%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET596^5 : 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 : 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 08:23:40 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 160 ( 14 ~; 15 |; 35 &; 86 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 79 ( 44 ^; 29 !; 6 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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_9,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_55_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X4: a] : $false ) )
& ! [X5: a] :
( ( X0 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X6: a] :
( ( X2 @ X6 )
& ( X0 @ X6 ) ) )
= ( ^ [X7: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( ( X1 @ X5 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f10]) ).
thf(f15,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f20,plain,
! [X1: a] :
( ( $true = $false )
| ( $false
= ( ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f21,plain,
! [X1: a] :
( ( $true = $false )
| ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
( ( ^ [Y0: a] : $false
@ sK3 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f24,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f28,plain,
( ( $true = $false )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f29,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f42,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f9,f31]) ).
thf(f43,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f46,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f32,f22]) ).
thf(f47,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f54,plain,
$true = $false,
inference(constrained_superposition,[],[f43,f47]) ).
thf(f55,plain,
$false,
inference(trivial_inequality_removal,[],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:40:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.26 % (78022)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (78028)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1830384406_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % Exception at run slice level
% 0.07/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.26 % (78029)% WARNING: option uhcvi not known.
% 0.07/0.26 % (78029)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=487262374:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (78031)dis+10_1_sil=32000:sp=arity:random_seed=2761905803:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.26 % (78029)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % (78029)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.26 % (78034)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1260602008:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (78033)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3176494761:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.26 % (78030)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=909199389:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (78029) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-78022-78029"...
% 0.07/0.26 % (78031) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-78022-78031"...
% 0.07/0.26 % (78034) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-78022-78034"...
% 0.07/0.26 % (78036)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3981183379:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.07/0.26 % (78033) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-78022-78033"...
% 0.07/0.26 % Exception at run slice level
% 0.07/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.26 % (78034)...printing done.
% 0.07/0.26 % (78031)...printing done.
% 0.07/0.26 % (78029)...printing done.
% 0.07/0.26 % (78030) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-78022-78030"...
% 0.07/0.26 % (78033)...printing done.
% 0.07/0.26 % (78029)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (78029)------------------------------
% 0.07/0.26 % (78029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (78029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (78029)CaDiCaL version: 2.1.3
% 0.07/0.26 % (78029)Termination reason: Refutation
% 0.07/0.26 % (78029)Time elapsed: 0.004 s
% 0.07/0.26 % (78029)Peak memory usage: 12 MB
% 0.07/0.26 % (78029)Instructions burned: 4 (million)
% 0.07/0.26 % (78022)Success in time 0.041 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------