%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:41:46 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 8 unt; 2 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 178 ( 69 ~; 60 |; 33 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 127 ( 0 sgn 111 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( maps(X1,X2,X3)
& maps(X0,X3,X2)
& identity(compose_function(X1,X0,X3,X2,X3),X3) )
=> surjective(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII25) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( maps(X1,X2,X3)
& maps(X0,X3,X2)
& identity(compose_function(X1,X0,X3,X2,X3),X3) )
=> surjective(X1,X2,X3) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f34,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( ~ surjective(X1,X2,X3)
& maps(X1,X2,X3)
& maps(X0,X3,X2)
& identity(compose_function(X1,X0,X3,X2,X3),X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ~ surjective(X1,X2,X3)
& maps(X1,X2,X3)
& maps(X0,X3,X2)
& identity(compose_function(X1,X0,X3,X2,X3),X3) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(ennf_transformation,[],[f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f43,plain,
( ~ surjective(sK1,sK2,sK3)
& maps(sK1,sK2,sK3)
& maps(sK0,sK3,sK2)
& identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(nnf_transformation,[],[f41]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X8] :
( member(X8,X3)
& apply(X1,X5,X8)
& apply(X0,X8,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ( member(sK5(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK5(X0,X1,X3,X5,X6))
& apply(X0,sK5(X0,X1,X3,X5,X6),X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X8,sK5(X0,X1,X3,X5,X6))],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK6(X0,X1,X2)) )
& member(sK6(X0,X1,X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f42]) ).
fof(f52,plain,
identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
~ surjective(sK1,sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X0,sK5(X0,X1,X3,X5,X6),X6)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK5(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ member(X4,X1)
| ~ apply(X0,X4,sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f80,plain,
! [X0] :
( apply(compose_function(sK1,sK0,sK3,sK2,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(resolution,[],[f59,f52]) ).
fof(f81,plain,
member(sK6(sK1,sK2,sK3),sK3),
inference(resolution,[],[f64,f55]) ).
fof(f86,plain,
! [X0] :
( ~ apply(sK1,X0,sK6(sK1,sK2,sK3))
| ~ member(X0,sK2) ),
inference(resolution,[],[f65,f55]) ).
fof(f87,plain,
! [X0] :
( member(sK5(sK1,sK0,sK2,X0,X0),sK2)
| ~ member(X0,sK3)
| ~ member(X0,sK3)
| ~ member(X0,sK3) ),
inference(resolution,[],[f62,f80]) ).
fof(f88,plain,
! [X0] :
( member(sK5(sK1,sK0,sK2,X0,X0),sK2)
| ~ member(X0,sK3) ),
inference(duplicate_literal_removal,[],[f87]) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(compose_function(sK1,X0,X3,X1,X4),X2,sK6(sK1,sK2,sK3))
| ~ member(sK5(sK1,X0,X1,X2,sK6(sK1,sK2,sK3)),sK2)
| ~ member(X2,X3)
| ~ member(sK6(sK1,sK2,sK3),X4) ),
inference(resolution,[],[f86,f60]) ).
fof(f92,plain,
( ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2)
| ~ member(sK6(sK1,sK2,sK3),sK3)
| ~ member(sK6(sK1,sK2,sK3),sK3)
| ~ member(sK6(sK1,sK2,sK3),sK3) ),
inference(resolution,[],[f90,f80]) ).
fof(f94,plain,
( ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2)
| ~ member(sK6(sK1,sK2,sK3),sK3) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f96,definition,
( spl8_1
<=> member(sK6(sK1,sK2,sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f97,plain,
( ~ member(sK6(sK1,sK2,sK3),sK3)
| spl8_1 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl8_2
<=> member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f100,plain,
( ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2)
| spl8_2 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f94,f99,f96]) ).
fof(f102,plain,
( $false
| spl8_1 ),
inference(resolution,[],[f97,f81]) ).
fof(f103,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f104,plain,
( ~ member(sK6(sK1,sK2,sK3),sK3)
| spl8_2 ),
inference(resolution,[],[f100,f88]) ).
fof(f105,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f104,f99,f96]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f101]) ).
cnf(s2,plain,
spl8_1,
inference(sat_conversion,[],[f103]) ).
cnf(s3,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
spl8_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:45:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.17/1.50 % (4164394)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (4164400)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=3364754952:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (4164403)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1543432784:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (4164405)dis-21_1_sil=8000:lcm=predicate:random_seed=193567139: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)
% 0.17/1.50 % (4164402)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1838594359:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (4164401)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=3015936443:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (4164399)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=903819694:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (4164405)First to succeed.
% 0.17/1.50 % (4164402)Refutation not found, incomplete strategy
% 0.17/1.50 % (4164402)------------------------------
% 0.17/1.50 % (4164402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (4164405)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4164394"
% 0.17/1.50 % (4164402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (4164402)CaDiCaL version: 2.1.3
% 0.17/1.50 % (4164402)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (4164402)Time elapsed: 0.004 s
% 0.17/1.50 % (4164402)Peak memory usage: 88 MB
% 0.17/1.50 % (4164402)Instructions burned: 4 (million)
% 0.17/1.50 % (4164404)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3278963867:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (4164403)Also succeeded, but the first one will report.
% 0.17/1.50 % (4164404)Also succeeded, but the first one will report.
% 0.17/1.50 % (4164402)------------------------------
% 0.17/1.50 % (4164402)------------------------------
% 0.17/1.50 % (4164405)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (4164405)------------------------------
% 0.17/1.50 % (4164405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (4164405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (4164405)CaDiCaL version: 2.1.3
% 0.17/1.50 % (4164405)Termination reason: Refutation
% 0.17/1.50 % (4164405)Time elapsed: 0.004 s
% 0.17/1.50 % (4164405)Peak memory usage: 89 MB
% 0.17/1.50 % (4164405)Instructions burned: 4 (million)
% 0.17/1.50 % (4164405)------------------------------
% 0.17/1.50 % (4164405)------------------------------
% 0.17/1.50 % (4164394)Success in time 0.439 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------