%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU849^5 : 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 : n002.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 08:34:17 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 331 ( 85 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 327 ( 65 ~; 94 |; 32 &; 119 @)
% ( 11 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 57 ( 0 sgn 26 !; 8 ?; 57 :)
% 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,
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 ).
thf(func_def_10,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM39_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 )
<=> ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 )
<=> ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 )
<~> ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X0 ) )
& ( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X0 ) )
& ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( $true
!= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
| ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( spl3_1
<=> ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f18,plain,
( ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f20,definition,
( spl3_2
<=> ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f10,f20,f16]) ).
thf(f24,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f11,f24,f16]) ).
thf(f29,definition,
( spl3_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f12,f29,f16]) ).
thf(f33,plain,
( ( ( sK0 @ sK4 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_1 ),
inference(negative_extensionality,[],[f17]) ).
thf(f34,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_1 ),
inference(xor_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_1 ),
inference(xor_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| spl3_1 ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| spl3_1 ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ sK4 ) )
| spl3_1 ),
inference(duplicate_literal_removal,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| spl3_1 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) )
| spl3_1 ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( ( $true
= ( sK0 @ sK4 ) )
| spl3_1 ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f44,definition,
( spl3_5
<=> ( $false
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f46,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl3_6
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f50,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl3_5
| spl3_6
| spl3_1 ),
inference(avatar_split_clause,[],[f38,f16,f48,f44]) ).
thf(f53,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK4 ) )
| spl3_1
| ~ spl3_2 ),
inference(constrained_superposition,[],[f21,f42]) ).
thf(f54,plain,
( ( $true
= ( sK1 @ sK4 ) )
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
( ( $true = $false )
| spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[],[f54,f46]) ).
thf(f56,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f57,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f56]) ).
thf(f69,plain,
( ( $true = $false )
| spl3_1
| ~ spl3_6 ),
inference(constrained_superposition,[],[f50,f42]) ).
thf(f76,plain,
( $false
| spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f77,plain,
( spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f76]) ).
thf(f83,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_1 ),
inference(argument_congruence,[],[f18]) ).
thf(f85,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ) )
| ~ spl3_1 ),
inference(iff_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_1 ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f97,plain,
( ( $true != $true )
| ( ( sK0 @ sK2 )
= $false )
| ~ spl3_1
| spl3_4 ),
inference(constrained_superposition,[],[f31,f87]) ).
thf(f98,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl3_1
| spl3_4 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f101,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(constrained_superposition,[],[f98,f26]) ).
thf(f107,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f108,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f107]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
( spl3_1
| spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
( spl3_1
| ~ spl3_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s10,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f108]) ).
cnf(s11,plain,
( spl3_1
| spl3_6 ),
inference(rat,[],[s5,s1,s4]) ).
cnf(s12,plain,
spl3_1,
inference(rat,[],[s11,s7]) ).
cnf(s13,plain,
~ spl3_4,
inference(rat,[],[s3,s12]) ).
cnf(s14,plain,
spl3_3,
inference(rat,[],[s2,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s10,s12,s13,s14]) ).
thf(f109,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU849^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 14:42:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.27 % (1382709)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (1382729)dis+10_1_sil=32000:sp=arity:random_seed=3608725282:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (1382729) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1382709-1382729"...
% 0.20/0.27 % (1382729)...printing done.
% 0.20/0.27 % (1382727)% WARNING: option uhcvi not known.
% 0.20/0.27 % (1382729)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 % (1382729)------------------------------
% 0.20/0.27 % (1382729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1382729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1382729)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1382729)Termination reason: Refutation
% 0.20/0.27 % (1382729)Time elapsed: 0.003 s
% 0.20/0.27 % (1382729)Peak memory usage: 12 MB
% 0.20/0.27 % (1382729)Instructions burned: 5 (million)
% 0.20/0.27 % (1382709)Success in time 0.034 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------