%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN575-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:01:00 PM UTC 2026
% Result : Unsatisfiable 0.21s 1.03s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 17 unt; 6 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 222 ( 110 ~; 106 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X0] : p7(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_2) ).
fof(f3,negated_conjecture,
! [X0] : p3(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_3) ).
fof(f4,negated_conjecture,
! [X0] : p2(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
fof(f5,negated_conjecture,
p9(c12,c13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_5) ).
fof(f6,negated_conjecture,
p11(c14,c15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_6) ).
fof(f8,negated_conjecture,
! [X0] : p3(f6(f5(X0)),f6(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_8) ).
fof(f9,negated_conjecture,
! [X0] :
( ~ p9(X0,f6(c14))
| p9(X0,c13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_9) ).
fof(f10,negated_conjecture,
! [X0] :
( p9(X0,f6(c14))
| ~ p9(X0,c13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_10) ).
fof(f16,negated_conjecture,
! [X2,X0,X1] :
( p3(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_16) ).
fof(f19,negated_conjecture,
! [X2,X3,X0,X1] :
( p9(X0,X1)
| ~ p7(X2,X0)
| ~ p9(X2,X3)
| ~ p3(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_19) ).
fof(f21,negated_conjecture,
! [X2,X0,X1] :
( p9(f8(X0,X1),f6(X1))
| p9(f8(X0,X1),X0)
| ~ p11(X2,c15)
| ~ p9(c12,X0)
| ~ p2(X1,f5(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_21) ).
fof(f22,negated_conjecture,
! [X2,X0,X1] :
( ~ p9(f8(X1,X2),f6(X2))
| ~ p9(c12,X1)
| ~ p2(X2,f5(X0))
| ~ p9(f8(X1,X2),X1)
| ~ p11(X0,c15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_22) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ p3(X2,f6(c14))
| ~ p9(X0,X2)
| ~ p7(X0,X1)
| p9(X1,c13) ),
inference(resolution,[],[f19,f9]) ).
fof(f25,plain,
! [X0,X1] :
( ~ p9(X0,f6(c14))
| ~ p7(X0,X1)
| p9(X1,c13) ),
inference(resolution,[],[f24,f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ p9(X0,f6(f5(c14)))
| ~ p7(X0,X1)
| p9(X1,c13) ),
inference(resolution,[],[f24,f8]) ).
fof(f37,plain,
! [X0,X1] :
( p9(X1,c13)
| ~ p7(X0,X1)
| ~ p9(X0,c13) ),
inference(resolution,[],[f25,f10]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( ~ p9(f8(X0,X1),X0)
| ~ p2(X1,f5(X2))
| ~ p9(c12,X0)
| ~ p11(X2,c15)
| ~ p7(X3,f8(X0,X1))
| ~ p9(X3,X4)
| ~ p3(X4,f6(X1)) ),
inference(resolution,[],[f22,f19]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ p9(f8(X0,X1),X0)
| ~ p2(X1,f5(X2))
| ~ p9(c12,X0)
| ~ p11(X2,c15)
| ~ p7(f8(X0,X1),f8(X0,X1))
| ~ p3(X0,f6(X1)) ),
inference(factoring,[],[f46]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ p9(f8(X0,X1),X0)
| ~ p2(X1,f5(X2))
| ~ p9(c12,X0)
| ~ p11(X2,c15)
| ~ p3(X0,f6(X1)) ),
inference(forward_subsumption_resolution,[],[f67,f2]) ).
fof(f73,definition,
( spl0_5
<=> p9(c12,f6(c14)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f74,plain,
( ~ p9(c12,f6(c14))
| spl0_5 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f80,plain,
( ~ p9(c12,c13)
| spl0_5 ),
inference(resolution,[],[f74,f10]) ).
fof(f82,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f80,f5]) ).
fof(f83,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f82]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ p7(f8(X0,f5(c14)),X1)
| p9(X1,c13)
| p9(f8(X0,f5(c14)),X0)
| ~ p11(X2,c15)
| ~ p9(c12,X0)
| ~ p2(f5(c14),f5(X2)) ),
inference(resolution,[],[f27,f21]) ).
fof(f87,definition,
( spl0_7
<=> ! [X2] :
( ~ p11(X2,c15)
| ~ p2(f5(c14),f5(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2] :
( ~ p2(f5(c14),f5(X2))
| ~ p11(X2,c15) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_8
<=> ! [X0,X1] :
( ~ p7(f8(X0,f5(c14)),X1)
| ~ p9(c12,X0)
| p9(f8(X0,f5(c14)),X0)
| p9(X1,c13) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0,X1] :
( p9(f8(X0,f5(c14)),X0)
| ~ p9(c12,X0)
| ~ p7(f8(X0,f5(c14)),X1)
| p9(X1,c13) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f85,f90,f87]) ).
fof(f98,plain,
( ~ p11(c14,c15)
| ~ spl0_7 ),
inference(resolution,[],[f88,f4]) ).
fof(f100,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f98,f6]) ).
fof(f101,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f116,plain,
! [X0,X1] :
( ~ p2(X0,f5(X1))
| ~ p9(c12,f6(c14))
| ~ p11(X1,c15)
| ~ p3(f6(c14),f6(X0))
| ~ p9(f8(f6(c14),X0),c13) ),
inference(resolution,[],[f70,f10]) ).
fof(f123,definition,
( spl0_9
<=> ! [X0,X1] :
( ~ p2(X0,f5(X1))
| ~ p9(f8(f6(c14),X0),c13)
| ~ p3(f6(c14),f6(X0))
| ~ p11(X1,c15) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f124,plain,
( ! [X0,X1] :
( ~ p9(f8(f6(c14),X0),c13)
| ~ p2(X0,f5(X1))
| ~ p3(f6(c14),f6(X0))
| ~ p11(X1,c15) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( ~ spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f116,f123,f73]) ).
fof(f197,plain,
( ! [X0] :
( ~ p9(c12,f6(c14))
| ~ p7(f8(f6(c14),f5(c14)),X0)
| p9(X0,c13)
| p9(f8(f6(c14),f5(c14)),c13) )
| ~ spl0_8 ),
inference(resolution,[],[f91,f9]) ).
fof(f218,plain,
( ! [X0] :
( ~ p9(c12,f6(c14))
| ~ p7(f8(f6(c14),f5(c14)),X0)
| p9(X0,c13) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f197,f37]) ).
fof(f220,definition,
( spl0_15
<=> ! [X1] :
( ~ p7(f8(f6(c14),f5(c14)),X1)
| p9(X1,c13) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f221,plain,
( ! [X1] :
( ~ p7(f8(f6(c14),f5(c14)),X1)
| p9(X1,c13) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f228,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f218,f90,f73,f220]) ).
fof(f234,plain,
( p9(f8(f6(c14),f5(c14)),c13)
| ~ spl0_15 ),
inference(resolution,[],[f221,f2]) ).
fof(f240,plain,
( ! [X0] :
( ~ p2(f5(c14),f5(X0))
| ~ p3(f6(c14),f6(f5(c14)))
| ~ p11(X0,c15) )
| ~ spl0_9
| ~ spl0_15 ),
inference(resolution,[],[f234,f124]) ).
fof(f252,definition,
( spl0_19
<=> p3(f6(c14),f6(f5(c14))) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f253,plain,
( ~ p3(f6(c14),f6(f5(c14)))
| spl0_19 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl0_19
| spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f240,f220,f123,f87,f252]) ).
fof(f273,plain,
( ! [X0] :
( ~ p3(X0,f6(f5(c14)))
| ~ p3(X0,f6(c14)) )
| spl0_19 ),
inference(resolution,[],[f253,f16]) ).
fof(f355,plain,
( ~ p3(f6(f5(c14)),f6(c14))
| spl0_19 ),
inference(resolution,[],[f273,f3]) ).
fof(f359,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f355,f8]) ).
fof(f360,plain,
spl0_19,
inference(avatar_contradiction_clause,[],[f359]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f83]) ).
cnf(s6,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s7,plain,
~ spl0_7,
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
( ~ spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f125]) ).
cnf(s17,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f228]) ).
cnf(s20,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f254]) ).
cnf(s23,plain,
spl0_19,
inference(sat_conversion,[],[f360]) ).
cnf(s24,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(rat,[],[s20,s23]) ).
cnf(s25,plain,
spl0_8,
inference(rat,[],[s6,s7]) ).
cnf(s27,plain,
spl0_15,
inference(rat,[],[s17,s25,s5]) ).
cnf(s28,plain,
spl0_9,
inference(rat,[],[s8,s5]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s24,s7,s27,s28]) ).
fof(f361,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN575-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 16:29:33 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 0.21/1.03 % (4139900)Input is clausal, will run a generic CNF schedule.
% 0.21/1.03 % (4139909)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1895501551:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.03 % (4139909)First to succeed.
% 0.21/1.03 % (4139909)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4139900"
% 0.21/1.03 % (4139907)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1507102609:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.03 % (4139910)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=227089105:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.03 % (4139905)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=3930771367:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.03 % (4139908)lrs+10_1_sil=8000:sp=occurrence:random_seed=2852380811:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.03 % (4139906)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=578383130:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.03 % (4139910)Also succeeded, but the first one will report.
% 0.21/1.03 % (4139911)dis-21_1_sil=8000:lcm=predicate:random_seed=2474038762:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.21/1.03 % (4139908)Also succeeded, but the first one will report.
% 0.21/1.03 % (4139911)Also succeeded, but the first one will report.
% 0.21/1.03 % (4139909)Refutation found. Thanks to Tanya!
% 0.21/1.03 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.03 % (4139909)------------------------------
% 0.21/1.03 % (4139909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.03 % (4139909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.03 % (4139909)CaDiCaL version: 2.1.3
% 0.21/1.03 % (4139909)Termination reason: Refutation
% 0.21/1.03 % (4139909)Time elapsed: 0.007 s
% 0.21/1.03 % (4139909)Peak memory usage: 89 MB
% 0.21/1.03 % (4139909)Instructions burned: 16 (million)
% 0.21/1.03 % (4139909)------------------------------
% 0.21/1.03 % (4139909)------------------------------
% 0.21/1.03 % (4139900)Success in time 0.27 s
% 0.21/1.03 % Vampire exiting
%------------------------------------------------------------------------------