%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:30:29 PM UTC 2026
% Result : Theorem 2.50s 1.05s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 45 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 46 ( 22 ~; 16 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f416,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
=> ( X0 = hAPP_pname_a(X1,X2)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
fof(f428,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
fof(f912,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f915,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f917,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f918,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[status(cth)],[f917]) ).
fof(f919,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(flattening,[],[f918]) ).
fof(f992,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| hAPP_pname_a(X1,X2) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(ennf_transformation,[],[f416]) ).
fof(f993,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| hAPP_pname_a(X1,X2) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(flattening,[],[f992]) ).
fof(f1129,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f428]) ).
fof(f1130,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(flattening,[],[f1129]) ).
fof(f1171,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f912]) ).
fof(f1174,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f915]) ).
fof(f1176,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f919]) ).
fof(f1231,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1130]) ).
fof(f1257,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| hAPP_pname_a(X1,X2) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(cnf_transformation,[],[f993]) ).
fof(f1405,plain,
! [X2,X3,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(equality_resolution,[],[f1257]) ).
fof(f1440,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
inference(resolution,[],[f1176,f1231]) ).
fof(f1446,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))),
inference(forward_subsumption_resolution,[],[f1440,f1171]) ).
fof(f1474,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(resolution,[],[f1446,f1405]) ).
fof(f1479,plain,
$false,
inference(forward_subsumption_resolution,[],[f1474,f1174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n026.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
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 14:09:12 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
% 2.50/1.05 % (3866692)Detected formulas, will run a generic FOF schedule.
% 2.50/1.05 % (3866700)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=635088449:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.05 % (3866700)First to succeed.
% 2.50/1.05 % (3866700)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3866692"
% 2.50/1.05 % (3866702)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=863689317:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.05 % (3866701)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4157553817:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.05 % (3866699)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=27291754:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.05 % (3866697)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=237837079:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.05 % (3866698)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=3297250495:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.05 % (3866703)dis-21_1_sil=8000:lcm=predicate:random_seed=605857297: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)
% 2.50/1.05 % (3866703)Instruction limit reached!
% 2.50/1.05 % (3866703)------------------------------
% 2.50/1.05 % (3866703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.05 % (3866703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.05 % (3866703)CaDiCaL version: 2.1.3
% 2.50/1.05 % (3866703)Termination reason: Instruction limit
% 2.50/1.05 % (3866703)Termination phase: Saturation
% 2.50/1.05 % (3866703)Time elapsed: 0.064 s
% 2.50/1.05 % (3866703)Peak memory usage: 91 MB
% 2.50/1.05 % (3866703)Instructions burned: 129 (million)
% 2.50/1.05 % (3866701)Instruction limit reached!
% 2.50/1.05 % (3866701)------------------------------
% 2.50/1.05 % (3866701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.05 % (3866701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.05 % (3866701)CaDiCaL version: 2.1.3
% 2.50/1.05 % (3866701)Termination reason: Instruction limit
% 2.50/1.05 % (3866701)Termination phase: Saturation
% 2.50/1.05 % (3866701)Time elapsed: 0.074 s
% 2.50/1.05 % (3866701)Peak memory usage: 90 MB
% 2.50/1.05 % (3866701)Instructions burned: 120 (million)
% 2.50/1.05 % (3866702)Instruction limit reached!
% 2.50/1.05 % (3866702)------------------------------
% 2.50/1.05 % (3866702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.05 % (3866702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.05 % (3866702)CaDiCaL version: 2.1.3
% 2.50/1.05 % (3866702)Termination reason: Instruction limit
% 2.50/1.05 % (3866702)Termination phase: Saturation
% 2.50/1.05 % (3866702)Time elapsed: 0.077 s
% 2.50/1.05 % (3866702)Peak memory usage: 91 MB
% 2.50/1.05 % (3866702)Instructions burned: 139 (million)
% 2.50/1.05 % (3866700)Refutation found. Thanks to Tanya!
% 2.50/1.05 % SZS status Theorem for theBenchmark
% 2.50/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.05 % (3866700)------------------------------
% 2.50/1.05 % (3866700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.05 % (3866700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.05 % (3866700)CaDiCaL version: 2.1.3
% 2.50/1.05 % (3866700)Termination reason: Refutation
% 2.50/1.05 % (3866700)Time elapsed: 0.008 s
% 2.50/1.05 % (3866700)Peak memory usage: 90 MB
% 2.50/1.05 % (3866700)Instructions burned: 25 (million)
% 2.50/1.05 % (3866700)------------------------------
% 2.50/1.05 % (3866700)------------------------------
% 2.50/1.05 % (3866692)Success in time 0.308 s
% 2.50/1.05 % Vampire exiting
%------------------------------------------------------------------------------