%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN100-1.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:49:40 PM UTC 2026
% Result : Unsatisfiable 3.88s 1.26s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 86 ( 17 unt; 11 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 223 ( 110 ~; 102 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 12 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] :
( ~ q_0(X0)
| ~ p_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_goal_1) ).
fof(f2,axiom,
! [X0] :
( p_0(X0)
| ~ p_1(X0)
| ~ p_2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_1) ).
fof(f4,axiom,
! [X0] :
( p_1(X0)
| ~ p_2(X0)
| ~ p_3(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_3) ).
fof(f6,axiom,
! [X0] :
( ~ p_3(X0)
| p_2(X0)
| ~ p_4(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_5) ).
fof(f8,axiom,
! [X0] :
( ~ p_5(X0)
| ~ p_4(X0)
| p_3(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_7) ).
fof(f10,axiom,
! [X0] :
( ~ p_6(X0)
| ~ p_5(X0)
| p_4(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_9) ).
fof(f12,axiom,
! [X0] :
( ~ p_7(X0)
| ~ p_6(X0)
| p_5(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_11) ).
fof(f14,axiom,
! [X0] :
( ~ p_8(X0)
| ~ p_7(X0)
| p_6(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_13) ).
fof(f16,axiom,
! [X0] :
( ~ p_9(X0)
| ~ p_8(X0)
| p_7(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_15) ).
fof(f18,axiom,
! [X0] :
( q_0(X0)
| ~ p_1(X0)
| ~ q_2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_1) ).
fof(f22,axiom,
! [X0] :
( ~ p_3(X0)
| q_2(X0)
| ~ q_4(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_5) ).
fof(f27,axiom,
! [X0] :
( ~ p_6(X0)
| ~ q_5(X0)
| q_4(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_10) ).
fof(f29,axiom,
! [X0] :
( ~ p_7(X0)
| ~ q_6(X0)
| q_5(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_12) ).
fof(f30,axiom,
! [X0] :
( ~ q_8(X0)
| ~ p_7(X0)
| q_6(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_13) ).
fof(f38,axiom,
p_8(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_1) ).
fof(f39,axiom,
p_9(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_2) ).
fof(f40,axiom,
q_8(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_3) ).
fof(f83,plain,
( ~ p_7(a)
| p_6(a) ),
inference(resolution,[],[f14,f38]) ).
fof(f85,definition,
( spl0_1
<=> p_6(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f86,plain,
( p_6(a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_2
<=> p_7(a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f90,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f83,f88,f85]) ).
fof(f96,plain,
( ~ p_8(a)
| p_7(a) ),
inference(resolution,[],[f16,f39]) ).
fof(f98,plain,
( p_7(a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f100,definition,
( spl0_4
<=> p_8(a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f101,plain,
( ~ p_8(a)
| spl0_4 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f96,f100,f88]) ).
fof(f103,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f101,f38]) ).
fof(f104,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f105,plain,
( ~ p_5(a)
| p_4(a)
| ~ spl0_1 ),
inference(resolution,[],[f86,f10]) ).
fof(f107,definition,
( spl0_5
<=> p_4(a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f110,definition,
( spl0_6
<=> p_5(a) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f112,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f105,f85,f110,f107]) ).
fof(f113,plain,
( ~ p_6(a)
| p_5(a)
| ~ spl0_2 ),
inference(resolution,[],[f98,f12]) ).
fof(f114,plain,
( p_5(a)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f116,plain,
( spl0_6
| ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f113,f88,f85,f110]) ).
fof(f119,plain,
( ~ p_4(a)
| p_3(a)
| ~ spl0_6 ),
inference(resolution,[],[f114,f8]) ).
fof(f121,definition,
( spl0_7
<=> p_3(a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f122,plain,
( p_3(a)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f119,f110,f107,f121]) ).
fof(f125,plain,
( p_2(a)
| ~ p_4(a)
| ~ spl0_7 ),
inference(resolution,[],[f122,f6]) ).
fof(f127,definition,
( spl0_8
<=> p_2(a) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f129,plain,
( ~ spl0_5
| spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f125,f121,f127,f107]) ).
fof(f130,plain,
! [X0] :
( ~ p_0(X0)
| ~ q_2(X0)
| ~ p_1(X0) ),
inference(resolution,[],[f18,f1]) ).
fof(f133,plain,
! [X0] :
( ~ q_2(X0)
| ~ p_1(X0)
| ~ p_1(X0)
| ~ p_2(X0) ),
inference(resolution,[],[f130,f2]) ).
fof(f134,plain,
! [X0] :
( ~ p_1(X0)
| ~ q_2(X0)
| ~ p_2(X0) ),
inference(duplicate_literal_removal,[],[f133]) ).
fof(f141,plain,
! [X0] :
( ~ q_2(X0)
| ~ p_2(X0)
| ~ p_2(X0)
| ~ p_3(X0) ),
inference(resolution,[],[f134,f4]) ).
fof(f142,plain,
! [X0] :
( ~ p_3(X0)
| ~ p_2(X0)
| ~ q_2(X0) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f144,plain,
( q_2(a)
| ~ q_4(a)
| ~ spl0_7 ),
inference(resolution,[],[f22,f122]) ).
fof(f146,definition,
( spl0_9
<=> q_4(a) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f149,definition,
( spl0_10
<=> q_2(a) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f151,plain,
( ~ spl0_9
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f144,f121,f149,f146]) ).
fof(f163,plain,
( ~ p_2(a)
| ~ q_2(a)
| ~ spl0_7 ),
inference(resolution,[],[f142,f122]) ).
fof(f166,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f163,f121,f127,f149]) ).
fof(f167,plain,
( ~ q_5(a)
| q_4(a)
| ~ spl0_1 ),
inference(resolution,[],[f27,f86]) ).
fof(f170,definition,
( spl0_11
<=> q_5(a) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f172,plain,
( spl0_9
| ~ spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f167,f85,f170,f146]) ).
fof(f181,plain,
( ~ q_6(a)
| q_5(a)
| ~ spl0_2 ),
inference(resolution,[],[f29,f98]) ).
fof(f184,definition,
( spl0_12
<=> q_6(a) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f186,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f181,f88,f184,f170]) ).
fof(f187,plain,
( ~ p_7(a)
| q_6(a) ),
inference(resolution,[],[f30,f40]) ).
fof(f189,plain,
( spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f187,f88,f184]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f124]) ).
cnf(s8,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f129]) ).
cnf(s9,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s10,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f166]) ).
cnf(s11,plain,
( ~ spl0_1
| spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f172]) ).
cnf(s12,plain,
( ~ spl0_2
| spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f186]) ).
cnf(s13,plain,
( ~ spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f189]) ).
cnf(s14,plain,
spl0_2,
inference(rat,[],[s3,s4]) ).
cnf(s15,plain,
spl0_12,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
spl0_11,
inference(rat,[],[s12,s15,s14]) ).
cnf(s17,plain,
spl0_1,
inference(rat,[],[s1,s14]) ).
cnf(s18,plain,
spl0_9,
inference(rat,[],[s11,s16,s17]) ).
cnf(s19,plain,
spl0_6,
inference(rat,[],[s6,s14,s17]) ).
cnf(s20,plain,
spl0_5,
inference(rat,[],[s5,s19,s17]) ).
cnf(s21,plain,
spl0_7,
inference(rat,[],[s7,s19,s20]) ).
cnf(s22,plain,
spl0_10,
inference(rat,[],[s9,s18,s21]) ).
cnf(s23,plain,
spl0_8,
inference(rat,[],[s8,s20,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s10,s21,s22,s23]) ).
fof(f190,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN100-1.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n015.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 15:36:32 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.88/1.26 % (2720585)Input is clausal, will run a generic CNF schedule.
% 3.88/1.26 % (2720617)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=69359763:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.88/1.26 % (2720621)dis-21_1_sil=8000:lcm=predicate:random_seed=2073510432: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)
% 3.88/1.26 % (2720620)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=965651331:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.88/1.26 % (2720619)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=386130144:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.88/1.26 % (2720616)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2088692825:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.88/1.26 % (2720615)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=469709674:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.88/1.26 % (2720621)First to succeed.
% 3.88/1.26 % (2720621)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2720585"
% 3.88/1.26 % (2720619)Also succeeded, but the first one will report.
% 3.88/1.26 % (2720620)Also succeeded, but the first one will report.
% 3.88/1.26 % (2720618)lrs+10_1_sil=8000:sp=occurrence:random_seed=1049349415:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.88/1.26 % (2720618)Refutation not found, incomplete strategy
% 3.88/1.26 % (2720618)------------------------------
% 3.88/1.26 % (2720618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.26 % (2720618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.26 % (2720618)CaDiCaL version: 2.1.3
% 3.88/1.26 % (2720618)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.26 % (2720618)Time elapsed: 0.001 s
% 3.88/1.26 % (2720618)Peak memory usage: 86 MB
% 3.88/1.26 % (2720621)Refutation found. Thanks to Tanya!
% 3.88/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.88/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.26 % (2720621)------------------------------
% 3.88/1.26 % (2720621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.26 % (2720621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.26 % (2720621)CaDiCaL version: 2.1.3
% 3.88/1.26 % (2720621)Termination reason: Refutation
% 3.88/1.26 % (2720621)Time elapsed: 0.004 s
% 3.88/1.26 % (2720621)Peak memory usage: 89 MB
% 3.88/1.26 % (2720621)Instructions burned: 3 (million)
% 3.88/1.26 % (2720621)------------------------------
% 3.88/1.26 % (2720621)------------------------------
% 3.88/1.26 % (2720585)Success in time 0.488 s
% 3.88/1.26 % Vampire exiting
%------------------------------------------------------------------------------