%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:41:59 PM UTC 2026
% Result : Theorem 3.29s 1.23s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 149 ( 54 ~; 51 |; 35 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 55 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( member(X1,X0)
=> subset(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_number) ).
fof(f21,conjecture,
! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV14) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
? [X0] :
( ~ subset(sum(X0),X0)
& member(X0,on) ),
inference(ennf_transformation,[],[f22]) ).
fof(f39,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,[],[f24]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f40]) ).
fof(f52,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f53,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK2(X0,X1),X1)
& member(X0,sK2(X0,X1)) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f53]) ).
fof(f58,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f60]) ).
fof(f81,plain,
( ~ subset(sum(sK14),sK14)
& member(sK14,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f36]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f102,plain,
! [X0,X1] :
( member(X0,sK2(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f103,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f108,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f145,plain,
member(sK14,on),
inference(cnf_transformation,[],[f81]) ).
fof(f146,plain,
~ subset(sum(sK14),sK14),
inference(cnf_transformation,[],[f81]) ).
fof(f152,plain,
member(sK1(sum(sK14),sK14),sum(sK14)),
inference(resolution,[],[f83,f146]) ).
fof(f157,plain,
member(sK2(sK1(sum(sK14),sK14),sK14),sK14),
inference(resolution,[],[f103,f152]) ).
fof(f159,plain,
! [X0] :
( ~ member(X0,sK14)
| subset(X0,sK14) ),
inference(resolution,[],[f108,f145]) ).
fof(f170,plain,
subset(sK2(sK1(sum(sK14),sK14),sK14),sK14),
inference(resolution,[],[f159,f157]) ).
fof(f171,plain,
! [X0] :
( ~ member(X0,sK2(sK1(sum(sK14),sK14),sK14))
| member(X0,sK14) ),
inference(resolution,[],[f170,f82]) ).
fof(f179,plain,
( member(sK1(sum(sK14),sK14),sK14)
| ~ member(sK1(sum(sK14),sK14),sum(sK14)) ),
inference(resolution,[],[f171,f102]) ).
fof(f180,plain,
member(sK1(sum(sK14),sK14),sK14),
inference(forward_subsumption_resolution,[],[f179,f152]) ).
fof(f182,plain,
subset(sum(sK14),sK14),
inference(resolution,[],[f180,f84]) ).
fof(f184,plain,
$false,
inference(forward_subsumption_resolution,[],[f182,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:55:30 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.29/1.23 % (1138249)Detected formulas, will run a generic FOF schedule.
% 3.29/1.23 % (1138260)dis-21_1_sil=8000:lcm=predicate:random_seed=4117654829: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)
% 3.29/1.23 % (1138260)Instruction limit reached!
% 3.29/1.23 % (1138260)------------------------------
% 3.29/1.23 % (1138260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.23 % (1138260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.23 % (1138260)CaDiCaL version: 2.1.3
% 3.29/1.23 % (1138260)Termination reason: Instruction limit
% 3.29/1.23 % (1138260)Termination phase: Saturation
% 3.29/1.23 % (1138260)Time elapsed: 0.043 s
% 3.29/1.23 % (1138260)Peak memory usage: 89 MB
% 3.29/1.23 % (1138260)Instructions burned: 130 (million)
% 3.29/1.23 % (1138255)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=3877935400:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.29/1.23 % (1138258)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2364223889:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.29/1.23 % (1138259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2860132198:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.29/1.23 % (1138257)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2251113992:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.29/1.23 % (1138256)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=3063447056:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.29/1.23 % (1138254)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=75253658:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.29/1.23 % (1138257)Refutation not found, incomplete strategy
% 3.29/1.23 % (1138257)------------------------------
% 3.29/1.23 % (1138257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.23 % (1138257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.23 % (1138257)CaDiCaL version: 2.1.3
% 3.29/1.23 % (1138257)Termination reason: Refutation not found, incomplete strategy
% 3.29/1.23 % (1138257)Time elapsed: 0.001 s
% 3.29/1.23 % (1138257)Peak memory usage: 88 MB
% 3.29/1.23 % (1138257)Instructions burned: 1 (million)
% 3.29/1.23 % (1138259)First to succeed.
% 3.29/1.23 % (1138259)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1138249"
% 3.29/1.23 % (1138258)Instruction limit reached!
% 3.29/1.23 % (1138258)------------------------------
% 3.29/1.23 % (1138258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.23 % (1138258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.23 % (1138258)CaDiCaL version: 2.1.3
% 3.29/1.23 % (1138258)Termination reason: Instruction limit
% 3.29/1.23 % (1138258)Termination phase: Saturation
% 3.29/1.23 % (1138258)Time elapsed: 0.077 s
% 3.29/1.23 % (1138258)Peak memory usage: 88 MB
% 3.29/1.23 % (1138258)Instructions burned: 119 (million)
% 3.29/1.23 % (1138262)lrs+10_1_sil=8000:sp=occurrence:random_seed=1593682721:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.29/1.23 % (1138262)Instruction limit reached!
% 3.29/1.23 % (1138262)------------------------------
% 3.29/1.23 % (1138262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.23 % (1138262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.23 % (1138262)CaDiCaL version: 2.1.3
% 3.29/1.23 % (1138262)Termination reason: Instruction limit
% 3.29/1.23 % (1138262)Termination phase: Saturation
% 3.29/1.23 % (1138262)Time elapsed: 0.101 s
% 3.29/1.23 % (1138262)Peak memory usage: 92 MB
% 3.29/1.23 % (1138262)Instructions burned: 288 (million)
% 3.29/1.23 % (1138269)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1962902767:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.29/1.23 % (1138269)Also succeeded, but the first one will report.
% 3.29/1.23 % (1138257)------------------------------
% 3.29/1.23 % (1138257)------------------------------
% 3.29/1.23 % (1138259)Refutation found. Thanks to Tanya!
% 3.29/1.23 % SZS status Theorem for theBenchmark
% 3.29/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.29/1.23 % (1138259)------------------------------
% 3.29/1.23 % (1138259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.23 % (1138259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.23 % (1138259)CaDiCaL version: 2.1.3
% 3.29/1.23 % (1138259)Termination reason: Refutation
% 3.29/1.23 % (1138259)Time elapsed: 0.005 s
% 3.29/1.23 % (1138259)Peak memory usage: 88 MB
% 3.29/1.23 % (1138259)Instructions burned: 5 (million)
% 3.29/1.23 % (1138259)------------------------------
% 3.29/1.23 % (1138259)------------------------------
% 3.29/1.23 % (1138249)Success in time 0.409 s
% 3.29/1.23 % Vampire exiting
%------------------------------------------------------------------------------