%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET731+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 : n018.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 3.37s 1.38s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 4 unt; 0 def)
% Number of atoms : 146 ( 7 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 174 ( 64 ~; 60 |; 37 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 113 ( 92 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
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(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,X2,X3)
& subset(X4,X3)
& image2(X0,X2) = X4
& ! [X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) ) )
=> surjective(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII22) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X2,X3)
& subset(X4,X3)
& image2(X0,X2) = X4
& ! [X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) ) )
=> surjective(X1,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,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(f35,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& maps(X0,X2,X3)
& subset(X4,X3)
& image2(X0,X2) = X4
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X5,X2)
| ~ member(X6,X4) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& maps(X0,X2,X3)
& subset(X4,X3)
& image2(X0,X2) = X4
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X5,X2)
| ~ member(X6,X4) ) ),
inference(flattening,[],[f35]) ).
fof(f40,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f41,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& maps(X0,X2,X3)
& subset(X4,X3)
& image2(X0,X2) = X4
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f42,plain,
( ~ surjective(sK1,sK2,sK4)
& maps(sK0,sK2,sK3)
& subset(sK4,sK3)
& sK4 = image2(sK0,sK2)
& ! [X5,X6] :
( ( ( apply(sK1,X5,X6)
| ~ apply(sK0,X5,X6) )
& ( apply(sK0,X5,X6)
| ~ apply(sK1,X5,X6) ) )
| ~ member(X5,sK2)
| ~ member(X6,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)],[f41]) ).
fof(f44,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))],[f40]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f49,plain,
! [X6,X5] :
( ~ apply(sK0,X5,X6)
| apply(sK1,X5,X6)
| ~ member(X5,sK2)
| ~ member(X6,sK4) ),
inference(cnf_transformation,[],[f42]) ).
fof(f50,plain,
sK4 = image2(sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f53,plain,
~ surjective(sK1,sK2,sK4),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK6(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f60,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(X2,image2(X0,X1))
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f66,plain,
! [X0,X1] :
( ~ apply(sK0,X1,X0)
| ~ member(X1,sK2)
| member(X0,sK4) ),
inference(superposition,[],[f62,f50]) ).
fof(f71,plain,
! [X0,X1] :
( ~ member(sK7(sK0,X0,X1),sK2)
| member(X1,sK4)
| ~ member(X1,image2(sK0,X0)) ),
inference(resolution,[],[f66,f60]) ).
fof(f73,plain,
! [X0,X1] :
( apply(sK1,sK7(sK0,X0,X1),X1)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(X1,sK4)
| ~ member(X1,image2(sK0,X0)) ),
inference(resolution,[],[f49,f60]) ).
fof(f74,plain,
! [X0,X1] :
( apply(sK1,sK7(sK0,X0,X1),X1)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(X1,image2(sK0,X0)) ),
inference(forward_subsumption_resolution,[],[f73,f71]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK0,X0,sK6(sK1,X1,X2)),sK2)
| ~ member(sK6(sK1,X1,X2),image2(sK0,X0))
| ~ member(sK7(sK0,X0,sK6(sK1,X1,X2)),X1)
| surjective(sK1,X1,X2) ),
inference(resolution,[],[f74,f59]) ).
fof(f102,plain,
! [X0,X1] :
( ~ member(sK6(sK1,X0,X1),image2(sK0,sK2))
| ~ member(sK7(sK0,sK2,sK6(sK1,X0,X1)),X0)
| surjective(sK1,X0,X1)
| ~ member(sK6(sK1,X0,X1),image2(sK0,sK2)) ),
inference(resolution,[],[f83,f61]) ).
fof(f103,plain,
! [X0,X1] :
( ~ member(sK6(sK1,X0,X1),image2(sK0,sK2))
| ~ member(sK7(sK0,sK2,sK6(sK1,X0,X1)),X0)
| surjective(sK1,X0,X1) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ~ member(sK7(sK0,sK2,sK6(sK1,X0,X1)),X0)
| ~ member(sK6(sK1,X0,X1),sK4)
| surjective(sK1,X0,X1) ),
inference(forward_demodulation,[],[f103,f50]) ).
fof(f105,plain,
! [X0] :
( ~ member(sK6(sK1,sK2,X0),sK4)
| surjective(sK1,sK2,X0)
| ~ member(sK6(sK1,sK2,X0),image2(sK0,sK2)) ),
inference(resolution,[],[f104,f61]) ).
fof(f107,plain,
! [X0] :
( ~ member(sK6(sK1,sK2,X0),sK4)
| ~ member(sK6(sK1,sK2,X0),sK4)
| surjective(sK1,sK2,X0) ),
inference(forward_demodulation,[],[f105,f50]) ).
fof(f108,plain,
! [X0] :
( ~ member(sK6(sK1,sK2,X0),sK4)
| surjective(sK1,sK2,X0) ),
inference(duplicate_literal_removal,[],[f107]) ).
fof(f111,plain,
( surjective(sK1,sK2,sK4)
| surjective(sK1,sK2,sK4) ),
inference(resolution,[],[f108,f58]) ).
fof(f112,plain,
surjective(sK1,sK2,sK4),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f113,plain,
$false,
inference(forward_subsumption_resolution,[],[f112,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET731+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n018.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 02:41:55 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 3.37/1.38 % (2942849)Detected formulas, will run a generic FOF schedule.
% 3.37/1.38 % (2942854)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=360586493:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.38 % (2942856)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=3810541389:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.38 % (2942858)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1779096468:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.38 % (2942857)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1820100269:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.38 % (2942855)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=3928424937:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.38 % (2942859)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2692016531:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.38 % (2942860)dis-21_1_sil=8000:lcm=predicate:random_seed=498376139: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)
% 3.37/1.38 % (2942857)First to succeed.
% 3.37/1.38 % (2942857)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2942849"
% 3.37/1.38 % (2942858)Also succeeded, but the first one will report.
% 3.37/1.38 % (2942859)Also succeeded, but the first one will report.
% 3.37/1.38 % (2942860)Instruction limit reached!
% 3.37/1.38 % (2942860)------------------------------
% 3.37/1.38 % (2942860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.38 % (2942860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.38 % (2942860)CaDiCaL version: 2.1.3
% 3.37/1.38 % (2942860)Termination reason: Instruction limit
% 3.37/1.38 % (2942860)Termination phase: Saturation
% 3.37/1.38 % (2942860)Time elapsed: 0.078 s
% 3.37/1.38 % (2942860)Peak memory usage: 90 MB
% 3.37/1.38 % (2942860)Instructions burned: 131 (million)
% 3.37/1.38 % (2942868)lrs+10_1_sil=8000:sp=occurrence:random_seed=2180429586:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.37/1.38 % (2942868)Also succeeded, but the first one will report.
% 3.37/1.38 % (2942857)Refutation found. Thanks to Tanya!
% 3.37/1.38 % SZS status Theorem for theBenchmark
% 3.37/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.38 % (2942857)------------------------------
% 3.37/1.38 % (2942857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.38 % (2942857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.38 % (2942857)CaDiCaL version: 2.1.3
% 3.37/1.38 % (2942857)Termination reason: Refutation
% 3.37/1.38 % (2942857)Time elapsed: 0.005 s
% 3.37/1.38 % (2942857)Peak memory usage: 88 MB
% 3.37/1.38 % (2942857)Instructions burned: 5 (million)
% 3.37/1.38 % (2942857)------------------------------
% 3.37/1.38 % (2942857)------------------------------
% 3.37/1.38 % (2942849)Success in time 0.408 s
% 3.37/1.38 % Vampire exiting
%------------------------------------------------------------------------------