%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN619-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 02:01:06 PM UTC 2026
% Result : Unsatisfiable 3.10s 1.26s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 77 ( 20 unt; 10 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 91 ~; 95 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,negated_conjecture,
! [X0] : p2(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
fof(f6,negated_conjecture,
! [X0] : p17(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17_6) ).
fof(f7,negated_conjecture,
p18(c24,f6(c25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_7) ).
fof(f8,negated_conjecture,
~ p18(c24,f6(f7(c22,c23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p18_8) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( ~ p17(f3(X0),X1)
| p17(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17_9) ).
fof(f24,negated_conjecture,
! [X0] :
( p18(X0,f6(c19))
| p2(f14(X0),c20)
| ~ p18(X0,f6(c25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_24) ).
fof(f25,negated_conjecture,
! [X2,X3,X0,X1] :
( p17(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p17(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17_25) ).
fof(f27,negated_conjecture,
! [X0] :
( p17(f3(c21),f15(X0))
| p18(X0,f6(c19))
| ~ p18(X0,f6(c25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_27) ).
fof(f32,negated_conjecture,
! [X2,X0,X1] :
( ~ p17(c21,X1)
| ~ p2(X0,c20)
| ~ p8(c24,f9(f13(X0,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_32) ).
fof(f33,negated_conjecture,
! [X0] :
( p18(X0,f6(c19))
| p8(X0,f9(f13(f14(X0),f15(X0)),f16(X0)))
| ~ p18(X0,f6(c25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_33) ).
fof(f34,negated_conjecture,
! [X0] :
( p18(X0,f6(f7(c22,c23)))
| p8(X0,f9(f13(c20,c21),f11(f12(f7(c22,c23)))))
| ~ p18(X0,f6(c19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_34) ).
fof(f63,plain,
! [X0] :
( p17(c21,f15(X0))
| ~ p18(X0,f6(c25))
| p18(X0,f6(c19)) ),
inference(resolution,[],[f27,f9]) ).
fof(f71,plain,
! [X0,X1] :
( ~ p8(c24,f9(f13(X0,c21),X1))
| ~ p2(X0,c20) ),
inference(resolution,[],[f32,f6]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] :
( ~ p17(X3,X4)
| ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p2(X3,c21)
| ~ p2(X4,X1)
| ~ p2(X0,c20) ),
inference(resolution,[],[f32,f25]) ).
fof(f82,plain,
( p8(c24,f9(f13(c20,c21),f11(f12(f7(c22,c23)))))
| ~ p18(c24,f6(c19)) ),
inference(resolution,[],[f34,f8]) ).
fof(f85,definition,
( spl0_1
<=> p18(c24,f6(c19)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f86,plain,
( ~ p18(c24,f6(c19))
| spl0_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_2
<=> p8(c24,f9(f13(c20,c21),f11(f12(f7(c22,c23))))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f89,plain,
( p8(c24,f9(f13(c20,c21),f11(f12(f7(c22,c23)))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f82,f88,f85]) ).
fof(f91,plain,
( p8(c24,f9(f13(f14(c24),f15(c24)),f16(c24)))
| ~ p18(c24,f6(c25))
| spl0_1 ),
inference(resolution,[],[f86,f33]) ).
fof(f92,plain,
( p2(f14(c24),c20)
| ~ p18(c24,f6(c25))
| spl0_1 ),
inference(resolution,[],[f86,f24]) ).
fof(f95,definition,
( spl0_3
<=> p18(c24,f6(c25)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f96,plain,
( ~ p18(c24,f6(c25))
| spl0_3 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_4
<=> p2(f14(c24),c20) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f100,plain,
( ~ spl0_3
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f92,f85,f98,f95]) ).
fof(f102,definition,
( spl0_5
<=> p8(c24,f9(f13(f14(c24),f15(c24)),f16(c24))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f103,plain,
( p8(c24,f9(f13(f14(c24),f15(c24)),f16(c24)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( ~ spl0_3
| spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f91,f85,f102,f95]) ).
fof(f107,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f96,f7]) ).
fof(f109,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f1101,plain,
! [X2,X3,X0,X1] :
( ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p2(c21,c21)
| ~ p2(f15(X3),X1)
| ~ p2(X0,c20)
| ~ p18(X3,f6(c25))
| p18(X3,f6(c19)) ),
inference(resolution,[],[f79,f63]) ).
fof(f1103,definition,
( spl0_6
<=> p2(c21,c21) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f1104,plain,
( ~ p2(c21,c21)
| spl0_6 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f1106,definition,
( spl0_7
<=> ! [X0,X3,X2,X1] :
( ~ p8(c24,f9(f13(X0,X1),X2))
| p18(X3,f6(c19))
| ~ p18(X3,f6(c25))
| ~ p2(X0,c20)
| ~ p2(f15(X3),X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f1107,plain,
( ! [X2,X3,X0,X1] :
( p18(X3,f6(c19))
| ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p18(X3,f6(c25))
| ~ p2(X0,c20)
| ~ p2(f15(X3),X1) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1108,plain,
( ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f1101,f1106,f1103]) ).
fof(f1113,plain,
( $false
| spl0_6 ),
inference(resolution,[],[f1104,f5]) ).
fof(f1118,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f1113]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p18(c24,f6(c25))
| ~ p2(X0,c20)
| ~ p2(f15(c24),X1) )
| spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f1107,f86]) ).
fof(f1133,definition,
( spl0_9
<=> ! [X2,X0,X1] :
( ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p2(f15(c24),X1)
| ~ p2(X0,c20) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f1134,plain,
( ! [X2,X0,X1] :
( ~ p8(c24,f9(f13(X0,X1),X2))
| ~ p2(f15(c24),X1)
| ~ p2(X0,c20) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f1135,plain,
( ~ spl0_3
| spl0_9
| spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1122,f1106,f85,f1133,f95]) ).
fof(f1168,plain,
( ~ p2(f15(c24),f15(c24))
| ~ p2(f14(c24),c20)
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[],[f1134,f103]) ).
fof(f1201,definition,
( spl0_12
<=> p2(f15(c24),f15(c24)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f1202,plain,
( ~ p2(f15(c24),f15(c24))
| spl0_12 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f1240,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f1168,f1133,f102,f1201,f98]) ).
fof(f1242,plain,
( $false
| spl0_12 ),
inference(resolution,[],[f1202,f5]) ).
fof(f1247,plain,
spl0_12,
inference(avatar_contradiction_clause,[],[f1242]) ).
fof(f1249,plain,
( ~ p2(c20,c20)
| ~ spl0_2 ),
inference(resolution,[],[f89,f71]) ).
fof(f1256,definition,
( spl0_18
<=> p2(c20,c20) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f1257,plain,
( ~ p2(c20,c20)
| spl0_18 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1263,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1249,f88,f1256]) ).
fof(f1264,plain,
( $false
| spl0_18 ),
inference(resolution,[],[f1257,f5]) ).
fof(f1269,plain,
spl0_18,
inference(avatar_contradiction_clause,[],[f1264]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f104]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f1108]) ).
cnf(s7,plain,
spl0_6,
inference(sat_conversion,[],[f1118]) ).
cnf(s8,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f1135]) ).
cnf(s33,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s34,plain,
spl0_12,
inference(sat_conversion,[],[f1247]) ).
cnf(s37,plain,
( ~ spl0_2
| ~ spl0_18 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s38,plain,
spl0_18,
inference(sat_conversion,[],[f1269]) ).
cnf(s39,plain,
~ spl0_2,
inference(rat,[],[s37,s38]) ).
cnf(s40,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(rat,[],[s33,s34]) ).
cnf(s63,plain,
spl0_7,
inference(rat,[],[s5,s7]) ).
cnf(s64,plain,
( spl0_1
| spl0_5 ),
inference(rat,[],[s3,s4]) ).
cnf(s65,plain,
( spl0_1
| spl0_4 ),
inference(rat,[],[s2,s4]) ).
cnf(s66,plain,
~ spl0_1,
inference(rat,[],[s1,s39]) ).
cnf(s67,plain,
spl0_9,
inference(rat,[],[s8,s4,s63,s66]) ).
cnf(s68,plain,
spl0_5,
inference(rat,[],[s64,s66]) ).
cnf(s69,plain,
spl0_4,
inference(rat,[],[s65,s66]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s40,s67,s68,s69]) ).
fof(f1270,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN619-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 16:35:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.10/1.26 % (1314428)Input is clausal, will run a generic CNF schedule.
% 3.10/1.26 % (1314524)dis-21_1_sil=8000:lcm=predicate:random_seed=2471026151: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)
% 3.10/1.26 % (1314524)First to succeed.
% 3.10/1.26 % (1314524)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1314428"
% 3.10/1.26 % (1314517)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2715792131:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.10/1.26 % (1314523)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3851608488:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.10/1.26 % (1314516)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=968564204:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.10/1.26 % (1314521)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4282037324:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.10/1.26 % (1314519)lrs+10_1_sil=8000:sp=occurrence:random_seed=1422541882:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.10/1.26 % (1314521)Also succeeded, but the first one will report.
% 3.10/1.26 % (1314523)Also succeeded, but the first one will report.
% 3.10/1.26 % (1314519)Also succeeded, but the first one will report.
% 3.10/1.26 % (1314518)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3446907147:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.10/1.26 % (1314524)Refutation found. Thanks to Tanya!
% 3.10/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.10/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.10/1.26 % (1314524)------------------------------
% 3.10/1.26 % (1314524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.26 % (1314524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.26 % (1314524)CaDiCaL version: 2.1.3
% 3.10/1.26 % (1314524)Termination reason: Refutation
% 3.10/1.26 % (1314524)Time elapsed: 0.028 s
% 3.10/1.26 % (1314524)Peak memory usage: 89 MB
% 3.10/1.26 % (1314524)Instructions burned: 91 (million)
% 3.10/1.26 % (1314524)------------------------------
% 3.10/1.26 % (1314524)------------------------------
% 3.10/1.26 % (1314428)Success in time 0.353 s
% 3.10/1.26 % Vampire exiting
%------------------------------------------------------------------------------