%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:05 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 79 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 38 ~; 33 |; 11 &; 110 @)
% ( 4 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 72 ( 38 ^; 22 !; 12 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_3,type,
sK0: a ).
thf(func_def_4,type,
sK1: a ).
thf(func_def_5,type,
sK2: a ).
thf(func_def_6,type,
sK3: a ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
sK4: a > a > a ).
thf(f1,conjecture,
! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X0 @ X1 ) )
= ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM182_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X0 @ X1 ) )
= ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X0 @ X1 ) )
= ( ^ [X5: a > a > a] : ( X5 @ X2 @ X3 ) ) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) )
<~> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( X1 != X3 )
| ( X0 != X2 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( X1 != X3 )
| ( X0 != X2 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X0 @ X1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X2 @ X3 ) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( sK1 != sK3 )
| ( sK0 != sK2 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 ) ) ) )
& ( ( ( sK1 = sK3 )
& ( sK0 = sK2 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 ) ) )
| ( sK0 = sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 ) ) )
| ( sK1 = sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 ) ) )
| ( sK0 != sK2 )
| ( sK1 != sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X1: a > a > a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 )
@ X1 )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 )
@ X1 ) )
| ( sK0 = sK2 ) ),
inference(argument_congruence,[],[f9]) ).
thf(f13,plain,
! [X1: a > a > a] :
( ( ( X1 @ sK0 @ sK1 )
= ( X1 @ sK2 @ sK3 ) )
| ( sK0 = sK2 ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
! [X1: a > a > a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 )
@ X1 )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 )
@ X1 ) )
| ( sK1 = sK3 ) ),
inference(argument_congruence,[],[f10]) ).
thf(f15,plain,
! [X1: a > a > a] :
( ( ( X1 @ sK0 @ sK1 )
= ( X1 @ sK2 @ sK3 ) )
| ( sK1 = sK3 ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f18,plain,
! [X0: a > a > a] :
( ( sK2
!= ( X0 @ sK2 @ sK3 ) )
| ( sK0 = sK2 )
| ( sK0
!= ( X0 @ sK0 @ sK1 ) ) ),
inference(equality_factoring,[],[f13]) ).
thf(f20,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK0 @ sK1 )
@ sK4 )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK2 @ sK3 )
@ sK4 ) )
| ( sK0 != sK2 )
| ( sK1 != sK3 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f23,plain,
( ( ( sK4 @ sK0 @ sK1 )
!= ( sK4 @ sK2 @ sK3 ) )
| ( sK0 != sK2 )
| ( sK1 != sK3 ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f28,plain,
! [X0: a > a > a] :
( ( sK3
!= ( X0 @ sK2 @ sK3 ) )
| ( sK1 = sK3 )
| ( sK1
!= ( X0 @ sK0 @ sK1 ) ) ),
inference(equality_factoring,[],[f15]) ).
thf(f37,plain,
( ( sK0 = sK2 )
| ( sK0
!= ( ^ [Y0: a,Y1: a] : Y0
@ sK0
@ sK1 ) ) ),
inference(equality_resolution,[],[f18]) ).
thf(f40,plain,
( ( sK0 = sK2 )
| ( sK0 != sK0 ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f41,plain,
sK0 = sK2,
inference(trivial_inequality_removal,[],[f40]) ).
thf(f113,plain,
( ( sK1 = sK3 )
| ( sK1
!= ( ^ [Y0: a,Y1: a] : Y1
@ sK0
@ sK1 ) ) ),
inference(equality_resolution,[],[f28]) ).
thf(f116,plain,
( ( sK1 = sK3 )
| ( sK1 != sK1 ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f117,plain,
sK1 = sK3,
inference(trivial_inequality_removal,[],[f116]) ).
thf(f150,plain,
( ( ( sK4 @ sK0 @ sK1 )
!= ( sK4 @ sK2 @ sK1 ) )
| ( sK0 != sK2 )
| ( sK1 != sK1 ) ),
inference(constrained_superposition,[],[f23,f117]) ).
thf(f151,plain,
( ( ( sK4 @ sK0 @ sK1 )
!= ( sK4 @ sK2 @ sK1 ) )
| ( sK0 != sK2 ) ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f166,plain,
( ( ( sK4 @ sK0 @ sK1 )
!= ( sK4 @ sK0 @ sK1 ) )
| ( sK0 != sK2 ) ),
inference(forward_demodulation,[],[f151,f41]) ).
thf(f167,plain,
sK0 != sK2,
inference(trivial_inequality_removal,[],[f166]) ).
thf(f174,plain,
sK0 != sK0,
inference(forward_demodulation,[],[f167,f41]) ).
thf(f175,plain,
$false,
inference(trivial_inequality_removal,[],[f174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:19:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.31 % (2631047)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (2631053)% WARNING: option uhcvi not known.
% 0.20/0.31 % (2631053)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2099749979:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (2631053)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2631053)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (2631052)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1174386502_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (2631054)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=656643666:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (2631055)dis+10_1_sil=32000:sp=arity:random_seed=1532753897:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (2631056)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2525902209:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (2631056)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2631055)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631055)------------------------------
% 0.20/0.31 % (2631055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631054)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631054)------------------------------
% 0.20/0.31 % (2631054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631055)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631054)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631055)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631055)Time elapsed: 0.002 s
% 0.20/0.31 % (2631054)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631054)Time elapsed: 0.002 s
% 0.20/0.31 % (2631055)Peak memory usage: 11 MB
% 0.20/0.31 % (2631054)Peak memory usage: 11 MB
% 0.20/0.31 % (2631055)Instructions burned: 2 (million)
% 0.20/0.31 % (2631054)Instructions burned: 2 (million)
% 0.20/0.31 % (2631056)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631056)------------------------------
% 0.20/0.31 % (2631056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631056)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631056)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631056)Time elapsed: 0.002 s
% 0.20/0.31 % (2631056)Peak memory usage: 12 MB
% 0.20/0.31 % (2631056)Instructions burned: 2 (million)
% 0.20/0.31 % (2631055)------------------------------
% 0.20/0.31 % (2631055)------------------------------
% 0.20/0.31 % (2631054)------------------------------
% 0.20/0.31 % (2631054)------------------------------
% 0.20/0.31 % (2631056)------------------------------
% 0.20/0.31 % (2631056)------------------------------
% 0.20/0.31 % (2631057)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3209703167:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2631057)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631057)------------------------------
% 0.20/0.31 % (2631057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631057)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631057)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631057)Time elapsed: 0.002 s
% 0.20/0.31 % (2631057)Peak memory usage: 12 MB
% 0.20/0.31 % (2631057)Instructions burned: 2 (million)
% 0.20/0.31 % (2631057)------------------------------
% 0.20/0.31 % (2631057)------------------------------
% 0.20/0.31 % (2631058)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3979453870:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (2631064)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=563975788:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (2631066)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1742156969:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.31 % (2631066)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2631067)ott-21_1_sil=16000:fs=off:random_seed=1796334292:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.31 % (2631066)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (2631066)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631066)------------------------------
% 0.20/0.31 % (2631066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631066)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631066)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631066)Time elapsed: 0.002 s
% 0.20/0.31 % (2631066)Peak memory usage: 12 MB
% 0.20/0.31 % (2631066)Instructions burned: 1 (million)
% 0.20/0.31 % (2631066)------------------------------
% 0.20/0.31 % (2631066)------------------------------
% 0.20/0.31 % (2631065)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2469309282:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2631067) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2631047-2631067"...
% 0.20/0.31 % (2631065)Refutation not found, incomplete strategy
% 0.20/0.31 % (2631065)------------------------------
% 0.20/0.31 % (2631065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631067)...printing done.
% 0.20/0.31 % (2631065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631065)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631065)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (2631065)Time elapsed: 0.002 s
% 0.20/0.31 % (2631065)Peak memory usage: 11 MB
% 0.20/0.31 % (2631065)Instructions burned: 2 (million)
% 0.20/0.31 % (2631067)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.31 % (2631067)------------------------------
% 0.20/0.31 % (2631067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2631067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2631067)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2631067)Termination reason: Refutation
% 0.20/0.31 % (2631067)Time elapsed: 0.006 s
% 0.20/0.31 % (2631067)Peak memory usage: 12 MB
% 0.20/0.31 % (2631067)Instructions burned: 9 (million)
% 0.20/0.31 % (2631047)Success in time 0.07 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------