%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET010^5 : 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 : n018.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 08:23:31 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 46 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 378 ( 105 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 443 ( 74 ~; 80 |; 77 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 20 ^; 12 !; 3 ?; 35 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_86_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f11,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f19,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f21]) ).
thf(f26,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f31,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f32,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f32]) ).
thf(f34,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f35,plain,
( ( $true
= ( ~ ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f36]) ).
thf(f39,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f50,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f35]) ).
thf(f51,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f52]) ).
thf(f60,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f53]) ).
thf(f61,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f64,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f65,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f64]) ).
thf(f74,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f22,f42]) ).
thf(f75,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(forward_demodulation,[],[f33,f42]) ).
thf(f77,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f78,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f65,f77]) ).
thf(f79,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f81,plain,
$true = $false,
inference(constrained_superposition,[],[f75,f79]) ).
thf(f82,plain,
$false,
inference(trivial_inequality_removal,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:37:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (70874)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (70879)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3557242597_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (70880)% WARNING: option uhcvi not known.
% 0.08/0.25 % (70881)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=605747067:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (70880)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=261079602:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (70882)dis+10_1_sil=32000:sp=arity:random_seed=3553282449:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (70883)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1664207522:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (70880)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (70885)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1255196015:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.25 % (70880)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (70883)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (70884)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2334711119:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (70887)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=710742397:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.25 % (70881) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70881"...
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (70883) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70883"...
% 0.08/0.25 % (70882) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70882"...
% 0.08/0.25 % (70885) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70885"...
% 0.08/0.25 % (70880) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70880"...
% 0.08/0.25 % (70884) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-70874-70884"...
% 0.08/0.25 % (70881)...printing done.
% 0.08/0.25 % (70881)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (70881)------------------------------
% 0.08/0.25 % (70881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (70881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (70881)CaDiCaL version: 2.1.3
% 0.08/0.25 % (70881)Termination reason: Refutation
% 0.08/0.25 % (70881)Time elapsed: 0.004 s
% 0.08/0.25 % (70881)Peak memory usage: 12 MB
% 0.08/0.25 % (70881)Instructions burned: 5 (million)
% 0.08/0.25 % (70874)Success in time 0.035 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------