%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO234^5 : 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 : n007.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 09:53:44 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 6 equ)
% Maximal formula atoms : 1 ( 10 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 66 ( 66 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-4 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 2 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
d: $tType ).
tff(type_def_6,type,
c: $tType ).
tff(func_def_0,type,
d: $tType ).
tff(func_def_1,type,
c: $tType ).
tff(func_def_2,type,
cB: sTfun(d,sTfun(c,$o)) ).
tff(func_def_3,type,
cA: sTfun(c,sTfun(d,$o)) ).
tff(f8,plain,
$false,
inference(equality_resolution,[status(thm)],[f7]) ).
tff(f7,plain,
! [X0: sTfun(c,sTfun(d,$o))] : ( vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) != X0 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
tff(f6,plain,
! [X0: sTfun(c,sTfun(d,$o))] : ( vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) != X0 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
tff(f5,plain,
~ ? [X0: sTfun(c,sTfun(d,$o))] : ( vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) = X0 ),
inference(fool_elimination,[status(thm)],[f4]) ).
tff(f4,plain,
~ ? [X0: sTfun(c,sTfun(d,$o))] :
( ( ^ [X1: c,X2: d] :
( vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2)
| vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1) ) )
= X0 ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ? [X0: sTfun(c,sTfun(d,$o))] :
( ( ^ [X1: c,X2: d] :
( vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2)
| vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1) ) )
= X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
? [X0: sTfun(c,sTfun(d,$o))] :
( ( ^ [X1: c,X2: d] :
( vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2)
| vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1) ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.vPMK9JeiN9/DTF2THF_16508.p',cSV4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO234^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n007.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 14:25:53 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
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO234^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0703 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.19/0.47 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 3 avg)
% 0.19/0.47 % Number of connectives : 5 ( 0 ~; 1 |; 0 &; 4 @)
% 0.19/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 2 ( 2 avg)
% 0.19/0.47 % Number of types : 3 ( 2 usr)
% 0.19/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.19/0.47 % Number of variables : 3 ( 2 ^; 0 !; 1 ?; 3 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(d_type,type,
% 0.19/0.47 d: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(c_type,type,
% 0.19/0.47 c: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(cB,type,
% 0.19/0.47 cB: d > c > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cA,type,
% 0.19/0.47 cA: c > d > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cSV4,conjecture,
% 0.19/0.47 ? [Xu: c > d > $o] :
% 0.19/0.47 ( Xu
% 0.19/0.47 = ( ^ [Xx: c,Xy: d] :
% 0.19/0.47 ( ( cA @ Xx @ Xy )
% 0.19/0.47 | ( cB @ Xy @ Xx ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 14:25:54 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vPMK9JeiN9/DTF2DTF16508.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(d_type,type,
% 1.48/1.25 d: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(c_type,type,
% 1.48/1.25 c: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(cB,type,
% 1.48/1.25 cB: d > c > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cA,type,
% 1.48/1.25 cA: c > d > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cSV4,conjecture,
% 1.48/1.25 ? [Xu: c > d > $o] :
% 1.48/1.25 ( Xu
% 1.48/1.25 = ( ^ [Xx: c,Xy: d] :
% 1.48/1.25 ( ( cA @ Xx @ Xy )
% 1.48/1.25 | ( cB @ Xy @ Xx ) ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.26 % (16700)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_16508 for (2999ds/2Mi)
% 1.48/1.26 % (16697)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_16508 for (2999ds/4Mi)
% 1.48/1.26 % (16697)First to succeed.
% 1.48/1.26 % (16700)Instruction limit reached!
% 1.48/1.26 % (16700)------------------------------
% 1.48/1.26 % (16700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (16700)Termination reason: Unknown
% 1.48/1.26 % (16700)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (16700)Memory used [KB]: 5500
% 1.48/1.26 % (16700)Time elapsed: 0.002 s
% 1.48/1.26 % (16700)Instructions burned: 2 (million)
% 1.48/1.26 % (16700)------------------------------
% 1.48/1.26 % (16700)------------------------------
% 1.48/1.26 % (16701)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_16508 for (2999ds/275Mi)
% 1.48/1.26 % (16701)Also succeeded, but the first one will report.
% 1.48/1.27 % (16697)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_16508
% 1.48/1.27 % SZS output start Proof for DTF2THF_16508
% 1.48/1.27 tff(type_def_5, type, d: $tType).
% 1.48/1.27 tff(type_def_6, type, c: $tType).
% 1.48/1.27 tff(func_def_0, type, d: $tType).
% 1.48/1.27 tff(func_def_1, type, c: $tType).
% 1.48/1.27 tff(func_def_2, type, cB: sTfun(d,sTfun(c,$o))).
% 1.48/1.27 tff(func_def_3, type, cA: sTfun(c,sTfun(d,$o))).
% 1.48/1.27 tff(f8,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(equality_resolution,[status(thm)],[f7])).
% 1.48/1.27 tff(f7,plain,(
% 1.48/1.27 ( ! [X0 : sTfun(c,sTfun(d,$o))] : (vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) != X0) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 1.48/1.27 tff(f6,plain,(
% 1.48/1.27 ! [X0 : sTfun(c,sTfun(d,$o))] : vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) != X0),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.27 tff(f5,plain,(
% 1.48/1.27 ~? [X0 : sTfun(c,sTfun(d,$o))] : vLAM(c,sTfun(d,$o),vLAM(d,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,db0(d)),db1(c))),vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,db1(c)),db0(d))))) = X0),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.27 tff(f4,plain,(
% 1.48/1.27 ~? [X0 : sTfun(c,sTfun(d,$o))] : (^[X1 : c, X2 : d] : (vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2) | vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1))) = X0),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 tff(f2,negated_conjecture,(
% 1.48/1.27 ~? [X0 : sTfun(c,sTfun(d,$o))] : (^[X1 : c, X2 : d] : (vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2) | vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1))) = X0),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.27 tff(f1,conjecture,(
% 1.48/1.27 ? [X0 : sTfun(c,sTfun(d,$o))] : (^[X1 : c, X2 : d] : (vAPP(d,$o,vAPP(c,sTfun(d,$o),cA,X1),X2) | vAPP(c,$o,vAPP(d,sTfun(c,$o),cB,X2),X1))) = X0),
% 1.48/1.27 file('/export/starexec/sandbox/tmp/tmp.vPMK9JeiN9/DTF2THF_16508.p',cSV4)).
% 1.48/1.27 % SZS output end Proof for DTF2THF_16508
% 1.48/1.27 % (16697)------------------------------
% 1.48/1.27 % (16697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (16697)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (16697)Memory used [KB]: 5373
% 1.48/1.27 % (16697)Time elapsed: 0.002 s
% 1.48/1.27 % (16697)------------------------------
% 1.48/1.27 % (16697)------------------------------
% 1.48/1.27 % (16695)Success in time 0.004 s
%------------------------------------------------------------------------------