%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 01:49:03 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.15s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 8 unt; 8 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 216 ( 108 ~; 100 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X2,X0,X1] :
( p(f1(X0,X1),f1(X0,X1))
| ~ s(X0,f1(X0,X1))
| q(f1(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
fof(f5,negated_conjecture,
! [X2,X3,X0,X1] :
( p(f1(X0,X1),f1(X0,X1))
| s(f1(X0,X1),X2)
| q(f1(X0,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
fof(f7,negated_conjecture,
! [X2,X0,X1] :
( p(f1(X0,X1),f1(X0,X1))
| ~ q(X2,X2)
| ~ q(X1,f1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
fof(f11,negated_conjecture,
! [X2,X0,X1] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1))
| ~ p(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
fof(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
fof(f16,negated_conjecture,
! [X2,X0,X1] :
( ~ p(X0,X0)
| ~ q(X1,X1)
| ~ q(X2,f1(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
fof(f18,negated_conjecture,
! [X2,X0,X1] :
( ~ p(X0,X0)
| ~ q(X1,X1)
| ~ s(X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_18) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( q(f1(X1,X2),X3)
| ~ s(X1,f1(X1,X2))
| s(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
fof(f29,definition,
( spl0_1
<=> ! [X3] : ~ s(X3,X3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f30,plain,
( ! [X3] : ~ s(X3,X3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,definition,
( spl0_2
<=> ! [X2] : ~ q(X2,X2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f33,plain,
( ! [X2] : ~ q(X2,X2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f43,definition,
( spl0_5
<=> ! [X0] : ~ p(X0,X0) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f44,plain,
( ! [X0] : ~ p(X0,X0)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl0_1
| spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f43,f32,f29]) ).
fof(f47,definition,
( spl0_6
<=> ! [X2,X0] :
( ~ p(X0,X0)
| ~ q(X2,f1(X0,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f48,plain,
( ! [X2,X0] :
( ~ q(X2,f1(X0,X2))
| ~ p(X0,X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f47,f32]) ).
fof(f55,definition,
( spl0_8
<=> ! [X0,X1] :
( p(f1(X0,X1),f1(X0,X1))
| ~ q(X1,f1(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f56,plain,
( ! [X0,X1] :
( p(f1(X0,X1),f1(X0,X1))
| ~ q(X1,f1(X0,X1)) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f7,f55,f32]) ).
fof(f64,plain,
( ! [X0,X1] :
( ~ s(X0,f1(X0,X1))
| ~ p(X0,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f11,f33]) ).
fof(f68,plain,
( ! [X2,X0,X1] :
( s(f1(X0,X1),X2)
| ~ p(X0,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f14,f33]) ).
fof(f77,plain,
( ! [X2,X0,X1] :
( ~ s(X0,f1(X0,X1))
| s(X2,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f20,f33]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( s(X0,f1(X1,X2))
| ~ p(X1,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f77,f68]) ).
fof(f100,plain,
( ! [X2,X0,X1] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1)) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f2,f44]) ).
fof(f101,plain,
( ! [X0,X1] : ~ s(X0,f1(X0,X1))
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f100,f33]) ).
fof(f116,plain,
( ! [X2,X3,X0,X1] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f5,f44]) ).
fof(f117,plain,
( ! [X2,X0,X1] : s(f1(X0,X1),X2)
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f116,f33]) ).
fof(f124,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f117,f101]) ).
fof(f130,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f137,plain,
( ! [X0] :
( ~ p(X0,X0)
| ~ p(X0,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f81,f64]) ).
fof(f140,plain,
( ! [X0] : ~ p(X0,X0)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f137]) ).
fof(f142,plain,
( spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f140,f32,f43]) ).
fof(f153,definition,
( spl0_12
<=> ! [X4,X2,X3] :
( s(f1(X2,X3),X4)
| ~ p(X2,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,plain,
( ! [X2,X3,X4] :
( s(f1(X2,X3),X4)
| ~ p(X2,X2) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f169,plain,
( ! [X2,X3,X0,X1] :
( ~ p(X0,X0)
| s(f1(X1,X2),X3)
| ~ p(X1,X1) )
| ~ spl0_6 ),
inference(resolution,[],[f48,f14]) ).
fof(f172,plain,
( spl0_12
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f169,f47,f43,f153]) ).
fof(f187,plain,
( ! [X0] : ~ p(X0,X0)
| ~ spl0_1
| ~ spl0_12 ),
inference(resolution,[],[f154,f30]) ).
fof(f188,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f187,f153,f29,f43]) ).
fof(f202,plain,
( ! [X0,X1] : ~ q(X1,f1(X0,X1))
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f56,f44]) ).
fof(f224,plain,
( ! [X2,X0,X1] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1)) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f2,f44]) ).
fof(f232,plain,
( ! [X0,X1] : ~ s(X0,f1(X0,X1))
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f224,f202]) ).
fof(f234,definition,
( spl0_15
<=> ! [X0,X1] : ~ s(X0,f1(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f235,plain,
( ! [X0,X1] : ~ s(X0,f1(X0,X1))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f237,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f232,f55,f43,f234]) ).
fof(f238,plain,
( ! [X2,X3,X0,X1] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f5,f44]) ).
fof(f249,plain,
( ! [X2,X0,X1] : s(f1(X0,X1),X2)
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f238,f202]) ).
fof(f251,definition,
( spl0_16
<=> ! [X2,X0,X1] : s(f1(X0,X1),X2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f252,plain,
( ! [X2,X0,X1] : s(f1(X0,X1),X2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( spl0_16
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f249,f55,f43,f251]) ).
fof(f255,plain,
( $false
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[],[f252,f235]) ).
fof(f261,plain,
( ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s3,plain,
( spl0_1
| spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
( spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s14,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_5
| ~ spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f172]) ).
cnf(s24,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_12 ),
inference(sat_conversion,[],[f188]) ).
cnf(s27,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f237]) ).
cnf(s29,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f254]) ).
cnf(s31,plain,
( ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f261]) ).
cnf(s32,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(rat,[],[s31,s27,s29]) ).
cnf(s33,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s32,s3,s6]) ).
cnf(s34,plain,
~ spl0_2,
inference(rat,[],[s10,s14]) ).
cnf(s35,plain,
spl0_8,
inference(rat,[],[s6,s34]) ).
cnf(s37,plain,
spl0_6,
inference(rat,[],[s4,s34]) ).
cnf(s39,plain,
spl0_1,
inference(rat,[],[s33,s34]) ).
cnf(s40,plain,
~ spl0_5,
inference(rat,[],[s32,s35]) ).
cnf(s43,plain,
spl0_12,
inference(rat,[],[s21,s40,s37]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s24,s39,s43,s40]) ).
fof(f262,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:21:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.68/1.15 % (860015)Input is clausal, will run a generic CNF schedule.
% 2.68/1.15 % (860024)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3815734469:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.15 % (860024)First to succeed.
% 2.68/1.15 % (860024)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-860015"
% 2.68/1.15 % (860025)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2304761350:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.15 % (860023)lrs+10_1_sil=8000:sp=occurrence:random_seed=4178979837:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.15 % (860021)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2282598808:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.15 % (860020)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=1402279579:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.15 % (860026)dis-21_1_sil=8000:lcm=predicate:random_seed=4138634409: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)
% 2.68/1.15 % (860022)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3240598345:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.15 % (860025)Also succeeded, but the first one will report.
% 2.68/1.15 % (860026)Also succeeded, but the first one will report.
% 2.68/1.15 % (860023)Also succeeded, but the first one will report.
% 2.68/1.15 % (860024)Refutation found. Thanks to Tanya!
% 2.68/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.15 % (860024)------------------------------
% 2.68/1.15 % (860024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.15 % (860024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.15 % (860024)CaDiCaL version: 2.1.3
% 2.68/1.15 % (860024)Termination reason: Refutation
% 2.68/1.15 % (860024)Time elapsed: 0.003 s
% 2.68/1.15 % (860024)Peak memory usage: 89 MB
% 2.68/1.15 % (860024)Instructions burned: 6 (million)
% 2.68/1.15 % (860024)------------------------------
% 2.68/1.15 % (860024)------------------------------
% 2.68/1.15 % (860015)Success in time 0.285 s
% 2.68/1.15 % Vampire exiting
%------------------------------------------------------------------------------