%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:30 PM UTC 2026
% Result : Theorem 2.72s 1.36s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 166 ( 33 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 211 ( 79 ~; 75 |; 43 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 70 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f24,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,X0)
& ! [X3] :
~ ( in(X3,relation_dom(X1))
& X2 = apply(X1,X3) ) )
=> subset(X0,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,X0)
& ! [X3] :
~ ( in(X3,relation_dom(X1))
& X2 = apply(X1,X3) ) )
=> subset(X0,relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f35,plain,
? [X0,X1] :
( ~ subset(X0,relation_rng(X1))
& ! [X2] :
( ~ in(X2,X0)
| ? [X3] :
( in(X3,relation_dom(X1))
& X2 = apply(X1,X3) ) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f36,plain,
? [X0,X1] :
( ~ subset(X0,relation_rng(X1))
& ! [X2] :
( ~ in(X2,X0)
| ? [X3] :
( in(X3,relation_dom(X1))
& X2 = apply(X1,X3) ) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f35]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f52,plain,
( ~ subset(sK0,relation_rng(sK1))
& ! [X2] :
( ~ in(X2,sK0)
| ( in(sK2(X2),relation_dom(sK1))
& apply(sK1,sK2(X2)) = X2 ) )
& relation(sK1)
& function(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2))],[f36]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK3(X0,X1) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK4(X0,X1),relation_dom(X0))
& sK3(X0,X1) = apply(X0,sK4(X0,X1)) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK5(X0,X5),relation_dom(X0))
& apply(X0,sK5(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f54]) ).
fof(f60,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f61,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f61]) ).
fof(f63,plain,
function(sK1),
inference(cnf_transformation,[],[f52]) ).
fof(f64,plain,
relation(sK1),
inference(cnf_transformation,[],[f52]) ).
fof(f65,plain,
! [X2] :
( apply(sK1,sK2(X2)) = X2
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f66,plain,
! [X2] :
( in(sK2(X2),relation_dom(sK1))
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f67,plain,
~ subset(sK0,relation_rng(sK1)),
inference(cnf_transformation,[],[f52]) ).
fof(f80,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f98,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f99,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f113,plain,
! [X0] :
( in(X0,relation_rng(sK1))
| ~ in(sK2(X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(superposition,[],[f99,f65]) ).
fof(f116,plain,
! [X0] :
( in(X0,relation_rng(sK1))
| ~ relation(sK1)
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f113,f66]) ).
fof(f118,plain,
! [X0] :
( in(X0,relation_rng(sK1))
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f116,f64]) ).
fof(f120,plain,
! [X0] :
( in(X0,relation_rng(sK1))
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f118,f63]) ).
fof(f123,plain,
! [X0] :
( ~ in(sK9(X0,relation_rng(sK1)),sK0)
| subset(X0,relation_rng(sK1)) ),
inference(resolution,[],[f120,f97]) ).
fof(f133,plain,
( subset(sK0,relation_rng(sK1))
| subset(sK0,relation_rng(sK1)) ),
inference(resolution,[],[f123,f96]) ).
fof(f134,plain,
subset(sK0,relation_rng(sK1)),
inference(duplicate_literal_removal,[],[f133]) ).
fof(f135,plain,
$false,
inference(forward_subsumption_resolution,[],[f134,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:21:54 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 2.72/1.36 % (1835785)Detected formulas, will run a generic FOF schedule.
% 2.72/1.36 % (1835793)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3025612985:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.36 % (1835793)First to succeed.
% 2.72/1.36 % (1835793)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1835785"
% 2.72/1.36 % (1835796)dis-21_1_sil=8000:lcm=predicate:random_seed=1668927948: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)
% 2.72/1.36 % (1835790)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=2513461156:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.36 % (1835792)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=1626108770:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.36 % (1835794)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4145426898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.36 % (1835791)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=683275392:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.36 % (1835795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4166147278:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.36 % (1835794)Also succeeded, but the first one will report.
% 2.72/1.36 % (1835795)Also succeeded, but the first one will report.
% 2.72/1.36 % (1835796)Instruction limit reached!
% 2.72/1.36 % (1835796)------------------------------
% 2.72/1.36 % (1835796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.36 % (1835796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.36 % (1835796)CaDiCaL version: 2.1.3
% 2.72/1.36 % (1835796)Termination reason: Instruction limit
% 2.72/1.36 % (1835796)Termination phase: Saturation
% 2.72/1.36 % (1835796)Time elapsed: 0.076 s
% 2.72/1.36 % (1835796)Peak memory usage: 89 MB
% 2.72/1.36 % (1835796)Instructions burned: 129 (million)
% 2.72/1.36 % (1835793)Refutation found. Thanks to Tanya!
% 2.72/1.36 % SZS status Theorem for theBenchmark
% 2.72/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.36 % (1835793)------------------------------
% 2.72/1.36 % (1835793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.36 % (1835793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.36 % (1835793)CaDiCaL version: 2.1.3
% 2.72/1.36 % (1835793)Termination reason: Refutation
% 2.72/1.36 % (1835793)Time elapsed: 0.002 s
% 2.72/1.36 % (1835793)Peak memory usage: 89 MB
% 2.72/1.36 % (1835793)Instructions burned: 4 (million)
% 2.72/1.36 % (1835793)------------------------------
% 2.72/1.36 % (1835793)------------------------------
% 2.72/1.36 % (1835785)Success in time 0.306 s
% 2.72/1.36 % Vampire exiting
%------------------------------------------------------------------------------