%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV065^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:37:34 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 174 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 289 ( 32 ~; 58 |; 57 &; 138 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 40 ( 22 ^; 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: a ).
thf(func_def_11,type,
sK1: b ).
thf(func_def_12,type,
sK2: b > a > $o ).
thf(func_def_13,type,
sK3: b ).
thf(func_def_14,type,
sK4: a ).
thf(f1,conjecture,
! [X0: b,X1: a,X2: b > a > $o] :
( ( X2 @ X0 @ X1 )
=> ( X2
= ( ^ [X3: b,X4: a] :
( ( ( X2 @ X3 @ X4 )
& ~ ( ( X4 = X1 )
& ( X3 = X0 ) ) )
| ( ( X3 = X0 )
& ( X4 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM177_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: b,X1: a,X2: b > a > $o] :
( ( X2 @ X0 @ X1 )
=> ( X2
= ( ^ [X3: b,X4: a] :
( ( ( X2 @ X3 @ X4 )
& ~ ( ( X4 = X1 )
& ( X3 = X0 ) ) )
| ( ( X3 = X0 )
& ( X4 = X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: b,X1: a,X2: b > a > $o] :
( ( X2 @ X0 @ X1 )
=> ( X2
= ( ^ [X3: b,X4: a] :
( ( ( X2 @ X3 @ X4 )
& ~ ( ( X4 = X1 )
& ( X3 = X0 ) ) )
| ( ( X3 = X0 )
& ( X4 = X1 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: b,X1: a,X2: b > a > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
=> ( ( ^ [Y0: b,Y1: a] :
( ( ( X1 = Y1 )
& ( X0 = Y0 ) )
| ( ~ ( ( X0 = Y0 )
& ( X1 = Y1 ) )
& ( X2 @ Y0 @ Y1 ) ) ) )
= X2 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a,X0: b,X2: b > a > $o] :
( ( ( ^ [Y0: b,Y1: a] :
( ( ( X1 = Y1 )
& ( X0 = Y0 ) )
| ( ~ ( ( X0 = Y0 )
& ( X1 = Y1 ) )
& ( X2 @ Y0 @ Y1 ) ) ) )
!= X2 )
& ( ( X2 @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a,X1: b,X2: b > a > $o] :
( ( ( ^ [Y0: b,Y1: a] :
( ( ( X0 = Y1 )
& ( X1 = Y0 ) )
| ( ~ ( ( X1 = Y0 )
& ( X0 = Y1 ) )
& ( X2 @ Y0 @ Y1 ) ) ) )
!= X2 )
& ( ( X2 @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( ^ [Y0: b,Y1: a] :
( ( ( sK0 = Y1 )
& ( sK1 = Y0 ) )
| ( ~ ( ( sK1 = Y0 )
& ( sK0 = Y1 ) )
& ( sK2 @ Y0 @ Y1 ) ) ) )
!= sK2 )
& ( ( sK2 @ sK1 @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( sK2 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ^ [Y0: b,Y1: a] :
( ( ( sK0 = Y1 )
& ( sK1 = Y0 ) )
| ( ~ ( ( sK1 = Y0 )
& ( sK0 = Y1 ) )
& ( sK2 @ Y0 @ Y1 ) ) ) )
!= sK2 ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: b,Y1: a] :
( ( ( sK0 = Y1 )
& ( sK1 = Y0 ) )
| ( ~ ( ( sK1 = Y0 )
& ( sK0 = Y1 ) )
& ( sK2 @ Y0 @ Y1 ) ) )
@ sK3 )
!= ( sK2 @ sK3 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f12,plain,
( ( sK2 @ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 = Y0 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = Y0 ) )
& ( sK2 @ sK3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( ( ( sK0 = Y0 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = Y0 ) )
& ( sK2 @ sK3 @ Y0 ) ) )
@ sK4 )
!= ( sK2 @ sK3 @ sK4 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f14,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 = Y0 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = Y0 ) )
& ( sK2 @ sK3 @ Y0 ) ) )
@ sK4 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK0 = Y0 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = Y0 ) )
& ( sK2 @ sK3 @ Y0 ) ) )
@ sK4 ) )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( ( ( sK0 = sK4 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = sK4 ) )
& ( sK2 @ sK3 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( ( sK1 = sK3 )
& ( sK0 = sK4 ) )
& ( sK2 @ sK3 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( ( sK0 = sK4 )
& ( sK1 = sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( ( sK0 = sK4 )
= $false )
| ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( sK1 = sK3 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( sK1 = sK3 ) )
| ( sK4 != sK0 ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( sK4 != sK0 )
| ( sK3 != sK1 )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( ~ ( ( sK1 = sK3 )
& ( sK0 = sK4 ) ) )
= $false )
| ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f23,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( ( sK1 = sK3 )
& ( sK0 = sK4 ) ) )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ( sK0 = sK4 )
= $true )
| ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 = sK3 ) )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( sK3 = sK1 )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( sK3 = sK1 ) ),
inference(duplicate_literal_removal,[],[f26]) ).
thf(f28,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( sK4 = sK0 )
| ( $false
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f29,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( sK4 = sK0 ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( ( ( sK0 = sK4 )
& ( sK1 = sK3 ) )
| ( ~ ( ( sK1 = sK3 )
& ( sK0 = sK4 ) )
& ( sK2 @ sK3 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f31,plain,
( ( $true
= ( ~ ( ( sK1 = sK3 )
& ( sK0 = sK4 ) )
& ( sK2 @ sK3 @ sK4 ) ) )
| ( ( ( sK0 = sK4 )
& ( sK1 = sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( ( ( sK0 = sK4 )
& ( sK1 = sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f45,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 = sK3 ) )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f46,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( ( sK0 = sK4 )
= $true )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f47,plain,
( ( sK4 = sK0 )
| ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( sK4 = sK0 )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(duplicate_literal_removal,[],[f47]) ).
thf(f49,plain,
( ( sK3 = sK1 )
| ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f50,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( sK3 = sK1 ) ),
inference(duplicate_literal_removal,[],[f49]) ).
thf(f51,plain,
( ( $false
= ( sK2 @ sK3 @ sK4 ) )
| ( sK3 != sK1 ) ),
inference(forward_subsumption_resolution,[],[f21,f29]) ).
thf(f52,plain,
( $false
= ( sK2 @ sK3 @ sK4 ) ),
inference(forward_subsumption_resolution,[],[f51,f27]) ).
thf(f53,plain,
( ( $false = $true )
| ( sK4 = sK0 ) ),
inference(forward_demodulation,[],[f48,f52]) ).
thf(f54,plain,
sK4 = sK0,
inference(trivial_inequality_removal,[],[f53]) ).
thf(f57,plain,
( ( $false = $true )
| ( sK3 = sK1 ) ),
inference(forward_demodulation,[],[f50,f52]) ).
thf(f58,plain,
sK3 = sK1,
inference(trivial_inequality_removal,[],[f57]) ).
thf(f60,plain,
( ( sK2 @ sK1 @ sK4 )
= $false ),
inference(superposition,[],[f52,f58]) ).
thf(f62,plain,
( ( sK2 @ sK1 @ sK0 )
= $false ),
inference(forward_demodulation,[],[f60,f54]) ).
thf(f64,plain,
$false = $true,
inference(superposition,[],[f8,f62]) ).
thf(f65,plain,
$false,
inference(trivial_inequality_removal,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV065^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n026.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 15:08:57 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.31 % (717381)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (717390)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3602410668:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (717390) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-717381-717390"...
% 0.23/0.31 % (717390)...printing done.
% 0.23/0.31 % (717392)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (717392)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.31 % (717390)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (717390)------------------------------
% 0.23/0.31 % (717390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (717390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (717390)CaDiCaL version: 2.1.3
% 0.23/0.31 % (717390)Termination reason: Refutation
% 0.23/0.31 % (717390)Time elapsed: 0.003 s
% 0.23/0.31 % (717390)Peak memory usage: 12 MB
% 0.23/0.31 % (717390)Instructions burned: 5 (million)
% 0.23/0.31 % (717381)Success in time 0.04 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------