%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV239^5 : 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 : n017.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 08:39:12 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 364 ( 141 equ; 23 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 340 ( 35 ~; 70 |; 38 &; 170 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 9 con; 0-4 aty)
% ( 0 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 76 ( 0 sgn 20 !; 6 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
y: a > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: a > $o ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_15,type,
sK4: ( a > $o ) > a > a ).
thf(func_def_16,type,
sK5: ( a > $o ) > a > a ).
thf(f1,conjecture,
( y
= ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) )
& ( y @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5211_pme) ).
thf(f2,negated_conjecture,
( y
!= ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) )
& ( y @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( y
!= ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( X1
= ( ^ [X3: a,X4: a] : ( X3 = X4 )
@ X2 ) )
& ( y @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( (=) @ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( y @ sK0 )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( (=) @ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( (=) @ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( y @ Y2 )
& ( Y1
= ( (=) @ Y2 ) ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( y @ Y1 )
& ( Y0
= ( (=) @ Y1 ) ) ) )
& ( Y0 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( y @ Y1 )
& ( Y0
= ( (=) @ Y1 ) ) ) )
& ( Y0 @ sK0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f13]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( ( ?? @ a
@ ^ [Y0: a] :
( ( y @ Y0 )
& ( X1
= ( (=) @ Y0 ) ) ) )
& ( X1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( X1 @ sK0 ) )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( y @ Y0 )
& ( X1
= ( (=) @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( X1 @ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ( y @ Y0 )
& ( X1
= ( (=) @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( X1 @ sK0 ) )
| ( $false
= ( ( y @ X2 )
& ( X1
= ( (=) @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( X1 @ sK0 ) )
| ( $false
= ( X1
= ( (=) @ X2 ) ) )
| ( ( y @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( y @ sK0 ) )
| ( $false
= ( X1 @ sK0 ) )
| ( ( (=) @ X2 )
!= X1 )
| ( ( y @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( y @ Y1 )
& ( Y0
= ( (=) @ Y1 ) ) ) )
& ( Y0 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f22,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( y @ Y1 )
& ( Y0
= ( (=) @ Y1 ) ) ) )
& ( Y0 @ sK0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ( ?? @ a
@ ^ [Y0: a] :
( ( y @ Y0 )
& ( sK1
= ( (=) @ Y0 ) ) ) )
& ( sK1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( sK1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( y @ Y0 )
& ( sK1
= ( (=) @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( y @ Y0 )
& ( sK1
= ( (=) @ Y0 ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( ( y @ sK2 )
& ( sK1
= ( (=) @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( sK1
= ( (=) @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( y @ sK0 ) )
| ( $true
= ( y @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( $true
= ( y @ sK0 ) )
| ( sK1
= ( (=) @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f28]) ).
thf(f32,definition,
( spl3_1
<=> ( $true
= ( sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,definition,
( spl3_2
<=> ( $true
= ( y @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
!= ( y @ sK0 ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f38,plain,
( ( $true
= ( y @ sK0 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f24,f36,f32]) ).
thf(f41,definition,
( spl3_3
<=> ( $true
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f29,f36,f41]) ).
thf(f45,plain,
( ! [X2: a,X1: a > $o] :
( ( $true = $false )
| ( $false
= ( X1 @ sK0 ) )
| ( ( (=) @ X2 )
!= X1 )
| ( ( y @ X2 )
= $false ) )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f20,f38]) ).
thf(f46,plain,
( ! [X2: a,X1: a > $o] :
( ( ( (=) @ X2 )
!= X1 )
| ( $false
= ( X1 @ sK0 ) )
| ( ( y @ X2 )
= $false ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f57,plain,
( ! [X0: a] :
( ( $false
= ( X0 = sK0 ) )
| ( $false
= ( y @ X0 ) ) )
| ~ spl3_2 ),
inference(equality_resolution,[],[f46]) ).
thf(f58,plain,
( ! [X0: a] :
( ( sK0 != X0 )
| ( $false
= ( y @ X0 ) ) )
| ~ spl3_2 ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f118,plain,
( ( $false
= ( y @ sK0 ) )
| ~ spl3_2 ),
inference(equality_resolution,[],[f58]) ).
thf(f121,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f118,f38]) ).
thf(f125,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f126,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f125]) ).
thf(f127,plain,
( ( sK1
= ( (=) @ sK2 ) )
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f30,f37]) ).
thf(f128,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( sK2 = X1 ) )
| spl3_2 ),
inference(argument_congruence,[],[f127]) ).
thf(f130,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK2 = X1 ) ) )
| spl3_2 ),
inference(iff_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK2 = X1 ) )
| spl3_2 ),
inference(equality_proxy_clausification,[],[f130]) ).
thf(f140,plain,
( ( $true = $false )
| ( sK0 = sK2 )
| ~ spl3_1
| spl3_2 ),
inference(constrained_superposition,[],[f34,f131]) ).
thf(f141,plain,
( ( sK0 = sK2 )
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f160,plain,
( ( $true
= ( y @ sK0 ) )
| ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(constrained_superposition,[],[f43,f141]) ).
thf(f161,plain,
( $false
| ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f160,f37]) ).
thf(f162,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f161]) ).
cnf(s11,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s15,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s52,plain,
~ spl3_2,
inference(sat_conversion,[],[f126]) ).
cnf(s86,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f162]) ).
cnf(s88,plain,
spl3_3,
inference(rat,[],[s15,s52]) ).
cnf(s90,plain,
~ spl3_1,
inference(rat,[],[s86,s52,s88]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s11,s52,s90]) ).
thf(f163,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV239^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:22:08 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 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
% 0.06/0.25 % (457755)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (457764)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=424557060:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.25 % (457764)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.25 % (457761)% WARNING: option uhcvi not known.
% 0.06/0.25 % (457760)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2153909785_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.25 % (457761)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3879421190:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.25 % (457763)dis+10_1_sil=32000:sp=arity:random_seed=367019679:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.25 % Exception at run slice level
% 0.06/0.25 User error: % (457762)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=202400361:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.25 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.25 % (457766)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3320473892:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.25 % (457761)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.25 % (457761)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.06/0.25 % (457765)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1992603598:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.25 % (457763) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-457755-457763"...
% 0.06/0.25 % (457762) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-457755-457762"...
% 0.06/0.25 % (457764) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-457755-457764"...
% 0.06/0.25 % (457763)...printing done.
% 0.06/0.25 % (457766) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-457755-457766"...
% 0.06/0.25 % (457764)...printing done.
% 0.06/0.25 % (457762)...printing done.
% 0.06/0.25 % (457762)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (457762)------------------------------
% 0.06/0.25 % (457762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (457762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (457762)CaDiCaL version: 2.1.3
% 0.06/0.25 % (457762)Termination reason: Refutation
% 0.06/0.25 % (457762)Time elapsed: 0.006 s
% 0.06/0.25 % (457762)Peak memory usage: 13 MB
% 0.06/0.25 % (457762)Instructions burned: 8 (million)
% 0.06/0.25 % (457755)Success in time 0.042 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------