%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET606^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:23:41 AM UTC 2026
% Result : Theorem 0.06s 0.18s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 62 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 239 ( 42 ~; 30 |; 47 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 20 ^; 8 !; 2 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ~ ( ( X1 @ X2 )
& ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_77_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ~ ( ( X1 @ X2 )
& ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ~ ( ( X1 @ X2 )
& ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] :
( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f11,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( ( sK0 @ sK2 )
& ~ ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ~ ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $true
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f22,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( ( sK0 @ sK2 )
& ~ ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f25,plain,
( ( $true
= ( ~ ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f28,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f31,plain,
( ( $false
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f32,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f39,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(forward_demodulation,[],[f23,f29]) ).
thf(f40,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(forward_demodulation,[],[f36,f40]) ).
thf(f42,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f44,plain,
$true = $false,
inference(constrained_superposition,[],[f29,f42]) ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET606^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.13 % Computer : n012.cluster.edu
% 0.06/0.13 % Model : x86_64 x86_64
% 0.06/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.13 % Memory : 8046.5625MB
% 0.06/0.13 % OS : Linux 6.8.0-71-generic
% 0.06/0.13 % CPULimit : 300
% 0.06/0.13 % WCLimit : 300
% 0.06/0.13 % DateTime : Tue Sep 29 13:38:34 UTC 2026
% 0.06/0.13 % CPUTime :
% 0.06/0.13 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.14 Running first-order model finding
% 0.06/0.14 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % (112170)Will run a generic schedule for satisfiability detection.
% 0.06/0.18 % (112176)% WARNING: option uhcvi not known.
% 0.06/0.18 % (112176)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4248616391:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.18 % (112180)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1195314918:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.18 % (112177)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4234233149:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.18 % (112175)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2034907403_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.18 % (112176)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.18 % (112176)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.06/0.18 % Exception at run slice level
% 0.06/0.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.18 % (112181)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=345717367:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.18 % (112177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112170-112177"...
% 0.06/0.18 % (112180) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112170-112180"...
% 0.06/0.18 % (112176) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112170-112176"...
% 0.06/0.18 % (112181) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112170-112181"...
% 0.06/0.18 % (112177)...printing done.
% 0.06/0.18 % (112180)...printing done.
% 0.06/0.18 % (112176)...printing done.
% 0.06/0.18 % (112177)Refutation found. Thanks to Tanya!
% 0.06/0.18 % SZS status Theorem for theBenchmark
% 0.06/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.18 % (112177)------------------------------
% 0.06/0.18 % (112177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.18 % (112177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.18 % (112177)CaDiCaL version: 2.1.3
% 0.06/0.18 % (112177)Termination reason: Refutation
% 0.06/0.18 % (112177)Time elapsed: 0.001 s
% 0.06/0.18 % (112177)Peak memory usage: 12 MB
% 0.06/0.18 % (112177)Instructions burned: 3 (million)
% 0.06/0.18 % (112170)Success in time 0.027 s
% 0.06/0.18 % Vampire exiting
%------------------------------------------------------------------------------