%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU615_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:49:54 PM UTC 2026
% Result : Theorem 3.35s 1.35s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 229 ( 28 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 187 ( 77 ~; 45 |; 25 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 117 ( 76 fml; 41 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 10 prp; 0-4 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 79 ( 0 sgn 73 !; 6 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_3,type,
sP0: ( $o * $i * $i * $i ) > $o ).
tff(f1,axiom,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> (X3) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> (X3) ) )
=> (X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
tff(f2,conjecture,
( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
=> ( ~ in(X2,X1)
=> ~ in(X2,symdiff(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
tff(f3,negated_conjecture,
~ ( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
=> ( ~ in(X2,X1)
=> ~ in(X2,symdiff(X0,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> (X3) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> (X3) ) )
=> (X3) ) ) ) ) ),
inference(rectify,[],[f1]) ).
tff(f5,plain,
( symdiffE
<=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
tff(f6,plain,
( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
tff(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) ) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(ennf_transformation,[],[f6]) ).
tff(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) ) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
& ~ in(X2,X1)
& ~ in(X2,X0) )
& symdiffE ),
inference(ennf_transformation,[],[f3]) ).
tff(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( in(X2,symdiff(X0,X1))
& ~ in(X2,X1)
& ~ in(X2,X0) )
& symdiffE ),
inference(flattening,[],[f9]) ).
tff(f11,definition,
! [X3: $o,X1: $i,X2: $i,X0: $i] :
( ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) )
| ~ sP0((X3),X1,X2,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| sP0((X3),X1,X2,X0) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(definition_folding,[],[f8,f11]) ).
tff(f13,plain,
! [X3: $o,X1: $i,X2: $i,X0: $i] :
( ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) )
| ~ sP0((X3),X1,X2,X0) ),
inference(nnf_transformation,[],[f11]) ).
tff(f14,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i] :
( ( ( $true != (X0) )
& ~ in(X2,X1)
& in(X2,X3) )
| ~ sP0((X0),X1,X2,X3) ),
inference(rectify,[],[f13]) ).
tff(f15,plain,
( in(sK3,symdiff(sK1,sK2))
& ~ in(sK3,sK2)
& ~ in(sK3,sK1)
& symdiffE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f10]) ).
tff(f16,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( in(X2,X3)
| ~ sP0((X0),X1,X2,X3) ),
inference(cnf_transformation,[],[f14]) ).
tff(f20,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true = (X3) )
| in(X2,X1)
| sP0((X3),X1,X2,X0)
| ~ in(X2,symdiff(X0,X1))
| ~ symdiffE ),
inference(cnf_transformation,[],[f12]) ).
tff(f22,plain,
symdiffE,
inference(cnf_transformation,[],[f15]) ).
tff(f23,plain,
~ in(sK3,sK1),
inference(cnf_transformation,[],[f15]) ).
tff(f24,plain,
~ in(sK3,sK2),
inference(cnf_transformation,[],[f15]) ).
tff(f25,plain,
in(sK3,symdiff(sK1,sK2)),
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f31,definition,
( spl4_1
<=> symdiffE ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f39,definition,
( spl4_3
<=> ! [X0: $i,X3: $o,X2: $i,X1: $i] :
( ( $true = (X3) )
| ~ in(X2,symdiff(X0,X1))
| sP0((X3),X1,X2,X0)
| in(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f40,plain,
( ! [X2: $i,X3: $o,X0: $i,X1: $i] :
( sP0((X3),X1,X2,X0)
| ~ in(X2,symdiff(X0,X1))
| ( $true = (X3) )
| in(X2,X1) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f41,plain,
( ~ spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f20,f39,f31]) ).
tff(f42,plain,
spl4_1,
inference(avatar_split_clause,[],[f22,f31]) ).
tff(f47,plain,
! [X0: $o,X1: $i] : ~ sP0((X0),X1,sK3,sK1),
inference(resolution,[],[f16,f23]) ).
tff(f51,plain,
( ! [X0: $i,X1: $o] :
( ~ in(sK3,symdiff(sK1,X0))
| ( $true = (X1) )
| in(sK3,X0) )
| ~ spl4_3 ),
inference(resolution,[],[f47,f40]) ).
tff(f54,definition,
( spl4_4
<=> ! [X1: $o] : ( $true = (X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f55,plain,
( ! [X1: $o] : ( $true = (X1) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f57,definition,
( spl4_5
<=> ! [X0: $i] :
( ~ in(sK3,symdiff(sK1,X0))
| in(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f58,plain,
( ! [X0: $i] :
( ~ in(sK3,symdiff(sK1,X0))
| in(sK3,X0) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f57]) ).
tff(f59,plain,
( spl4_4
| spl4_5
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f51,f39,f57,f54]) ).
tff(f66,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl4_4 ),
inference(superposition,[],[f55,f55]) ).
tff(f73,plain,
( ! [X0: $o] : ( $false != (X0) )
| ~ spl4_4 ),
inference(superposition,[],[f26,f66]) ).
tff(f81,plain,
( $false
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f73,f66]) ).
tff(f82,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f81]) ).
tff(f94,plain,
( in(sK3,sK2)
| ~ spl4_5 ),
inference(resolution,[],[f58,f25]) ).
tff(f96,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f94,f24]) ).
tff(f97,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f96]) ).
cnf(s2,plain,
( ~ spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f42]) ).
cnf(s4,plain,
( ~ spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f59]) ).
cnf(s7,plain,
~ spl4_4,
inference(sat_conversion,[],[f82]) ).
cnf(s9,plain,
~ spl4_5,
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
~ spl4_3,
inference(rat,[],[s4,s9,s7]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s11,s3]) ).
tff(f98,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU615_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 05:46:50 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.35/1.35 % (4110362)Detected formulas, will run a generic FOF schedule.
% 3.35/1.35 % (4110447)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3055639945:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.35 % (4110450)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1507675959:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.35 % (4110450)First to succeed.
% 3.35/1.35 % (4110450)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4110362"
% 3.35/1.35 % (4110446)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2101578976:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.35 % (4110445)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=991385979:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.35 % (4110449)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2053069120:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.35 % (4110448)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2734112159:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.35 % (4110449)Refutation not found, incomplete strategy
% 3.35/1.35 % (4110449)------------------------------
% 3.35/1.35 % (4110449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.35 % (4110449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.35 % (4110449)CaDiCaL version: 2.1.3
% 3.35/1.35 % (4110449)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.35 % (4110449)Time elapsed: 0.001 s
% 3.35/1.35 % (4110449)Peak memory usage: 87 MB
% 3.35/1.35 % (4110448)Refutation not found, incomplete strategy
% 3.35/1.35 % (4110448)------------------------------
% 3.35/1.35 % (4110448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.35 % (4110448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.35 % (4110448)CaDiCaL version: 2.1.3
% 3.35/1.35 % (4110448)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.35 % (4110448)Time elapsed: 0.001 s
% 3.35/1.35 % (4110448)Peak memory usage: 87 MB
% 3.35/1.35 % (4110451)dis-21_1_sil=8000:lcm=predicate:random_seed=2011949610:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.35/1.35 % (4110451)Also succeeded, but the first one will report.
% 3.35/1.35 % (4110449)------------------------------
% 3.35/1.35 % (4110449)------------------------------
% 3.35/1.35 % (4110448)------------------------------
% 3.35/1.35 % (4110448)------------------------------
% 3.35/1.35 % (4110450)Refutation found. Thanks to Tanya!
% 3.35/1.35 % SZS status Theorem for theBenchmark
% 3.35/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.36 % (4110450)------------------------------
% 3.35/1.36 % (4110450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.36 % (4110450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.36 % (4110450)CaDiCaL version: 2.1.3
% 3.35/1.36 % (4110450)Termination reason: Refutation
% 3.35/1.36 % (4110450)Time elapsed: 0.004 s
% 3.35/1.36 % (4110450)Peak memory usage: 90 MB
% 3.35/1.36 % (4110450)Instructions burned: 3 (million)
% 3.35/1.36 % (4110450)------------------------------
% 3.35/1.36 % (4110450)------------------------------
% 3.35/1.36 % (4110362)Success in time 0.397 s
% 3.35/1.36 % Vampire exiting
%------------------------------------------------------------------------------