%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU746_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 12:50:41 PM UTC 2026
% Result : Theorem 2.39s 1.07s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 247 ( 17 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 153 ( 42 ~; 43 |; 21 &)
% ( 7 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 117 ( 95 fml; 22 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 56 ( 0 sgn 46 !; 10 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK3: $o ).
tff(pred_def_3,type,
sQ5_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,binunion(X0,X1))
=> ( in(X2,X0)
| in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
tff(f2,conjecture,
( binunionE
=> ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
=> ! [X2: $i] :
( in(X2,powerset(X0))
=> ! [X3: $o,X4: $i] :
( in(X4,X0)
=> ( in(X4,binunion(X1,X2))
=> ( ( in(X4,X1)
=> (X3) )
=> ( ( in(X4,X2)
=> (X3) )
=> (X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTE) ).
tff(f3,negated_conjecture,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
=> ! [X2: $i] :
( in(X2,powerset(X0))
=> ! [X3: $o,X4: $i] :
( in(X4,X0)
=> ( in(X4,binunion(X1,X2))
=> ( ( in(X4,X1)
=> (X3) )
=> ( ( in(X4,X2)
=> (X3) )
=> (X3) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( binunionE
<=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,binunion(X0,X1))
=> ( in(X2,X0)
| in(X2,X1) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f5,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
=> ! [X2: $i] :
( in(X2,powerset(X0))
=> ! [X3: $o,X4: $i] :
( in(X4,X0)
=> ( in(X4,binunion(X1,X2))
=> ( ( in(X4,X1)
=> (X3) )
=> ( ( in(X4,X2)
=> (X3) )
=> (X3) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f6,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
=> ! [X2: $i] :
( in(X2,powerset(X0))
=> ! [X3: $o,X4: $i] :
( in(X4,X0)
=> ( in(X4,binunion(X1,X2))
=> ( ( in(X4,X1)
=> ( $true = (X3) ) )
=> ( ( in(X4,X2)
=> ( $true = (X3) ) )
=> ( $true = (X3) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( binunionE
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,binunion(X0,X1))
=> ( in(X2,X0)
| in(X2,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
tff(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,X1)
| ~ in(X2,binunion(X0,X1)) )
| ~ binunionE ),
inference(ennf_transformation,[],[f7]) ).
tff(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,X1)
| ~ in(X2,binunion(X0,X1)) )
| ~ binunionE ),
inference(flattening,[],[f8]) ).
tff(f10,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $o,X4: $i] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X4,X2) )
& ( ( $true = (X3) )
| ~ in(X4,X1) )
& in(X4,binunion(X1,X2))
& in(X4,X0) )
& in(X2,powerset(X0)) )
& in(X1,powerset(X0)) )
& binunionE ),
inference(ennf_transformation,[],[f6]) ).
tff(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $o,X4: $i] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X4,X2) )
& ( ( $true = (X3) )
| ~ in(X4,X1) )
& in(X4,binunion(X1,X2))
& in(X4,X0) )
& in(X2,powerset(X0)) )
& in(X1,powerset(X0)) )
& binunionE ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ~ in(sK4,sK2) )
& ( ( $true = sK3 )
| ~ in(sK4,sK1) )
& in(sK4,binunion(sK1,sK2))
& in(sK4,sK0)
& in(sK2,powerset(sK0))
& in(sK1,powerset(sK0))
& binunionE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f11]) ).
tff(f13,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,X0)
| in(X2,X1)
| ~ in(X2,binunion(X0,X1))
| ~ binunionE ),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
binunionE,
inference(cnf_transformation,[],[f12]) ).
tff(f18,plain,
in(sK4,binunion(sK1,sK2)),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
( ( $true = sK3 )
| ~ in(sK4,sK1) ),
inference(cnf_transformation,[],[f12]) ).
tff(f20,plain,
( ( $true = sK3 )
| ~ in(sK4,sK2) ),
inference(cnf_transformation,[],[f12]) ).
tff(f21,plain,
$true != sK3,
inference(cnf_transformation,[],[f12]) ).
tff(f24,definition,
! [X0: $o,X1: $o] :
( sQ5_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
tff(f27,plain,
~ sQ5_eqProxy($true,sK3),
inference(equality_proxy_replacement,[],[f21,f24]) ).
tff(f28,plain,
( sQ5_eqProxy($true,sK3)
| ~ in(sK4,sK2) ),
inference(equality_proxy_replacement,[],[f20,f24]) ).
tff(f29,plain,
( sQ5_eqProxy($true,sK3)
| ~ in(sK4,sK1) ),
inference(equality_proxy_replacement,[],[f19,f24]) ).
tff(f33,definition,
( spl6_1
<=> in(sK4,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f36,definition,
( spl6_2
<=> sQ5_eqProxy($true,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f37,plain,
( sQ5_eqProxy($true,sK3)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f38,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f29,f36,f33]) ).
tff(f40,definition,
( spl6_3
<=> in(sK4,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f42,plain,
( ~ spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f28,f36,f40]) ).
tff(f44,definition,
( spl6_4
<=> binunionE ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f45,plain,
( ~ binunionE
| spl6_4 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f47,definition,
( spl6_5
<=> ! [X2: $i,X0: $i,X1: $i] :
( in(X2,X0)
| ~ in(X2,binunion(X0,X1))
| in(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f48,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ~ in(X2,binunion(X0,X1))
| in(X2,X0)
| in(X2,X1) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f49,plain,
( ~ spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f13,f47,f44]) ).
tff(f50,plain,
( $false
| spl6_4 ),
inference(resolution,[],[f45,f14]) ).
tff(f51,plain,
spl6_4,
inference(avatar_contradiction_clause,[],[f50]) ).
tff(f52,plain,
( in(sK4,sK1)
| in(sK4,sK2)
| ~ spl6_5 ),
inference(resolution,[],[f18,f48]) ).
tff(f55,plain,
( spl6_3
| spl6_1
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f52,f47,f33,f40]) ).
tff(f56,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f37,f27]) ).
tff(f57,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f56]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( ~ spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
spl6_4,
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( spl6_1
| spl6_3
| ~ spl6_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s6,plain,
~ spl6_2,
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
spl6_5,
inference(rat,[],[s3,s4]) ).
cnf(s8,plain,
~ spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s9,plain,
spl6_1,
inference(rat,[],[s5,s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s6,s9]) ).
tff(f58,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU746_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n014.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 05:54:31 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.39/1.07 % (1518677)Detected formulas, will run a generic FOF schedule.
% 2.39/1.07 % (1518762)dis-21_1_sil=8000:lcm=predicate:random_seed=463775769: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)
% 2.39/1.07 % (1518762)First to succeed.
% 2.39/1.07 % (1518762)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1518677"
% 2.39/1.07 % (1518757)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=3762732299:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.39/1.07 % (1518759)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3822529060:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.39/1.07 % (1518756)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=4073347804:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.39/1.07 % (1518758)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=1893169477:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.39/1.07 % (1518760)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2972610116:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.39/1.07 % (1518760)Also succeeded, but the first one will report.
% 2.39/1.07 % (1518759)Also succeeded, but the first one will report.
% 2.39/1.07 % (1518761)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=204204593:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.39/1.07 % (1518761)Also succeeded, but the first one will report.
% 2.39/1.07 % (1518762)Refutation found. Thanks to Tanya!
% 2.39/1.07 % SZS status Theorem for theBenchmark
% 2.39/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/1.07 % (1518762)------------------------------
% 2.39/1.07 % (1518762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/1.07 % (1518762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/1.07 % (1518762)CaDiCaL version: 2.1.3
% 2.39/1.07 % (1518762)Termination reason: Refutation
% 2.39/1.07 % (1518762)Time elapsed: 0.002 s
% 2.39/1.07 % (1518762)Peak memory usage: 90 MB
% 2.39/1.07 % (1518762)Instructions burned: 2 (million)
% 2.39/1.07 % (1518762)------------------------------
% 2.39/1.07 % (1518762)------------------------------
% 2.39/1.07 % (1518677)Success in time 0.288 s
% 2.39/1.07 % Vampire exiting
%------------------------------------------------------------------------------