%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP026+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:33:54 PM UTC 2026
% Result : Theorem 2.45s 0.81s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 145 ( 20 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 186 ( 77 ~; 67 |; 27 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> k6_pre_topc(X0,X2) = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k6_pre_topc(X0,X2))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tsp_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> k6_pre_topc(X0,X2) = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k6_pre_topc(X0,X2))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f71,axiom,
! [X0,X1] :
( ( l1_pre_topc(X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> m1_subset_1(k6_pre_topc(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f76,axiom,
! [X0,X1] :
( ( v2_pre_topc(X0)
& l1_pre_topc(X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> v4_pre_topc(k6_pre_topc(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f79,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v4_pre_topc(X2,X0)
=> X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tsp_2) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k6_pre_topc(X0,X2) != k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k6_pre_topc(X0,X2)))
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k6_pre_topc(X0,X2) != k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k6_pre_topc(X0,X2)))
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(flattening,[],[f98]) ).
fof(f168,plain,
! [X0,X1] :
( m1_subset_1(k6_pre_topc(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f71]) ).
fof(f169,plain,
! [X0,X1] :
( m1_subset_1(k6_pre_topc(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f168]) ).
fof(f171,plain,
! [X0,X1] :
( v4_pre_topc(k6_pre_topc(X0,X1),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f76]) ).
fof(f172,plain,
! [X0,X1] :
( v4_pre_topc(k6_pre_topc(X0,X1),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f171]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2))
| ~ v4_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f177,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2))
| ~ v4_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(flattening,[],[f176]) ).
fof(f182,plain,
( k6_pre_topc(sK2,sK4) != k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,sK4)))
& m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2)))
& v1_tsp_2(sK3,sK2)
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
& ~ v3_struct_0(sK2)
& v2_pre_topc(sK2)
& l1_pre_topc(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f99]) ).
fof(f201,plain,
l1_pre_topc(sK2),
inference(cnf_transformation,[],[f182]) ).
fof(f202,plain,
v2_pre_topc(sK2),
inference(cnf_transformation,[],[f182]) ).
fof(f203,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f182]) ).
fof(f204,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2))),
inference(cnf_transformation,[],[f182]) ).
fof(f205,plain,
v1_tsp_2(sK3,sK2),
inference(cnf_transformation,[],[f182]) ).
fof(f206,plain,
m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))),
inference(cnf_transformation,[],[f182]) ).
fof(f207,plain,
k6_pre_topc(sK2,sK4) != k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,sK4))),
inference(cnf_transformation,[],[f182]) ).
fof(f353,plain,
! [X0,X1] :
( m1_subset_1(k6_pre_topc(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f169]) ).
fof(f356,plain,
! [X0,X1] :
( v4_pre_topc(k6_pre_topc(X0,X1),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f172]) ).
fof(f360,plain,
! [X2,X0,X1] :
( ~ v2_pre_topc(X0)
| ~ v4_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2)) = X2
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f527,plain,
! [X0,X1] :
( ~ v4_pre_topc(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v1_tsp_2(X1,sK2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2)))
| v3_struct_0(sK2)
| k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),X1,X0)) = X0
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f360,f202]) ).
fof(f528,plain,
! [X0,X1] :
( ~ v4_pre_topc(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v1_tsp_2(X1,sK2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2)))
| k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),X1,X0)) = X0
| ~ l1_pre_topc(sK2) ),
inference(forward_subsumption_resolution,[],[f527,f203]) ).
fof(f529,plain,
! [X0,X1] :
( ~ v1_tsp_2(X1,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v4_pre_topc(X0,sK2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2)))
| k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),X1,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f528,f201]) ).
fof(f536,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v4_pre_topc(X0,sK2)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
| k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,X0)) = X0 ),
inference(resolution,[],[f529,f205]) ).
fof(f537,plain,
! [X0] :
( ~ v4_pre_topc(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f536,f204]) ).
fof(f548,plain,
! [X0] :
( ~ m1_subset_1(k6_pre_topc(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2)))
| k6_pre_topc(sK2,X0) = k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,X0)))
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(resolution,[],[f537,f356]) ).
fof(f560,plain,
! [X0] :
( k6_pre_topc(sK2,X0) = k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,X0)))
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(forward_subsumption_resolution,[],[f548,f353]) ).
fof(f566,plain,
! [X0] :
( k6_pre_topc(sK2,X0) = k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,X0)))
| ~ l1_pre_topc(sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(forward_subsumption_resolution,[],[f560,f202]) ).
fof(f571,plain,
! [X0] :
( k6_pre_topc(sK2,X0) = k3_tex_4(sK2,k5_subset_1(u1_struct_0(sK2),sK3,k6_pre_topc(sK2,X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(forward_subsumption_resolution,[],[f566,f201]) ).
fof(f891,plain,
( k6_pre_topc(sK2,sK4) != k6_pre_topc(sK2,sK4)
| ~ m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(superposition,[],[f207,f571]) ).
fof(f893,plain,
~ m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))),
inference(trivial_inequality_removal,[],[f891]) ).
fof(f894,plain,
$false,
inference(forward_subsumption_resolution,[],[f893,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP026+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 18:49:10 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.45/0.81 % (2684378)Detected formulas, will run a generic FOF schedule.
% 2.45/0.81 % (2684388)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2718439802:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/0.81 % (2684388)First to succeed.
% 2.45/0.81 % (2684388)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2684378"
% 2.45/0.81 % (2684389)dis-21_1_sil=8000:lcm=predicate:random_seed=929172673: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)
% 2.45/0.81 % (2684385)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=2233727112:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/0.81 % (2684383)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=997895370:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/0.81 % (2684386)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2469709192:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/0.81 % (2684384)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=1300325795:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/0.81 % (2684387)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2626856257:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/0.81 % (2684386)Also succeeded, but the first one will report.
% 2.45/0.81 % (2684387)Also succeeded, but the first one will report.
% 2.45/0.81 % (2684389)Also succeeded, but the first one will report.
% 2.45/0.81 % (2684388)Refutation found. Thanks to Tanya!
% 2.45/0.81 % SZS status Theorem for theBenchmark
% 2.45/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/0.81 % (2684388)------------------------------
% 2.45/0.81 % (2684388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/0.81 % (2684388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/0.81 % (2684388)CaDiCaL version: 2.1.3
% 2.45/0.81 % (2684388)Termination reason: Refutation
% 2.45/0.81 % (2684388)Time elapsed: 0.011 s
% 2.45/0.81 % (2684388)Peak memory usage: 89 MB
% 2.45/0.81 % (2684388)Instructions burned: 26 (million)
% 2.45/0.81 % (2684388)------------------------------
% 2.45/0.81 % (2684388)------------------------------
% 2.45/0.81 % (2684378)Success in time 0.299 s
% 2.45/0.81 % Vampire exiting
%------------------------------------------------------------------------------