%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO516^1 : TPTP v9.2.1. Released v4.1.0.
% 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 09:54:26 AM UTC 2026
% Result : Theorem 1.46s 1.30s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 39 equ; 1 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 94 ( 13 ~; 3 |; 2 &; 69 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 10 ^; 27 !; 14 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
r: $i > $i > $o ).
thf(func_def_7,type,
sK0: $i > $i ).
thf(func_def_8,type,
sK1: ( $i > $i ) > $i ).
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f25,plain,
$false,
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i > $i] :
( ( X0 @ ( sK1 @ X0 ) )
!= ( sK0 @ ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i > $i] :
( ( ( X0 @ ( sK1 @ X0 ) )
!= ( sK0 @ ( sK1 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( r @ X0 @ X1 ) )
| ( ( sK0 @ X0 )
!= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( r @ X0 @ X1 ) )
| ( ( ( sK0 @ X0 )
= X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 )
= X1 )
= ( r @ X0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( r @ X0 )
= ( (=) @ ( sK0 @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] :
( ( sK0 @ X0 )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] :
( ( sK0 @ X0 )
= Y0 ) ) )
& ! [X2: $i > $i] :
( $true
!= ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) )
=> ( ( r @ X0 )
= ( ^ [Y0: $i] :
( ( sK0 @ X0 )
= Y0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X2: $i > $i] :
( ? [X3: $i] :
( $true
!= ( r @ X3 @ ( X2 @ X3 ) ) )
=> ( $true
!= ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) )
& ! [X2: $i > $i] :
? [X3: $i] :
( $true
!= ( r @ X3 @ ( X2 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) )
=> ? [X2: $i > $i] :
! [X3: $i] :
( $true
= ( r @ X3 @ ( X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) )
=> ? [X3: $i > $i] :
! [X4: $i] :
( $true
= ( r @ X4 @ ( X3 @ X4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [X2: $i] : ( X1 = X2 ) ) )
=> ? [X3: $i > $i] :
! [X4: $i] : ( r @ X4 @ ( X3 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [X2: $i] : ( X1 = X2 ) ) )
=> ? [X3: $i > $i] :
! [X0: $i] : ( r @ X0 @ ( X3 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 )
= ( ^ [X2: $i] : ( X1 = X2 ) ) )
=> ? [X3: $i > $i] :
! [X0: $i] : ( r @ X0 @ ( X3 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SLICYPLf6K/DTF2THF_5188.p',descr2) ).
thf(f11,plain,
! [X2: $i > $i] :
( $true
!= ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO516^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n025.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:33:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SYO516^1 : TPTP v9.2.1. Released v4.1.0.
% 0.31/0.45 % Domain : Syntactic
% 0.31/0.45 % Problem : Every functional relation corresponds to a function
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : descr2 [Bro09]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0
% 0.31/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.45 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 2 ( 4 avg)
% 0.31/0.45 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.31/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.31/0.45 % Number of types : 2 ( 0 usr)
% 0.31/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.31/0.45 % Number of variables : 5 ( 1 ^; 2 !; 2 ?; 5 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : Requires description but does not use the description operator.
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(r_type,type,
% 0.31/0.45 r: $i > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(descr2,conjecture,
% 0.31/0.45 ( ! [X: $i] :
% 0.31/0.45 ? [Y: $i] :
% 0.31/0.45 ( ( r @ X )
% 0.31/0.45 = ( ^ [Z: $i] : ( Y = Z ) ) )
% 0.31/0.45 => ? [F: $i > $i] :
% 0.31/0.45 ! [X: $i] : ( r @ X @ ( F @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 14:33:28 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SLICYPLf6K/DTF2DTF5188.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(r_type,type,
% 1.46/1.28 r: $i > $i > $o ).
% 1.46/1.28
% 1.46/1.28 thf(descr2,conjecture,
% 1.46/1.28 ( ! [X: $i] :
% 1.46/1.28 ? [Y: $i] :
% 1.46/1.28 ( ( r @ X )
% 1.46/1.28 = ( ^ [Z: $i] : ( Y = Z ) ) )
% 1.46/1.28 => ? [F: $i > $i] :
% 1.46/1.28 ! [X: $i] : ( r @ X @ ( F @ X ) ) ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (5382)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_5188 for (3000ds/275Mi)
% 1.46/1.29 % (5377)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5188 for (3000ds/183Mi)
% 1.46/1.30 % (5382)First to succeed.
% 1.46/1.30 % (5377)Also succeeded, but the first one will report.
% 1.46/1.30 % (5382)Refutation found. Thanks to Tanya!
% 1.46/1.30 % SZS status Theorem for DTF2THF_5188
% 1.46/1.30 % SZS output start Proof for DTF2THF_5188
% 1.46/1.30 thf(func_def_0, type, r: $i > $i > $o).
% 1.46/1.30 thf(func_def_7, type, sK0: $i > $i).
% 1.46/1.30 thf(func_def_8, type, sK1: ($i > $i) > $i).
% 1.46/1.30 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 1.46/1.30 thf(f25,plain,(
% 1.46/1.30 $false),
% 1.46/1.30 inference(equality_resolution,[status(thm)],[f20])).
% 1.46/1.30 thf(f20,plain,(
% 1.46/1.30 ( ! [X0 : $i > $i] : (((X0 @ (sK1 @ X0)) != (sK0 @ (sK1 @ X0)))) )),
% 1.46/1.30 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.46/1.30 thf(f19,plain,(
% 1.46/1.30 ( ! [X0 : $i > $i] : (((X0 @ (sK1 @ X0)) != (sK0 @ (sK1 @ X0))) | ($true != $true)) )),
% 1.46/1.30 inference(superposition,[status(thm)],[f11,f17])).
% 1.46/1.30 thf(f17,plain,(
% 1.46/1.30 ( ! [X0 : $i,X1 : $i] : (($true = (r @ X0 @ X1)) | ((sK0 @ X0) != X1)) )),
% 1.46/1.30 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.46/1.30 thf(f16,plain,(
% 1.46/1.30 ( ! [X0 : $i,X1 : $i] : (($true = (r @ X0 @ X1)) | (((sK0 @ X0) = X1) = $false)) )),
% 1.46/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.46/1.30 thf(f14,plain,(
% 1.46/1.30 ( ! [X0 : $i,X1 : $i] : ((((sK0 @ X0) = X1) = (r @ X0 @ X1))) )),
% 1.46/1.30 inference(argument_congruence,[status(thm)],[f13])).
% 1.46/1.30 thf(f13,plain,(
% 1.46/1.30 ( ! [X0 : $i] : (((r @ X0) = (= @ (sK0 @ X0)))) )),
% 1.46/1.30 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.46/1.30 thf(f12,plain,(
% 1.46/1.30 ( ! [X0 : $i] : (((r @ X0) = (^[Y0 : $i]: ((sK0 @ X0) = Y0)))) )),
% 1.46/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.30 thf(f10,plain,(
% 1.46/1.30 ! [X0 : $i] : ((r @ X0) = (^[Y0 : $i]: ((sK0 @ X0) = Y0))) & ! [X2 : $i > $i] : ($true != (r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))))),
% 1.46/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.46/1.30 thf(f8,plain,(
% 1.46/1.30 ! [X0 : $i] : (? [X1 : $i] : ((r @ X0) = (^[Y0 : $i]: (X1 = Y0))) => ((r @ X0) = (^[Y0 : $i]: ((sK0 @ X0) = Y0))))),
% 1.46/1.30 introduced(definition,[],[choice_axiom])).
% 1.46/1.30 thf(f9,plain,(
% 1.46/1.30 ! [X2 : $i > $i] : (? [X3 : $i] : ($true != (r @ X3 @ (X2 @ X3))) => ($true != (r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2)))))),
% 1.46/1.30 introduced(definition,[],[choice_axiom])).
% 1.46/1.30 thf(f7,plain,(
% 1.46/1.30 ! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[Y0 : $i]: (X1 = Y0))) & ! [X2 : $i > $i] : ? [X3 : $i] : ($true != (r @ X3 @ (X2 @ X3)))),
% 1.46/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.46/1.30 thf(f6,plain,(
% 1.46/1.30 ~(! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[Y0 : $i]: (X1 = Y0))) => ? [X2 : $i > $i] : ! [X3 : $i] : ($true = (r @ X3 @ (X2 @ X3))))),
% 1.46/1.30 inference(rectify,[status(thm)],[f5])).
% 1.46/1.30 thf(f5,plain,(
% 1.46/1.30 ~(! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[Y0 : $i]: (X1 = Y0))) => ? [X3 : $i > $i] : ! [X4 : $i] : ($true = (r @ X4 @ (X3 @ X4))))),
% 1.46/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.30 thf(f4,plain,(
% 1.46/1.30 ~(! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : $i > $i] : ! [X4 : $i] : (r @ X4 @ (X3 @ X4)))),
% 1.46/1.30 inference(rectify,[status(thm)],[f2])).
% 1.46/1.30 thf(f2,negated_conjecture,(
% 1.46/1.30 ~(! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : $i > $i] : ! [X0 : $i] : (r @ X0 @ (X3 @ X0)))),
% 1.46/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.30 thf(f1,conjecture,(
% 1.46/1.30 ! [X0 : $i] : ? [X1 : $i] : ((r @ X0) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : $i > $i] : ! [X0 : $i] : (r @ X0 @ (X3 @ X0))),
% 1.46/1.30 file('/export/starexec/sandbox/tmp/tmp.SLICYPLf6K/DTF2THF_5188.p',descr2)).
% 1.46/1.30 thf(f11,plain,(
% 1.46/1.30 ( ! [X2 : $i > $i] : (($true != (r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))))) )),
% 1.46/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.30 % SZS output end Proof for DTF2THF_5188
% 1.46/1.30 % (5382)------------------------------
% 1.46/1.30 % (5382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (5382)Termination reason: Refutation
% 1.46/1.30
% 1.46/1.30 % (5382)Memory used [KB]: 5500
% 1.46/1.30 % (5382)Time elapsed: 0.003 s
% 1.46/1.30 % (5382)Instructions burned: 2 (million)
% 1.46/1.30 % (5382)------------------------------
% 1.46/1.30 % (5382)------------------------------
% 1.46/1.30 % (5376)Success in time 0.002 s
%------------------------------------------------------------------------------