%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET751+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 : n016.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 12:41:49 PM UTC 2026
% Result : Theorem 5.01s 1.78s
% Output : Refutation 5.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 113 ( 41 ~; 35 |; 31 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 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 : 84 ( 69 !; 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(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1)
& subset(X3,X4) )
=> subset(image2(X0,X3),image2(X0,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa01) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1)
& subset(X3,X4) )
=> subset(image2(X0,X3),image2(X0,X4)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,X3),image2(X0,X4))
& maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1)
& subset(X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,X3),image2(X0,X4))
& maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1)
& subset(X3,X4) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,plain,
( ~ subset(image2(sK0,sK3),image2(sK0,sK4))
& maps(sK0,sK1,sK2)
& subset(sK3,sK1)
& subset(sK4,sK1)
& subset(sK3,sK4) ),
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)],[f34]) ).
fof(f40,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,[],[f35]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK7(X0,X1,X2),X1)
& apply(X0,sK7(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f45]) ).
fof(f50,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
~ subset(image2(sK0,sK3),image2(sK0,sK4)),
inference(cnf_transformation,[],[f38]) ).
fof(f57,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
member(sK5(image2(sK0,sK3),image2(sK0,sK4)),image2(sK0,sK3)),
inference(resolution,[],[f58,f54]) ).
fof(f87,plain,
~ member(sK5(image2(sK0,sK3),image2(sK0,sK4)),image2(sK0,sK4)),
inference(resolution,[],[f59,f54]) ).
fof(f89,plain,
! [X0] :
( member(X0,sK4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f57,f50]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ~ member(sK7(X0,X1,X2),X3)
| member(X2,image2(X0,X3))
| ~ member(X2,image2(X0,X1)) ),
inference(resolution,[],[f65,f63]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ member(sK7(X1,X2,X0),sK3)
| ~ member(X0,image2(X1,X2))
| member(X0,image2(X1,sK4)) ),
inference(resolution,[],[f98,f89]) ).
fof(f1232,plain,
! [X0,X1] :
( ~ member(X0,image2(X1,sK3))
| member(X0,image2(X1,sK4))
| ~ member(X0,image2(X1,sK3)) ),
inference(resolution,[],[f140,f64]) ).
fof(f1235,plain,
! [X0,X1] :
( member(X0,image2(X1,sK4))
| ~ member(X0,image2(X1,sK3)) ),
inference(duplicate_literal_removal,[],[f1232]) ).
fof(f1366,plain,
~ member(sK5(image2(sK0,sK3),image2(sK0,sK4)),image2(sK0,sK3)),
inference(resolution,[],[f1235,f87]) ).
fof(f1928,plain,
$false,
inference(resolution,[],[f1366,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET751+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 02:48:02 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 5.01/1.78 % (3207028)Detected formulas, will run a generic FOF schedule.
% 5.01/1.78 % (3207134)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=504508744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.01/1.78 % (3207135)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=3011741715:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.01/1.78 % (3207136)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=4075102686:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.01/1.78 % (3207140)dis-21_1_sil=8000:lcm=predicate:random_seed=3004781622: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)
% 5.01/1.78 % (3207138)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1691429582:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.01/1.78 % (3207137)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2878715758:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.01/1.78 % (3207137)Refutation not found, incomplete strategy
% 5.01/1.78 % (3207137)------------------------------
% 5.01/1.78 % (3207137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.78 % (3207137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.78 % (3207137)CaDiCaL version: 2.1.3
% 5.01/1.78 % (3207137)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.78 % (3207137)Time elapsed: 0.005 s
% 5.01/1.78 % (3207137)Peak memory usage: 88 MB
% 5.01/1.78 % (3207137)Instructions burned: 3 (million)
% 5.01/1.78 % (3207140)First to succeed.
% 5.01/1.78 % (3207140)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3207028"
% 5.01/1.78 % (3207138)Instruction limit reached!
% 5.01/1.78 % (3207138)------------------------------
% 5.01/1.78 % (3207138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.78 % (3207138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.78 % (3207138)CaDiCaL version: 2.1.3
% 5.01/1.78 % (3207138)Termination reason: Instruction limit
% 5.01/1.78 % (3207138)Termination phase: Saturation
% 5.01/1.78 % (3207138)Time elapsed: 0.065 s
% 5.01/1.78 % (3207138)Peak memory usage: 87 MB
% 5.01/1.78 % (3207138)Instructions burned: 120 (million)
% 5.01/1.78 % (3207139)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2777114299:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.01/1.78 % (3207139)Also succeeded, but the first one will report.
% 5.01/1.78 % (3207174)lrs+10_1_sil=8000:sp=occurrence:random_seed=3230768897:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.01/1.78 % (3207137)------------------------------
% 5.01/1.78 % (3207137)------------------------------
% 5.01/1.78 % (3207140)Refutation found. Thanks to Tanya!
% 5.01/1.78 % SZS status Theorem for theBenchmark
% 5.01/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.01/1.78 % (3207140)------------------------------
% 5.01/1.78 % (3207140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.78 % (3207140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.78 % (3207140)CaDiCaL version: 2.1.3
% 5.01/1.78 % (3207140)Termination reason: Refutation
% 5.01/1.78 % (3207140)Time elapsed: 0.040 s
% 5.01/1.78 % (3207140)Peak memory usage: 89 MB
% 5.01/1.78 % (3207140)Instructions burned: 38 (million)
% 5.01/1.78 % (3207140)------------------------------
% 5.01/1.78 % (3207140)------------------------------
% 5.01/1.78 % (3207028)Success in time 0.618 s
% 5.01/1.78 % Vampire exiting
%------------------------------------------------------------------------------