%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Tue Sep 29 12:52:42 PM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 7 unt; 5 def)
% Number of atoms : 219 ( 37 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 242 ( 97 ~; 104 |; 25 &)
% ( 11 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 72 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( in(X2,X0)
& ordinal(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( in(X2,X0)
& ordinal(X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( X1 = X2
& ordinal(X2)
& X1 = X3
& ordinal(X3) )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& X3 = X2
& ordinal(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(f8,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( X1 = X2
& ordinal(X2)
& X1 = X3
& ordinal(X3) )
=> X2 = X3 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,X0)
& X5 = X6
& ordinal(X5) ) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
? [X0] :
! [X1] :
? [X2] :
( in(X2,X1)
<~> ( in(X2,X0)
& ordinal(X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,X0)
& X5 = X6
& ordinal(X5) ) )
| ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ordinal(X2)
& X1 = X3
& ordinal(X3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,X0)
& X5 = X6
& ordinal(X5) ) )
| ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ordinal(X2)
& X1 = X3
& ordinal(X3) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X1] :
( ~ ordinal(sK1(X1))
| ~ in(sK1(X1),sK0)
| ~ in(sK1(X1),X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X1] :
( ordinal(sK1(X1))
| in(sK1(X1),X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X1] :
( in(sK1(X1),sK0)
| in(sK1(X1),X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X6,X5] :
( ~ ordinal(X5)
| X5 != X6
| ~ in(X6,X0)
| sP7(X5,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X5] :
( ordinal(X5)
| ~ sP7(X5,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X5] :
( ~ sP7(X5,X0)
| sK8(X0,X5) = X5 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X5] :
( ~ sP7(X5,X0)
| in(sK8(X0,X5),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X5] :
( sK4 != sK5
| ~ sP7(X5,X0)
| in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0,X5] :
( sK4 != sK5
| sP7(X5,X0)
| ~ in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X0,X5] :
( sK3 = sK4
| ~ sP7(X5,X0)
| in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
! [X0,X5] :
( sK3 = sK4
| sP7(X5,X0)
| ~ in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X5] :
( sK3 = sK5
| ~ sP7(X5,X0)
| in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0,X5] :
( sK3 = sK5
| sP7(X5,X0)
| ~ in(X5,sK6(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0,X6] :
( ~ ordinal(X6)
| ~ in(X6,X0)
| sP7(X6,X0) ),
inference(equality_resolution,[],[f26]) ).
fof(f42,definition,
( spl9_1
<=> ! [X5,X0] :
( ~ sP7(X5,X0)
| in(X5,sK6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f43,plain,
( ! [X0,X5] :
( ~ sP7(X5,X0)
| in(X5,sK6(X0)) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl9_2
<=> sK4 = sK5 ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f47,plain,
( sK4 != sK5
| spl9_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f30,f45,f42]) ).
fof(f50,definition,
( spl9_3
<=> ! [X5,X0] :
( sP7(X5,X0)
| ~ in(X5,sK6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0,X5] :
( sP7(X5,X0)
| ~ in(X5,sK6(X0)) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( spl9_3
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f31,f45,f50]) ).
fof(f54,definition,
( spl9_4
<=> sK3 = sK4 ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f56,plain,
( sK3 = sK4
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f32,f54,f42]) ).
fof(f58,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f33,f54,f50]) ).
fof(f66,definition,
( spl9_6
<=> sK3 = sK5 ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f68,plain,
( sK3 = sK5
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl9_1
| spl9_6 ),
inference(avatar_split_clause,[],[f36,f66,f42]) ).
fof(f70,plain,
( spl9_3
| spl9_6 ),
inference(avatar_split_clause,[],[f37,f66,f50]) ).
fof(f77,plain,
( sK4 = sK5
| ~ spl9_4
| ~ spl9_6 ),
inference(forward_demodulation,[],[f68,f56]) ).
fof(f78,plain,
( $false
| spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(forward_subsumption_resolution,[],[f77,f47]) ).
fof(f79,plain,
( spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( ~ sP7(sK1(X0),X1)
| ~ in(sK1(X0),sK0)
| ~ in(sK1(X0),X0) ),
inference(resolution,[],[f27,f16]) ).
fof(f91,plain,
( ! [X0,X1] :
( ~ in(sK1(X0),sK6(X1))
| ~ in(sK1(X0),X0)
| ~ in(sK1(X0),sK0) )
| ~ spl9_3 ),
inference(resolution,[],[f51,f83]) ).
fof(f95,plain,
( ! [X0,X1] :
( ~ in(X1,sK6(X0))
| sK8(X0,X1) = X1 )
| ~ spl9_3 ),
inference(resolution,[],[f28,f51]) ).
fof(f98,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| ~ in(X1,sK6(X0)) )
| ~ spl9_3 ),
inference(resolution,[],[f29,f51]) ).
fof(f100,plain,
! [X0,X1] :
( sP7(sK1(X0),X1)
| ~ in(sK1(X0),X1)
| in(sK1(X0),X0) ),
inference(resolution,[],[f40,f17]) ).
fof(f109,plain,
( ! [X0,X1] :
( in(sK1(X0),X0)
| in(sK1(X0),sK6(X1))
| ~ in(sK1(X0),X1) )
| ~ spl9_1 ),
inference(resolution,[],[f100,f43]) ).
fof(f127,plain,
( ! [X0] :
( in(sK1(sK6(X0)),sK6(X0))
| ~ in(sK1(sK6(X0)),X0) )
| ~ spl9_1 ),
inference(factoring,[],[f109]) ).
fof(f131,plain,
( ! [X0] :
( in(sK1(sK6(X0)),sK0)
| sK1(sK6(X0)) = sK8(X0,sK1(sK6(X0))) )
| ~ spl9_3 ),
inference(resolution,[],[f95,f18]) ).
fof(f133,plain,
( ! [X0,X1] :
( ~ in(sK1(sK6(X0)),X0)
| ~ in(sK1(sK6(X0)),sK6(X1))
| ~ in(sK1(sK6(X0)),sK0) )
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f127,f91]) ).
fof(f134,plain,
( ! [X0] :
( ~ in(sK1(sK6(X0)),X0)
| sK1(sK6(X0)) = sK8(X0,sK1(sK6(X0))) )
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f127,f95]) ).
fof(f199,plain,
( sK1(sK6(sK0)) = sK8(sK0,sK1(sK6(sK0)))
| sK1(sK6(sK0)) = sK8(sK0,sK1(sK6(sK0)))
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f134,f131]) ).
fof(f200,plain,
( sK1(sK6(sK0)) = sK8(sK0,sK1(sK6(sK0)))
| ~ spl9_1
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f205,plain,
( in(sK1(sK6(sK0)),sK0)
| ~ in(sK1(sK6(sK0)),sK6(sK0))
| ~ spl9_1
| ~ spl9_3 ),
inference(superposition,[],[f98,f200]) ).
fof(f206,plain,
( in(sK1(sK6(sK0)),sK0)
| ~ spl9_1
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f205,f18]) ).
fof(f295,plain,
( ! [X0] :
( ~ in(sK1(sK6(X0)),X0)
| ~ in(sK1(sK6(X0)),sK0)
| ~ in(sK1(sK6(X0)),X0) )
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f133,f127]) ).
fof(f308,plain,
( ! [X0] :
( ~ in(sK1(sK6(X0)),X0)
| ~ in(sK1(sK6(X0)),sK0) )
| ~ spl9_1
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f354,plain,
( ~ in(sK1(sK6(sK0)),sK0)
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f308,f206]) ).
fof(f361,plain,
( $false
| ~ spl9_1
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f354,f206]) ).
fof(f362,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f361]) ).
cnf(s1,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( ~ spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
( spl9_1
| spl9_6 ),
inference(sat_conversion,[],[f69]) ).
cnf(s8,plain,
( spl9_3
| spl9_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s11,plain,
( spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(sat_conversion,[],[f79]) ).
cnf(s13,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(sat_conversion,[],[f362]) ).
cnf(s14,plain,
spl9_1,
inference(rat,[],[s11,s1,s3,s7]) ).
cnf(s15,plain,
~ spl9_3,
inference(rat,[],[s13,s14]) ).
cnf(s17,plain,
spl9_6,
inference(rat,[],[s8,s15]) ).
cnf(s19,plain,
spl9_4,
inference(rat,[],[s4,s15]) ).
cnf(s20,plain,
~ spl9_2,
inference(rat,[],[s2,s15]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s11,s17,s19,s20]) ).
fof(f363,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 04:28:54 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.18/0.46 % (1873628)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (1873642)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1989692183:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (1873639)% WARNING: option uhcvi not known.
% 0.18/0.46 % (1873642) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1873628-1873642"...
% 0.18/0.46 % (1873639)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1946602598:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.46 % (1873641)dis+10_1_sil=32000:sp=arity:random_seed=2377894017:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (1873638)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1942156066_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.46 % (1873640)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=125822540:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.46 % (1873642)...printing done.
% 0.18/0.46 % (1873642)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (1873642)------------------------------
% 0.18/0.46 % (1873642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (1873642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (1873642)CaDiCaL version: 2.1.3
% 0.18/0.46 % (1873642)Termination reason: Refutation
% 0.18/0.46 % (1873642)Time elapsed: 0.007 s
% 0.18/0.46 % (1873642)Peak memory usage: 12 MB
% 0.18/0.46 % (1873642)Instructions burned: 17 (million)
% 0.18/0.46 % (1873628)Success in time 0.03 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------