termination phase: shuffling
% 1.68/1.25
% 1.68/1.25 % (753)Memory used [KB]: 1023
% 1.68/1.25 % (753)Time elapsed: 0.002 s
% 1.68/1.25 % (753)Instructions burned: 2 (million)
% 1.68/1.25 % (753)------------------------------
% 1.68/1.25 % (753)------------------------------
% 1.68/1.25 % (754)Termination reason: Unknown
% 1.68/1.25 % (754)Termination phase: shuffling
% 1.68/1.25
% 1.68/1.25 % (754)Memory used [KB]: 1023
% 1.68/1.25 % (754)Time elapsed: 0.002 s
% 1.68/1.25 % (754)Instructions burned: 2 (million)
% 1.68/1.25 % (754)------------------------------
% 1.68/1.25 % (754)------------------------------
% 1.68/1.25 % (751)Instruction limit reached!
% 1.68/1.25 % (751)------------------------------
% 1.68/1.25 % (751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.25 % (751)Termination reason: Unknown
% 1.68/1.25 % (751)Termination phase: shuffling
% 1.68/1.25
% 1.68/1.25 % (751)Memory used [KB]: 1023
% 1.68/1.25 % (751)Time elapsed: 0.003 s
% 1.68/1.25 % (751)Instructions burned: 4 (million)
% 1.68/1.25 % (751)------------------------------
% 1.68/1.25 % (751)------------------------------
% 1.68/1.26 % (756)Instruction limit reached!
% 1.68/1.26 % (756)------------------------------
% 1.68/1.26 % (756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.26 % (756)Termination reason: Unknown
% 1.68/1.26 % (756)Termination phase: Saturation
% 1.68/1.26
% 1.68/1.26 % (756)Memory used [KB]: 5628
% 1.68/1.26 % (756)Time elapsed: 0.010 s
% 1.68/1.26 % (756)Instructions burned: 18 (million)
% 1.68/1.26 % (756)------------------------------
% 1.68/1.26 % (756)------------------------------
% 1.68/1.26 % (752)Instruction limit reached!
% 1.68/1.26 % (752)------------------------------
% 1.68/1.26 % (752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.26 % (752)Termination reason: Unknown
% 1.68/1.26 % (752)Termination phase: Saturation
% 1.68/1.26
% 1.68/1.26 % (752)Memory used [KB]: 5756
% 1.68/1.26 % (752)Time elapsed: 0.015 s
% 1.68/1.26 % (752)Instructions burned: 28 (million)
% 1.68/1.26 % (752)------------------------------
% 1.68/1.26 % (752)------------------------------
% 1.68/1.26 % (755)First to succeed.
% 1.68/1.27 % (757)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_625 for (2999ds/3Mi)
% 1.68/1.27 % (758)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_625 for (2999ds/37Mi)
% 1.68/1.27 % (759)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_625 for (2999ds/15Mi)
% 1.68/1.27 % (757)Instruction limit reached!
% 1.68/1.27 % (757)------------------------------
% 1.68/1.27 % (757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.27 % (757)Termination reason: Unknown
% 1.68/1.27 % (757)Termination phase: shuffling
% 1.68/1.27
% 1.68/1.27 % (757)Memory used [KB]: 1023
% 1.68/1.27 % (757)Time elapsed: 0.003 s
% 1.68/1.27 % (757)Instructions burned: 3 (million)
% 1.68/1.27 % (757)------------------------------
% 1.68/1.27 % (757)------------------------------
% 1.68/1.27 % (755)Refutation found. Thanks to Tanya!
% 1.68/1.27 % SZS status Theorem for DTF2THF_625
% 1.68/1.27 % SZS output start Proof for DTF2THF_625
% 1.68/1.27 thf(type_def_6, type, color: $tType).
% 1.68/1.27 thf(type_def_7, type, nat: $tType).
% 1.68/1.27 thf(type_def_8, type, tree: ($tType) > $tType).
% 1.68/1.27 thf(type_def_9, type, sK6: $tType).
% 1.68/1.27 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.68/1.27 thf(func_def_2, type, color: $tType).
% 1.68/1.27 thf(func_def_3, type, colorStar: color > color > $o).
% 1.68/1.27 thf(func_def_4, type, black: color).
% 1.68/1.27 thf(func_def_5, type, red: color).
% 1.68/1.27 thf(func_def_6, type, nat: $tType).
% 1.68/1.27 thf(func_def_7, type, natStar: nat > nat > $o).
% 1.68/1.27 thf(func_def_8, type, zero: nat).
% 1.68/1.27 thf(func_def_9, type, suc: nat > nat).
% 1.68/1.27 thf(func_def_10, type, tree: ($tType) > $tType).
% 1.68/1.27 thf(func_def_11, type, treeStar: !>[X0: $tType]:((X0 > X0 > $o) > color > nat > tree @ X0 > tree @ X0 > $o)).
% 1.68/1.27 thf(func_def_12, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 1.68/1.27 thf(func_def_13, type, rt: !>[X0: $tType]:(nat > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.68/1.27 thf(func_def_14, type, bt: !>[X0: $tType]:(nat > color > color > tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 1.68/1.27 thf(func_def_15, type, rev: !>[X0: $tType]:(color > nat > tree @ X0 > tree @ X0)).
% 1.68/1.27 thf(func_def_18, type, sK0: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.68/1.27 thf(func_def_19, type, sK1: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.68/1.27 thf(func_def_20, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.68/1.27 thf(func_def_21, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.68/1.27 thf(func_def_22, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.68/1.27 thf(func_def_23, type, sK5: (nat > $o) > nat).
% 1.68/1.27 thf(func_def_24, type, sK7: sK6 > sK6 > $o).
% 1.68/1.27 thf(func_def_26, type, ph9: !>[X0: $tType]:(X0)).
% 1.68/1.27 thf(f157,plain,(
% 1.68/1.27 $false),
% 1.68/1.27 inference(avatar_sat_refutation,[status(thm)],[f103,f112,f155])).
% 1.68/1.27 thf(f155,plain,(
% 1.68/1.27 ~spl8_2),
% 1.68/1.27 inference(avatar_contradiction_clause,[status(thm)],[f154])).
% 1.68/1.27 thf(f154,plain,(
% 1.68/1.27 $false | ~spl8_2),
% 1.68/1.27 inference(subsumption_resolution,[status(thm)],[f151,f90])).
% 1.68/1.27 thf(f90,plain,(
% 1.68/1.27 ($true = (isPer @ sK6 @ sK7))),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f73])).
% 1.68/1.27 thf(f73,plain,(
% 1.68/1.27 ((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ leaf @ sK6) != $true) & ($true = (isPer @ sK6 @ sK7))),
% 1.68/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f56,f72])).
% 1.68/1.27 thf(f72,plain,(
% 1.68/1.27 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0) != $true) & ((isPer @ X0 @ X1) = $true)) => (((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ leaf @ sK6) != $true) & ($true = (isPer @ sK6 @ sK7)))),
% 1.68/1.27 introduced(definition,[],[choice_axiom])).
% 1.68/1.27 thf(f56,plain,(
% 1.68/1.27 ? [X0 : $tType,X1 : X0 > X0 > $o] : (((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0) != $true) & ((isPer @ X0 @ X1) = $true))),
% 1.68/1.27 inference(ennf_transformation,[status(thm)],[f40])).
% 1.68/1.27 thf(f40,plain,(
% 1.68/1.27 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0) = $true))),
% 1.68/1.27 inference(fool_elimination,[status(thm)],[f39])).
% 1.68/1.27 thf(f39,plain,(
% 1.68/1.27 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0))),
% 1.68/1.27 inference(rectify,[status(thm)],[f19])).
% 1.68/1.27 thf(f19,negated_conjecture,(
% 1.68/1.27 ~! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0))),
% 1.68/1.27 inference(negated_conjecture,[status(cth)],[f18])).
% 1.68/1.27 thf(f18,conjecture,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0)) @ leaf @ X0))),
% 1.68/1.27 file('/export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2THF_625.p',bt_base)).
% 1.68/1.27 thf(f151,plain,(
% 1.68/1.27 ($true != (isPer @ sK6 @ sK7)) | ~spl8_2),
% 1.68/1.27 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.68/1.27 thf(f150,plain,(
% 1.68/1.27 ($true != (isPer @ sK6 @ sK7)) | ($true != $true) | ~spl8_2),
% 1.68/1.27 inference(duplicate_literal_removal,[status(thm)],[f145])).
% 1.68/1.27 thf(f145,plain,(
% 1.68/1.27 ($true != $true) | ($true != $true) | ($true != (isPer @ sK6 @ sK7)) | ~spl8_2),
% 1.68/1.27 inference(superposition,[status(thm)],[f126,f84])).
% 1.68/1.27 thf(f84,plain,(
% 1.68/1.27 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0) @ leaf @ X0) = $true) | ((isPer @ X0 @ X1) != $true)) )),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.68/1.27 thf(f53,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0) @ leaf @ X0) = $true))),
% 1.68/1.27 inference(ennf_transformation,[status(thm)],[f38])).
% 1.68/1.27 thf(f38,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ((treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0) @ leaf @ X0) = $true))),
% 1.68/1.27 inference(fool_elimination,[status(thm)],[f37])).
% 1.68/1.27 thf(f37,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0) @ leaf @ X0))),
% 1.68/1.27 inference(rectify,[status(thm)],[f15])).
% 1.68/1.27 thf(f15,axiom,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => (treeStar @ X0 @ X1 @ black @ zero @ (rev @ X0 @ black @ zero @ leaf @ X0) @ leaf @ X0))),
% 1.68/1.27 file('/export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2THF_625.p',rev_leaf)).
% 1.68/1.27 thf(f126,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6) @ X0)) | ((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ X0) @ leaf @ sK6) != $true)) ) | ~spl8_2),
% 1.68/1.27 inference(subsumption_resolution,[status(thm)],[f121,f90])).
% 1.68/1.27 thf(f121,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (($true != (isPer @ sK6 @ sK7)) | ((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ X0) @ leaf @ sK6) != $true) | ($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6) @ X0))) ) | ~spl8_2),
% 1.68/1.27 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.68/1.27 thf(f118,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6) @ X0)) | ($true != $true) | ((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ X0) @ leaf @ sK6) != $true) | ($true != (isPer @ sK6 @ sK7))) ) | ~spl8_2),
% 1.68/1.27 inference(superposition,[status(thm)],[f102,f89])).
% 1.68/1.27 thf(f89,plain,(
% 1.68/1.27 ( ! [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) | ((treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5) != $true)) )),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f57])).
% 1.68/1.27 thf(f57,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5) != $true) | ($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)))) | ((isPer @ X0 @ X1) != $true))),
% 1.68/1.27 inference(ennf_transformation,[status(thm)],[f32])).
% 1.68/1.27 thf(f32,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : color,X3 : nat,X4 : tree @ X0,X5 : tree @ X0] : (((treeStar @ X0 @ X1 @ X2 @ X3 @ X4 @ X5) = $true) => ($true = (treeStar @ X0 @ X1 @ X2 @ X3 @ (rev @ X0 @ X2 @ X3 @ X4) @ (rev @ X0 @ X2 @ X3 @ X5)))))),
% 1.68/1.27 inference(fool_elimination,[status(thm)],[f31])).
% 1.68/1.27 thf(f31,plain,(
% 1.68/1.27 ! [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))))),
% 1.68/1.27 inference(rectify,[status(thm)],[f8])).
% 1.68/1.27 thf(f8,axiom,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X7 : color,X9 : nat,X10 : tree @ X0,X11 : tree @ X0] : ((treeStar @ X0 @ X1 @ X7 @ X9 @ X10 @ X11) => (treeStar @ X0 @ X1 @ X7 @ X9 @ (rev @ X0 @ X7 @ X9 @ X10) @ (rev @ X0 @ X7 @ X9 @ X11))))),
% 1.68/1.27 file('/export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2THF_625.p',rev_tp_ax)).
% 1.68/1.27 thf(f102,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ X0)) | ((treeStar @ sK6 @ sK7 @ black @ zero @ X0 @ leaf @ sK6) != $true)) ) | ~spl8_2),
% 1.68/1.27 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.68/1.27 thf(f101,definition,(
% 1.68/1.27 spl8_2 <=> ! [X0 : tree @ sK6] : (((treeStar @ sK6 @ sK7 @ black @ zero @ X0 @ leaf @ sK6) != $true) | ($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ X0)))),
% 1.68/1.27 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.68/1.27 thf(f112,plain,(
% 1.68/1.27 spl8_1),
% 1.68/1.27 inference(avatar_contradiction_clause,[status(thm)],[f111])).
% 1.68/1.27 thf(f111,plain,(
% 1.68/1.27 $false | spl8_1),
% 1.68/1.27 inference(subsumption_resolution,[status(thm)],[f110,f90])).
% 1.68/1.27 thf(f110,plain,(
% 1.68/1.27 ($true != (isPer @ sK6 @ sK7)) | spl8_1),
% 1.68/1.27 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.68/1.27 thf(f109,plain,(
% 1.68/1.27 ($true != (isPer @ sK6 @ sK7)) | ($true != $true) | spl8_1),
% 1.68/1.27 inference(superposition,[status(thm)],[f99,f74])).
% 1.68/1.27 thf(f74,plain,(
% 1.68/1.27 ( ! [X0 : $tType,X2 : color,X3 : nat,X1 : X0 > X0 > $o] : (($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))) | ((isPer @ X0 @ X1) != $true)) )),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f55])).
% 1.68/1.27 thf(f55,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) != $true) | ! [X2 : color,X3 : nat] : ($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))))),
% 1.68/1.27 inference(ennf_transformation,[status(thm)],[f42])).
% 1.68/1.27 thf(f42,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) => ! [X2 : color,X3 : nat] : ($true = (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3))))),
% 1.68/1.27 inference(fool_elimination,[status(thm)],[f41])).
% 1.68/1.27 thf(f41,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) => ! [X2 : color,X3 : nat] : (isPer @ tree @ X0 @ (treeStar @ X0 @ X1 @ X2 @ X3)))),
% 1.68/1.27 inference(rectify,[status(thm)],[f4])).
% 1.68/1.27 thf(f4,axiom,(
% 1.68/1.27 ! [X5 : $tType,X6 : X5 > X5 > $o] : ((isPer @ X5 @ X6) => ! [X7 : color,X8 : nat] : (isPer @ tree @ X5 @ (treeStar @ X5 @ X6 @ X7 @ X8)))),
% 1.68/1.27 file('/export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2THF_625.p','\'treeStar\'_is_per')).
% 1.68/1.27 thf(f99,plain,(
% 1.68/1.27 ($true != (isPer @ tree @ sK6 @ (treeStar @ sK6 @ sK7 @ black @ zero))) | spl8_1),
% 1.68/1.27 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.68/1.27 thf(f97,definition,(
% 1.68/1.27 spl8_1 <=> ($true = (isPer @ tree @ sK6 @ (treeStar @ sK6 @ sK7 @ black @ zero)))),
% 1.68/1.27 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.68/1.27 thf(f103,plain,(
% 1.68/1.27 ~spl8_1 | spl8_2),
% 1.68/1.27 inference(avatar_split_clause,[status(thm)],[f95,f101,f97])).
% 1.68/1.27 thf(f95,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (($true != (isPer @ tree @ sK6 @ (treeStar @ sK6 @ sK7 @ black @ zero))) | ((treeStar @ sK6 @ sK7 @ black @ zero @ X0 @ leaf @ sK6) != $true) | ($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ X0))) )),
% 1.68/1.27 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.68/1.27 thf(f92,plain,(
% 1.68/1.27 ( ! [X0 : tree @ sK6] : (((treeStar @ sK6 @ sK7 @ black @ zero @ X0 @ leaf @ sK6) != $true) | ($true != (isPer @ tree @ sK6 @ (treeStar @ sK6 @ sK7 @ black @ zero))) | ($true != $true) | ($true != (treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ X0))) )),
% 1.68/1.27 inference(superposition,[status(thm)],[f91,f82])).
% 1.68/1.27 thf(f82,plain,(
% 1.68/1.27 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X6 : X0,X4 : X0,X5 : X0] : (((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X4 @ X5)) | ((isPer @ X0 @ X1) != $true) | ($true != (X1 @ X5 @ X6))) )),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f68])).
% 1.68/1.27 thf(f68,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X5 @ X6)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true = (X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) & ($true != (X1 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1)))) | (($true = (X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ($true != (X1 @ (sK2 @ X0 @ X1) @ (sK4 @ X0 @ X1))) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1))))))),
% 1.68/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f65,f67,f66])).
% 1.68/1.27 thf(f66,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X8 @ X7))) => (($true = (X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) & ($true != (X1 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1)))))),
% 1.68/1.27 introduced(definition,[],[choice_axiom])).
% 1.68/1.27 thf(f67,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X9 : X0,X10 : X0,X11 : X0] : (($true = (X1 @ X9 @ X10)) & ($true != (X1 @ X9 @ X11)) & ((X1 @ X10 @ X11) = $true)) => (($true = (X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ($true != (X1 @ (sK2 @ X0 @ X1) @ (sK4 @ X0 @ X1))) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)))))),
% 1.68/1.27 introduced(definition,[],[choice_axiom])).
% 1.68/1.27 thf(f65,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (($true != (X1 @ X4 @ X5)) | ((X1 @ X4 @ X6) = $true) | ($true != (X1 @ X5 @ X6)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X8 @ X7))) | ? [X9 : X0,X10 : X0,X11 : X0] : (($true = (X1 @ X9 @ X10)) & ($true != (X1 @ X9 @ X11)) & ((X1 @ X10 @ X11) = $true))))),
% 1.68/1.27 inference(rectify,[status(thm)],[f64])).
% 1.68/1.27 thf(f64,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ($true != (X1 @ X6 @ X5))) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true) & ((X1 @ X3 @ X4) = $true))))),
% 1.68/1.27 inference(flattening,[status(thm)],[f63])).
% 1.68/1.27 thf(f63,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) & ($true != (X1 @ X6 @ X5))) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true) & ((X1 @ X3 @ X4) = $true)))))),
% 1.68/1.27 inference(nnf_transformation,[status(thm)],[f62])).
% 1.68/1.27 thf(f62,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.68/1.27 inference(flattening,[status(thm)],[f61])).
% 1.68/1.27 thf(f61,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (($true != (X1 @ X5 @ X6)) | ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : ((((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) | ((X1 @ X2 @ X3) != $true))))),
% 1.68/1.27 inference(ennf_transformation,[status(thm)],[f26])).
% 1.68/1.27 thf(f26,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (($true = (X1 @ X5 @ X6)) => ($true = (X1 @ X6 @ X5))) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) => (((X1 @ X3 @ X4) = $true) => ((X1 @ X2 @ X4) = $true)))))),
% 1.68/1.27 inference(fool_elimination,[status(thm)],[f25])).
% 1.68/1.27 thf(f25,plain,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X5 : X0,X6 : X0] : ((X1 @ X5 @ X6) => (X1 @ X6 @ X5))) <=> (isPer @ X0 @ X1))),
% 1.68/1.27 inference(rectify,[status(thm)],[f1])).
% 1.68/1.27 thf(f1,axiom,(
% 1.68/1.27 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2))) <=> (isPer @ X0 @ X1))),
% 1.68/1.27 file('/export/starexec/sandbox/tmp/tmp.7po1fbuFxT/DTF2THF_625.p',is_per)).
% 1.68/1.27 thf(f91,plain,(
% 1.68/1.27 ((treeStar @ sK6 @ sK7 @ black @ zero @ (rev @ sK6 @ black @ zero @ (rev @ sK6 @ black @ zero @ leaf @ sK6)) @ leaf @ sK6) != $true)),
% 1.68/1.27 inference(cnf_transformation,[status(thm)],[f73])).
% 1.68/1.27 % SZS output end Proof for DTF2THF_625
% 1.68/1.27 % (755)------------------------------
% 1.68/1.27 % (755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.27 % (755)Termination reason: Refutation
% 1.68/1.27
% 1.68/1.27 % (755)Memory used [KB]: 5756
% 1.68/1.27 % (755)Time elapsed: 0.019 s
% 1.68/1.27 % (755)Instructions burned: 29 (million)
% 1.68/1.27 % (755)------------------------------
% 1.68/1.27 % (755)------------------------------
% 1.68/1.27 % (748)Success in time 0.032 s
%------------------------------------------------------------------------------