%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET169^5 : 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 : n019.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 08:23:35 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 306 ( 84 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 322 ( 7 ~; 77 |; 56 &; 182 @)
% ( 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 : 12 ( 9 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,
vOR: $o > $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_7,type,
sK2: a > $o ).
thf(func_def_10,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_70_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,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f18,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f23,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f27,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f28,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f30,plain,
( ( $true
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f36,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f36]) ).
thf(f42,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f43,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f50,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f53,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f50]) ).
thf(f62,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f20,f37]) ).
thf(f63,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(forward_demodulation,[],[f28,f37]) ).
thf(f65,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f53,f65]) ).
thf(f67,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
$true = $false,
inference(forward_demodulation,[],[f67,f63]) ).
thf(f69,plain,
$false,
inference(trivial_inequality_removal,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:37:19 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.20/0.27 % (771030)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (771038)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=416734117:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.20/0.27 % (771038) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-771030-771038"...
% 0.20/0.27 % (771038)...printing done.
% 0.20/0.27 % (771038)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (771038)------------------------------
% 0.20/0.27 % (771038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (771038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (771038)CaDiCaL version: 2.1.3
% 0.20/0.27 % (771038)Termination reason: Refutation
% 0.20/0.27 % (771038)Time elapsed: 0.002 s
% 0.20/0.27 % (771038)Peak memory usage: 12 MB
% 0.20/0.27 % (771038)Instructions burned: 4 (million)
% 0.20/0.27 % (771030)Success in time 0.017 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------