%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU934^5 : 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 : n007.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 08:31:58 AM UTC 2026
% Result : Theorem 0.30s 0.27s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 116 ( 58 equ; 6 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 58 ( 25 ~; 18 |; 3 &; 6 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn 14 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_1,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
! [X0: $i,X1: $i] :
( ( ( ^ [X2: $i] : ( X2 = X1 ) )
= ( ^ [X2: $i] : ( X2 = X0 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM14_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( ( ^ [X2: $i] : ( X2 = X1 ) )
= ( ^ [X2: $i] : ( X2 = X0 ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i] :
( ( ( ^ [X2: $i] : ( X2 = X1 ) )
= ( ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( X0 = Y0 ) )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: $i,X0: $i] :
( ( X0 != X1 )
& ( ( ^ [Y0: $i] : ( X0 = Y0 ) )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( ^ [Y0: $i] : ( X0 = Y0 ) )
= ( ^ [Y0: $i] : ( X1 = Y0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( (=) @ sK1 )
= ( (=) @ sK0 ) ),
inference(beta-eta_normalization,[],[f8]) ).
thf(f13,definition,
( spl2_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f15,plain,
( ( sK1 != sK0 )
| spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f16,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f9,f13]) ).
thf(f18,definition,
( spl2_2
<=> ( ( (=) @ sK1 )
= ( (=) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f20,plain,
( ( ( (=) @ sK1 )
= ( (=) @ sK0 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
spl2_2,
inference(avatar_split_clause,[],[f11,f18]) ).
thf(f22,plain,
( ! [X1: $i] :
( ( sK1 = X1 )
= ( sK0 = X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[],[f20]) ).
thf(f23,plain,
( ! [X1: $i] :
( ( ( sK0 = X1 )
= $false )
| ( $true
= ( sK1 = X1 ) ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( sK0 != X1 )
| ( $true
= ( sK1 = X1 ) ) )
| ~ spl2_2 ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f28,plain,
( ! [X1: $i] :
( ( sK1 = X1 )
| ( sK0 != X1 ) )
| ~ spl2_2 ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f31,plain,
( ! [X0: $i] :
( ( sK0 != X0 )
| ( sK0 != X0 ) )
| spl2_1
| ~ spl2_2 ),
inference(superposition,[],[f15,f28]) ).
thf(f33,plain,
( ! [X0: $i] : ( sK0 != X0 )
| spl2_1
| ~ spl2_2 ),
inference(duplicate_literal_removal,[],[f31]) ).
thf(f45,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(equality_resolution,[],[f33]) ).
thf(f48,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f16]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f21]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
spl2_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
thf(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU934^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:45:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.30/0.27 % (3459915)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.27 % (3459930)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3344734365:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.30/0.27 % (3459930) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3459915-3459930"...
% 0.30/0.27 % (3459930)...printing done.
% 0.30/0.27 % (3459930)Refutation found. Thanks to Tanya!
% 0.30/0.27 % SZS status Theorem for theBenchmark
% 0.30/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.27 % (3459930)------------------------------
% 0.30/0.27 % (3459930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.27 % (3459930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.27 % (3459930)CaDiCaL version: 2.1.3
% 0.30/0.27 % (3459930)Termination reason: Refutation
% 0.30/0.27 % (3459930)Time elapsed: 0.002 s
% 0.30/0.27 % (3459930)Peak memory usage: 13 MB
% 0.30/0.27 % (3459930)Instructions burned: 2 (million)
% 0.30/0.27 % (3459915)Success in time 0.026 s
% 0.30/0.27 % Vampire exiting
%------------------------------------------------------------------------------