%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU956^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:50 AM UTC 2026
% Result : Theorem 1.22s 1.03s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 66 equ; 2 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 62 ( 17 ~; 8 |; 6 &; 14 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 18 ^; 32 !; 4 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f25,plain,
$false,
inference(equality_resolution,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] : ( sK0 != X0 ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( sK0 != X0 )
| ( sK0 != X0 ) ),
inference(superposition,[status(thm)],[f10,f18]) ).
thf(f18,plain,
! [X1: $i] :
( ( sK1 = X1 )
| ( sK0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i] :
( ( $true
= ( sK1 = X1 ) )
| ( sK0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( $false
= ( sK0 = X1 ) )
| ( $true
= ( sK1 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( sK0 = X1 )
= ( sK1 = X1 ) ),
inference(argument_congruence,[status(thm)],[f13]) ).
thf(f13,plain,
( ( (=) @ sK0 )
= ( (=) @ sK1 ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ( X0 != X1 ) )
& ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X3: $i,X4: $i] :
( ( X3 != X4 )
& ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) ) )
=> ( ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ( X0 != X1 ) )
& ? [X3: $i,X4: $i] :
( ( X3 != X4 )
& ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) )
=> ( X3 = X4 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( ^ [X5: $i] : ( X3 = X5 ) )
= ( ^ [X6: $i] : ( X4 = X6 ) ) )
=> ( X3 = X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i > $o,X0: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) )
=> ! [X4: $i,X3: $i] :
( ( ( ^ [X5: $i] : ( X4 = X5 ) )
= ( ^ [X5: $i] : ( X3 = X5 ) ) )
=> ( X3 = X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: $i > $o,X0: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) )
=> ! [X4: $i,X3: $i] :
( ( ( ^ [X5: $i] : ( X4 = X5 ) )
= ( ^ [X5: $i] : ( X3 = X5 ) ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qQErMaj2n3/DTF2THF_15428.p',cTHM13_pme) ).
thf(f10,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU956^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n025.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 12:37:42 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
% 0.18/0.37 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU956^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.38 % Domain : Set Theory (Functions)
% 0.18/0.38 % Problem : TPS problem from FUNCTION-THMS
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Bro09]
% 0.18/0.38 % Names : tps_0867 [Bro09]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.18/0.38 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.18/0.38 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 3 ( 5 avg)
% 0.18/0.38 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 2 @)
% 0.18/0.38 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 8 ( 8 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.38 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(cTHM13_pme,conjecture,
% 0.18/0.38 ( ! [R: $i > $o,S: $i > $o] :
% 0.18/0.38 ( ( R = S )
% 0.18/0.38 => ! [X: $i] :
% 0.18/0.38 ( ( S @ X )
% 0.18/0.38 => ( R @ X ) ) )
% 0.18/0.38 => ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( ( ^ [Y: $i] : ( Xx = Y ) )
% 0.18/0.38 = ( ^ [Y: $i] : ( Xy = Y ) ) )
% 0.18/0.38 => ( Xx = Xy ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 0.99/1.00 ---- Embedded in THF ---
% 0.99/1.00 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.99/1.00 %%% Generated on Tue Feb 24 12:37:43 EST 2026
% 0.99/1.00 %%% using '$$dhol' embedding, version 1.3.0.
% 0.99/1.00 %%% Logic specification used:
% 0.99/1.00 %%% thf(spec, logic, $$dhol).
% 0.99/1.00
% 0.99/1.00 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qQErMaj2n3/DTF2DTF15428.p
% See solution above
% 0.99/1.00 ------------------------
% 0.99/1.01 ---- Cleaned THF ---
% 0.99/1.01 thf(cTHM13_pme,conjecture,
% 0.99/1.01 ( ! [R: $i > $o,S: $i > $o] :
% 0.99/1.01 ( ( R = S )
% 0.99/1.01 => ! [X: $i] :
% 0.99/1.01 ( ( S @ X )
% 0.99/1.01 => ( R @ X ) ) )
% 0.99/1.01 => ! [Xx: $i,Xy: $i] :
% 0.99/1.01 ( ( ( ^ [Y: $i] : ( Xx = Y ) )
% 0.99/1.01 = ( ^ [Y: $i] : ( Xy = Y ) ) )
% 0.99/1.01 => ( Xx = Xy ) ) ) ).
% 0.99/1.01 ------------------------
% 1.22/1.02 % (15529)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15428 for (3000ds/183Mi)
% 1.22/1.03 % (15529)First to succeed.
% 1.22/1.03 % (15529)Refutation found. Thanks to Tanya!
% 1.22/1.03 % SZS status Theorem for DTF2THF_15428
% 1.22/1.03 % SZS output start Proof for DTF2THF_15428
% 1.22/1.03 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 1.22/1.03 thf(f25,plain,(
% 1.22/1.03 $false),
% 1.22/1.03 inference(equality_resolution,[status(thm)],[f24])).
% 1.22/1.03 thf(f24,plain,(
% 1.22/1.03 ( ! [X0 : $i] : ((sK0 != X0)) )),
% 1.22/1.03 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.22/1.03 thf(f23,plain,(
% 1.22/1.03 ( ! [X0 : $i] : ((sK0 != X0) | (sK0 != X0)) )),
% 1.22/1.03 inference(superposition,[status(thm)],[f10,f18])).
% 1.22/1.03 thf(f18,plain,(
% 1.22/1.03 ( ! [X1 : $i] : ((sK1 = X1) | (sK0 != X1)) )),
% 1.22/1.03 inference(equality_proxy_clausification,[status(thm)],[f17])).
% 1.22/1.03 thf(f17,plain,(
% 1.22/1.03 ( ! [X1 : $i] : (($true = (sK1 = X1)) | (sK0 != X1)) )),
% 1.22/1.03 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.22/1.03 thf(f16,plain,(
% 1.22/1.03 ( ! [X1 : $i] : (($false = (sK0 = X1)) | ($true = (sK1 = X1))) )),
% 1.22/1.03 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.22/1.03 thf(f14,plain,(
% 1.22/1.03 ( ! [X1 : $i] : (((sK0 = X1) = (sK1 = X1))) )),
% 1.22/1.03 inference(argument_congruence,[status(thm)],[f13])).
% 1.22/1.03 thf(f13,plain,(
% 1.22/1.03 ((= @ sK0) = (= @ sK1))),
% 1.22/1.03 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.22/1.03 thf(f9,plain,(
% 1.22/1.03 ((^[Y0 : $i]: (sK0 = Y0)) = (^[Y0 : $i]: (sK1 = Y0)))),
% 1.22/1.03 inference(cnf_transformation,[status(thm)],[f8])).
% 1.22/1.03 thf(f8,plain,(
% 1.22/1.03 ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : (((X1 @ X2) = $true) | ((X0 @ X2) != $true)) | (X0 != X1)) & ((sK1 != sK0) & ((^[Y0 : $i]: (sK0 = Y0)) = (^[Y0 : $i]: (sK1 = Y0))))),
% 1.22/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.22/1.03 thf(f7,plain,(
% 1.22/1.03 ? [X3 : $i,X4 : $i] : ((X3 != X4) & ((^[Y0 : $i]: (X4 = Y0)) = (^[Y0 : $i]: (X3 = Y0)))) => ((sK1 != sK0) & ((^[Y0 : $i]: (sK0 = Y0)) = (^[Y0 : $i]: (sK1 = Y0))))),
% 1.22/1.03 introduced(definition,[],[choice_axiom])).
% 1.22/1.03 thf(f6,plain,(
% 1.22/1.03 ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : (((X1 @ X2) = $true) | ((X0 @ X2) != $true)) | (X0 != X1)) & ? [X3 : $i,X4 : $i] : ((X3 != X4) & ((^[Y0 : $i]: (X4 = Y0)) = (^[Y0 : $i]: (X3 = Y0))))),
% 1.22/1.03 inference(ennf_transformation,[status(thm)],[f5])).
% 1.22/1.03 thf(f5,plain,(
% 1.22/1.03 ~(! [X0 : $i > $o,X1 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : (((X0 @ X2) = $true) => ((X1 @ X2) = $true))) => ! [X3 : $i,X4 : $i] : (((^[Y0 : $i]: (X4 = Y0)) = (^[Y0 : $i]: (X3 = Y0))) => (X3 = X4)))),
% 1.22/1.03 inference(fool_elimination,[status(thm)],[f4])).
% 1.22/1.03 thf(f4,plain,(
% 1.22/1.03 ~(! [X0 : $i > $o,X1 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X0 @ X2) => (X1 @ X2))) => ! [X3 : $i,X4 : $i] : (((^[X5 : $i] : ((X3 = X5))) = (^[X6 : $i] : ((X4 = X6)))) => (X3 = X4)))),
% 1.22/1.03 inference(rectify,[status(thm)],[f2])).
% 1.22/1.03 thf(f2,negated_conjecture,(
% 1.22/1.03 ~(! [X1 : $i > $o,X0 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X1 @ X2) => (X0 @ X2))) => ! [X4 : $i,X3 : $i] : (((^[X5 : $i] : ((X4 = X5))) = (^[X5 : $i] : ((X3 = X5)))) => (X3 = X4)))),
% 1.22/1.03 inference(negated_conjecture,[status(cth)],[f1])).
% 1.22/1.03 thf(f1,conjecture,(
% 1.22/1.03 ! [X1 : $i > $o,X0 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X1 @ X2) => (X0 @ X2))) => ! [X4 : $i,X3 : $i] : (((^[X5 : $i] : ((X4 = X5))) = (^[X5 : $i] : ((X3 = X5)))) => (X3 = X4))),
% 1.22/1.03 file('/export/starexec/sandbox/tmp/tmp.qQErMaj2n3/DTF2THF_15428.p',cTHM13_pme)).
% 1.22/1.03 thf(f10,plain,(
% 1.22/1.03 (sK1 != sK0)),
% 1.22/1.03 inference(cnf_transformation,[status(thm)],[f8])).
% 1.22/1.03 % SZS output end Proof for DTF2THF_15428
% 1.22/1.03 % (15529)------------------------------
% 1.22/1.03 % (15529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.22/1.03 % (15529)Termination reason: Refutation
% 1.22/1.03
% 1.22/1.03 % (15529)Memory used [KB]: 5500
% 1.22/1.03 % (15529)Time elapsed: 0.003 s
% 1.22/1.03 % (15529)Instructions burned: 1 (million)
% 1.22/1.03 % (15529)------------------------------
% 1.22/1.03 % (15529)------------------------------
% 1.22/1.03 % (15528)Success in time 0.011 s
%------------------------------------------------------------------------------