%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU633_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:50:00 PM UTC 2026
% Result : Theorem 3.60s 1.49s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 195 ( 27 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 144 ( 54 ~; 53 |; 12 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 106 ( 67 fml; 39 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 3-3 aty)
% Number of variables : 64 ( 0 sgn 58 !; 6 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_3,type,
sK0: ( $i * $i * $o ) > $i ).
tff(f1,axiom,
( setunionE
= ( ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
tff(f2,conjecture,
( setunionE
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ? [X2: $i] :
( in(X2,X0)
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
tff(f3,negated_conjecture,
~ ( setunionE
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ? [X2: $i] :
( in(X2,X0)
& in(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( setunionE
= ( ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ) ),
inference(rectify,[],[f1]) ).
tff(f5,plain,
( setunionE
<=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> ( $true = (X2) ) ) )
=> ( $true = (X2) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
tff(f6,plain,
( setunionE
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> ( $true = (X2) ) ) )
=> ( $true = (X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
tff(f7,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = (X2) )
| ? [X3: $i] :
( ( $true != (X2) )
& in(X3,X0)
& in(X1,X3) ) )
| ~ in(X1,setunion(X0)) )
| ~ setunionE ),
inference(ennf_transformation,[],[f6]) ).
tff(f8,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = (X2) )
| ? [X3: $i] :
( ( $true != (X2) )
& in(X3,X0)
& in(X1,X3) ) )
| ~ in(X1,setunion(X0)) )
| ~ setunionE ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X2) )
& in(X1,setunion(X0)) )
& setunionE ),
inference(ennf_transformation,[],[f3]) ).
tff(f10,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = (X2) )
| ( ( $true != (X2) )
& in(sK0(X0,X1,(X2)),X0)
& in(X1,sK0(X0,X1,(X2))) ) )
| ~ in(X1,setunion(X0)) )
| ~ setunionE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f8]) ).
tff(f11,plain,
( ! [X2: $i] :
( ~ in(X2,sK1)
| ~ in(sK2,X2) )
& in(sK2,setunion(sK1))
& setunionE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f9]) ).
tff(f12,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true = (X2) )
| in(X1,sK0(X0,X1,(X2)))
| ~ in(X1,setunion(X0))
| ~ setunionE ),
inference(cnf_transformation,[],[f10]) ).
tff(f13,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true = (X2) )
| in(sK0(X0,X1,(X2)),X0)
| ~ in(X1,setunion(X0))
| ~ setunionE ),
inference(cnf_transformation,[],[f10]) ).
tff(f15,plain,
setunionE,
inference(cnf_transformation,[],[f11]) ).
tff(f16,plain,
in(sK2,setunion(sK1)),
inference(cnf_transformation,[],[f11]) ).
tff(f17,plain,
! [X2: $i] :
( ~ in(X2,sK1)
| ~ in(sK2,X2) ),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f22,definition,
( spl3_1
<=> setunionE ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f26,definition,
( spl3_2
<=> ! [X2: $o,X0: $i,X1: $i] :
( ( $true = (X2) )
| ~ in(X1,setunion(X0))
| in(X1,sK0(X0,X1,(X2))) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f27,plain,
( ! [X2: $o,X0: $i,X1: $i] :
( in(X1,sK0(X0,X1,(X2)))
| ~ in(X1,setunion(X0))
| ( $true = (X2) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f28,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f12,f26,f22]) ).
tff(f30,definition,
( spl3_3
<=> ! [X2: $o,X0: $i,X1: $i] :
( ( $true = (X2) )
| ~ in(X1,setunion(X0))
| in(sK0(X0,X1,(X2)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f31,plain,
( ! [X2: $o,X0: $i,X1: $i] :
( ~ in(X1,setunion(X0))
| ( $true = (X2) )
| in(sK0(X0,X1,(X2)),X0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f32,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f13,f30,f22]) ).
tff(f33,plain,
spl3_1,
inference(avatar_split_clause,[],[f15,f22]) ).
tff(f36,plain,
( ! [X0: $o] :
( in(sK0(sK1,sK2,(X0)),sK1)
| ( $true = (X0) ) )
| ~ spl3_3 ),
inference(resolution,[],[f31,f16]) ).
tff(f37,plain,
( ! [X0: $o] :
( ~ in(sK2,sK0(sK1,sK2,(X0)))
| ( $true = (X0) ) )
| ~ spl3_3 ),
inference(resolution,[],[f36,f17]) ).
tff(f38,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ~ in(sK2,setunion(sK1))
| ( $true = (X0) ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(resolution,[],[f37,f27]) ).
tff(f39,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ~ in(sK2,setunion(sK1)) )
| ~ spl3_2
| ~ spl3_3 ),
inference(duplicate_literal_removal,[],[f38]) ).
tff(f40,plain,
( ! [X0: $o] : ( $true = (X0) )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f39,f16]) ).
tff(f41,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f40,f40]) ).
tff(f44,plain,
( ! [X0: $o] : ( $false != (X0) )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f18,f41]) ).
tff(f51,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f44,f41]) ).
tff(f52,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s6,plain,
spl3_3,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
~ spl3_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s3]) ).
tff(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU633_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:46:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.60/1.49 % (1502636)Detected formulas, will run a generic FOF schedule.
% 3.60/1.49 % (1502746)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2475462536:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.49 % (1502746)Refutation not found, incomplete strategy
% 3.60/1.49 % (1502746)------------------------------
% 3.60/1.49 % (1502746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (1502746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (1502746)CaDiCaL version: 2.1.3
% 3.60/1.49 % (1502746)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.49 % (1502746)Time elapsed: 0.001 s
% 3.60/1.49 % (1502746)Peak memory usage: 88 MB
% 3.60/1.49 % (1502744)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=1002299434:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.49 % (1502742)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=2498071166:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.49 % (1502747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4191827719:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.49 % (1502743)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=4290202056:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.49 % (1502745)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=375178701:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.49 % (1502745)Refutation not found, incomplete strategy
% 3.60/1.49 % (1502745)------------------------------
% 3.60/1.49 % (1502745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (1502745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (1502745)CaDiCaL version: 2.1.3
% 3.60/1.49 % (1502745)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.49 % (1502745)Time elapsed: 0.001 s
% 3.60/1.49 % (1502745)Peak memory usage: 87 MB
% 3.60/1.49 % (1502747)First to succeed.
% 3.60/1.49 % (1502747)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1502636"
% 3.60/1.49 % (1502748)dis-21_1_sil=8000:lcm=predicate:random_seed=4237519031: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)
% 3.60/1.49 % (1502748)Also succeeded, but the first one will report.
% 3.60/1.49 % (1502746)------------------------------
% 3.60/1.49 % (1502746)------------------------------
% 3.60/1.49 % (1502745)------------------------------
% 3.60/1.49 % (1502745)------------------------------
% 3.60/1.49 % (1502747)Refutation found. Thanks to Tanya!
% 3.60/1.49 % SZS status Theorem for theBenchmark
% 3.60/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.49 % (1502747)------------------------------
% 3.60/1.49 % (1502747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (1502747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (1502747)CaDiCaL version: 2.1.3
% 3.60/1.49 % (1502747)Termination reason: Refutation
% 3.60/1.49 % (1502747)Time elapsed: 0.004 s
% 3.60/1.49 % (1502747)Peak memory usage: 90 MB
% 3.60/1.49 % (1502747)Instructions burned: 2 (million)
% 3.60/1.49 % (1502747)------------------------------
% 3.60/1.49 % (1502747)------------------------------
% 3.60/1.49 % (1502636)Success in time 0.433 s
% 3.60/1.49 % Vampire exiting
%------------------------------------------------------------------------------