%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:19:28 AM UTC 2026
% Result : Theorem 2.67s 1.15s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 11 unt; 1 def)
% Number of atoms : 130 ( 42 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 156 ( 60 ~; 51 |; 29 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 48 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_pboole(X2,X1) )
=> ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f33,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f34,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(flattening,[],[f38]) ).
fof(f46,plain,
( k1_xboole_0 != k1_funct_1(sK1,sK2)
& ~ r2_hidden(sK2,k1_closure3(sK0,sK1))
& m1_subset_1(sK2,sK0)
& m1_pboole(sK1,sK0)
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f34]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_closure3(X0,X1)
| a_2_0_closure3(X0,X1) != X2 )
& ( X2 = a_2_0_closure3(X0,X1)
| k1_closure3(X0,X1) != X2 ) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(nnf_transformation,[],[f39]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X4] :
( m1_subset_1(X4,X1)
& X0 = X4
& k1_xboole_0 != k1_funct_1(X2,X4) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ( m1_subset_1(sK6(X0,X1,X2),X1)
& sK6(X0,X1,X2) = X0
& k1_xboole_0 != k1_funct_1(X2,sK6(X0,X1,X2)) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f53]) ).
fof(f57,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
m1_subset_1(sK2,sK0),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
~ r2_hidden(sK2,k1_closure3(sK0,sK1)),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
k1_xboole_0 != k1_funct_1(sK1,sK2),
inference(cnf_transformation,[],[f46]) ).
fof(f66,plain,
! [X2,X0,X1] :
( k1_closure3(X0,X1) = X2
| a_2_0_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f81,definition,
~ sP9(k1_xboole_0),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f82,plain,
sP9(k1_funct_1(sK1,sK2)),
inference(inequality_splitting,[],[f61,f81]) ).
fof(f85,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f66]) ).
fof(f87,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(equality_resolution,[],[f72]) ).
fof(f95,plain,
( ~ r2_hidden(sK2,a_2_0_closure3(sK0,sK1))
| ~ m1_pboole(sK1,sK0)
| v1_xboole_0(sK0) ),
inference(superposition,[],[f60,f85]) ).
fof(f96,plain,
( ~ r2_hidden(sK2,a_2_0_closure3(sK0,sK1))
| v1_xboole_0(sK0) ),
inference(forward_subsumption_resolution,[],[f95,f58]) ).
fof(f98,plain,
~ r2_hidden(sK2,a_2_0_closure3(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f96,f57]) ).
fof(f101,plain,
( ~ m1_subset_1(sK2,sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK2)
| v1_xboole_0(sK0)
| ~ m1_pboole(sK1,sK0) ),
inference(resolution,[],[f98,f87]) ).
fof(f102,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK2)
| v1_xboole_0(sK0)
| ~ m1_pboole(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f101,f59]) ).
fof(f103,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK2)
| ~ m1_pboole(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f102,f57]) ).
fof(f104,plain,
k1_xboole_0 = k1_funct_1(sK1,sK2),
inference(forward_subsumption_resolution,[],[f103,f58]) ).
fof(f106,plain,
sP9(k1_xboole_0),
inference(superposition,[],[f82,f104]) ).
fof(f107,plain,
$false,
inference(forward_subsumption_resolution,[],[f106,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 19:53:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.67/1.15 % (2250572)Detected formulas, will run a generic FOF schedule.
% 2.67/1.15 % (2250580)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2746533840:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.15 % (2250580)First to succeed.
% 2.67/1.15 % (2250580)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2250572"
% 2.67/1.15 % (2250582)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2394884095:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.15 % (2250578)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=549514499:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.15 % (2250577)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=2399651453:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.15 % (2250579)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=1027779869:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.15 % (2250583)dis-21_1_sil=8000:lcm=predicate:random_seed=665834824: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)
% 2.67/1.15 % (2250581)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3074310018:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.15 % (2250582)Also succeeded, but the first one will report.
% 2.67/1.15 % (2250581)Also succeeded, but the first one will report.
% 2.67/1.15 % (2250583)Instruction limit reached!
% 2.67/1.15 % (2250583)------------------------------
% 2.67/1.15 % (2250583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.15 % (2250583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.15 % (2250583)CaDiCaL version: 2.1.3
% 2.67/1.15 % (2250583)Termination reason: Instruction limit
% 2.67/1.15 % (2250583)Termination phase: Saturation
% 2.67/1.15 % (2250583)Time elapsed: 0.052 s
% 2.67/1.15 % (2250583)Peak memory usage: 91 MB
% 2.67/1.15 % (2250583)Instructions burned: 130 (million)
% 2.67/1.15 % (2250580)Refutation found. Thanks to Tanya!
% 2.67/1.15 % SZS status Theorem for theBenchmark
% 2.67/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.15 % (2250580)------------------------------
% 2.67/1.15 % (2250580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.15 % (2250580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.15 % (2250580)CaDiCaL version: 2.1.3
% 2.67/1.15 % (2250580)Termination reason: Refutation
% 2.67/1.15 % (2250580)Time elapsed: 0.002 s
% 2.67/1.15 % (2250580)Peak memory usage: 89 MB
% 2.67/1.15 % (2250580)Instructions burned: 3 (million)
% 2.67/1.15 % (2250580)------------------------------
% 2.67/1.15 % (2250580)------------------------------
% 2.67/1.15 % (2250572)Success in time 0.282 s
% 2.67/1.15 % Vampire exiting
%------------------------------------------------------------------------------