%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW473+3 : 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 : n013.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 01:30:30 PM UTC 2026
% Result : Theorem 4.08s 1.43s
% Output : Refutation 4.08s
% 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 : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f543,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_436_rev__image__eqI) ).
fof(f560,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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_453_insert__subset) ).
fof(f1410,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(f1413,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f1415,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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(f1416,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[status(cth)],[f1415]) ).
fof(f1417,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(flattening,[],[f1416]) ).
fof(f1519,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,[],[f543]) ).
fof(f1520,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,[],[f1519]) ).
fof(f1684,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f560]) ).
fof(f1685,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(flattening,[],[f1684]) ).
fof(f1758,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1410]) ).
fof(f1761,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1413]) ).
fof(f1763,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1417]) ).
fof(f1859,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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,[],[f1685]) ).
fof(f1928,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,[],[f1520]) ).
fof(f2145,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,[],[f1928]) ).
fof(f2182,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,[],[f1763,f1859]) ).
fof(f2189,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,[],[f2182,f1758]) ).
fof(f2207,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(resolution,[],[f2189,f2145]) ).
fof(f2210,plain,
$false,
inference(forward_subsumption_resolution,[],[f2207,f1761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW473+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:06:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 4.08/1.43 % (1197725)Detected formulas, will run a generic FOF schedule.
% 4.08/1.43 % (1197855)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2438937602:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.08/1.43 % (1197851)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=922396704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.08/1.43 % (1197854)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4198228518:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.08/1.43 % (1197857)dis-21_1_sil=8000:lcm=predicate:random_seed=185547297: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)
% 4.08/1.43 % (1197852)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=3048104658:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.08/1.43 % (1197853)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=1489973708:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.08/1.43 % (1197855)Instruction limit reached!
% 4.08/1.43 % (1197855)------------------------------
% 4.08/1.43 % (1197855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.43 % (1197855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.43 % (1197855)CaDiCaL version: 2.1.3
% 4.08/1.43 % (1197855)Termination reason: Instruction limit
% 4.08/1.43 % (1197855)Termination phase: Saturation
% 4.08/1.43 % (1197855)Time elapsed: 0.041 s
% 4.08/1.43 % (1197855)Peak memory usage: 90 MB
% 4.08/1.43 % (1197855)Instructions burned: 120 (million)
% 4.08/1.43 % (1197854)First to succeed.
% 4.08/1.43 % (1197854)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1197725"
% 4.08/1.43 % (1197856)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2105647161:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.08/1.43 % (1197857)Instruction limit reached!
% 4.08/1.43 % (1197857)------------------------------
% 4.08/1.43 % (1197857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.43 % (1197857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.43 % (1197857)CaDiCaL version: 2.1.3
% 4.08/1.43 % (1197857)Termination reason: Instruction limit
% 4.08/1.43 % (1197857)Termination phase: Property scanning
% 4.08/1.43 % (1197857)Time elapsed: 0.072 s
% 4.08/1.43 % (1197857)Peak memory usage: 89 MB
% 4.08/1.43 % (1197857)Instructions burned: 130 (million)
% 4.08/1.43 % (1197856)Instruction limit reached!
% 4.08/1.43 % (1197856)------------------------------
% 4.08/1.43 % (1197856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.43 % (1197856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.43 % (1197856)CaDiCaL version: 2.1.3
% 4.08/1.43 % (1197856)Termination reason: Instruction limit
% 4.08/1.43 % (1197856)Termination phase: Saturation
% 4.08/1.43 % (1197856)Time elapsed: 0.065 s
% 4.08/1.43 % (1197856)Peak memory usage: 90 MB
% 4.08/1.43 % (1197856)Instructions burned: 140 (million)
% 4.08/1.43 % (1197864)lrs+10_1_sil=8000:sp=occurrence:random_seed=3189245218:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.08/1.43 % (1197866)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3520258746:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.08/1.43 % (1197867)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2234071239:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.08/1.43 % (1197854)Refutation found. Thanks to Tanya!
% 4.08/1.43 % SZS status Theorem for theBenchmark
% 4.08/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.08/1.43 % (1197854)------------------------------
% 4.08/1.43 % (1197854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.43 % (1197854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.43 % (1197854)CaDiCaL version: 2.1.3
% 4.08/1.43 % (1197854)Termination reason: Refutation
% 4.08/1.43 % (1197854)Time elapsed: 0.025 s
% 4.08/1.43 % (1197854)Peak memory usage: 90 MB
% 4.08/1.43 % (1197854)Instructions burned: 44 (million)
% 4.08/1.43 % (1197854)------------------------------
% 4.08/1.43 % (1197854)------------------------------
% 4.08/1.43 % (1197725)Success in time 0.557 s
% 4.08/1.43 % Vampire exiting
%------------------------------------------------------------------------------