%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET755+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 : 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 12:41:50 PM UTC 2026
% Result : Theorem 5.68s 1.94s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 109 ( 40 ~; 32 |; 31 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 78 ( 63 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa05) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f41,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f42,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f44]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X2,X4) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ( member(sK7(X0,X1,X2),X1)
& apply(X0,X2,sK7(X0,X1,X2)) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f75]) ).
fof(f81,plain,
( ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))
& maps(sK9,sK10,sK11)
& subset(sK12,sK11)
& subset(sK13,sK11)
& subset(sK12,sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f42]) ).
fof(f82,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f124,plain,
! [X2,X0,X1] :
( apply(X0,X2,sK7(X0,X1,X2))
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f125,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f131,plain,
subset(sK12,sK13),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),
inference(cnf_transformation,[],[f81]) ).
fof(f140,plain,
member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12)),
inference(resolution,[],[f83,f135]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| member(X2,inverse_image2(X0,X3))
| ~ member(sK7(X0,X1,X2),X3) ),
inference(resolution,[],[f126,f124]) ).
fof(f315,plain,
! [X0] :
( member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,X0))
| ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0) ),
inference(resolution,[],[f150,f140]) ).
fof(f377,plain,
( ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13)
| subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)) ),
inference(resolution,[],[f315,f84]) ).
fof(f412,plain,
~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13),
inference(forward_subsumption_resolution,[],[f377,f135]) ).
fof(f416,plain,
! [X0] :
( ~ subset(X0,sK13)
| ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0) ),
inference(resolution,[],[f412,f82]) ).
fof(f430,plain,
~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12),
inference(resolution,[],[f416,f131]) ).
fof(f468,plain,
~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12)),
inference(resolution,[],[f430,f125]) ).
fof(f470,plain,
$false,
inference(forward_subsumption_resolution,[],[f468,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET755+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 28 02:43:16 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.48 Running first-order theorem proving
% 0.24/0.48 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
% 5.68/1.94 % (1387699)Detected formulas, will run a generic FOF schedule.
% 5.68/1.94 % (1387706)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=225751504:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.68/1.94 % (1387708)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3009527622:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.68/1.94 % (1387709)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=991028108:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.68/1.94 % (1387705)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=990545757:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.68/1.94 % (1387704)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=2317204027:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.68/1.94 % (1387707)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1566935969:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.68/1.94 % (1387707)Refutation not found, incomplete strategy
% 5.68/1.94 % (1387707)------------------------------
% 5.68/1.94 % (1387707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.94 % (1387707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.94 % (1387707)CaDiCaL version: 2.1.3
% 5.68/1.94 % (1387707)Termination reason: Refutation not found, incomplete strategy
% 5.68/1.94 % (1387707)Time elapsed: 0.004 s
% 5.68/1.94 % (1387707)Peak memory usage: 88 MB
% 5.68/1.94 % (1387707)Instructions burned: 2 (million)
% 5.68/1.94 % (1387710)dis-21_1_sil=8000:lcm=predicate:random_seed=1097236325: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)
% 5.68/1.94 % (1387709)First to succeed.
% 5.68/1.94 % (1387709)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1387699"
% 5.68/1.94 % (1387710)Also succeeded, but the first one will report.
% 5.68/1.94 % (1387708)Instruction limit reached!
% 5.68/1.94 % (1387708)------------------------------
% 5.68/1.94 % (1387708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.94 % (1387708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.94 % (1387708)CaDiCaL version: 2.1.3
% 5.68/1.94 % (1387708)Termination reason: Instruction limit
% 5.68/1.94 % (1387708)Termination phase: Saturation
% 5.68/1.94 % (1387708)Time elapsed: 0.077 s
% 5.68/1.94 % (1387708)Peak memory usage: 87 MB
% 5.68/1.94 % (1387708)Instructions burned: 119 (million)
% 5.68/1.94 % (1387718)lrs+10_1_sil=8000:sp=occurrence:random_seed=4101225731:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.68/1.94 % (1387707)------------------------------
% 5.68/1.94 % (1387707)------------------------------
% 5.68/1.94 % (1387709)Refutation found. Thanks to Tanya!
% 5.68/1.94 % SZS status Theorem for theBenchmark
% 5.68/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.68/1.94 % (1387709)------------------------------
% 5.68/1.94 % (1387709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.94 % (1387709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.94 % (1387709)CaDiCaL version: 2.1.3
% 5.68/1.94 % (1387709)Termination reason: Refutation
% 5.68/1.94 % (1387709)Time elapsed: 0.028 s
% 5.68/1.94 % (1387709)Peak memory usage: 89 MB
% 5.68/1.94 % (1387709)Instructions burned: 22 (million)
% 5.68/1.94 % (1387709)------------------------------
% 5.68/1.94 % (1387709)------------------------------
% 5.68/1.94 % (1387699)Success in time 0.687 s
% 5.68/1.95 % Vampire exiting
%------------------------------------------------------------------------------