%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN724+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 : n017.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 02:01:20 PM UTC 2026
% Result : Theorem 2.68s 1.18s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 6 unt; 4 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 193 ( 69 ~; 76 |; 31 &)
% ( 12 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 25 ( 0 sgn 20 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X0] :
( ( r(X0)
& s(X0) )
<=> r(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm31) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X0] :
( ( r(X0)
& s(X0) )
<=> r(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( r(X0)
=> s(X0) )
<=> ! [X1] :
( ( r(X1)
& s(X1) )
<=> r(X1) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( s(X0)
| ~ r(X0) )
<~> ! [X1] :
( ( r(X1)
& s(X1) )
<=> r(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,definition,
( sP0
<=> ! [X1] :
( ( r(X1)
& s(X1) )
<=> r(X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,plain,
( ! [X0] :
( s(X0)
| ~ r(X0) )
<~> sP0 ),
inference(definition_folding,[],[f4,f5]) ).
fof(f7,plain,
( ( sP0
| ? [X1] :
( ( ~ r(X1)
| ~ r(X1)
| ~ s(X1) )
& ( r(X1)
| ( r(X1)
& s(X1) ) ) ) )
& ( ! [X1] :
( ( ( r(X1)
& s(X1) )
| ~ r(X1) )
& ( r(X1)
| ~ r(X1)
| ~ s(X1) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f8,plain,
( ( sP0
| ? [X1] :
( ( ~ r(X1)
| ~ r(X1)
| ~ s(X1) )
& ( r(X1)
| ( r(X1)
& s(X1) ) ) ) )
& ( ! [X1] :
( ( ( r(X1)
& s(X1) )
| ~ r(X1) )
& ( r(X1)
| ~ r(X1)
| ~ s(X1) ) )
| ~ sP0 ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ( sP0
| ? [X0] :
( ( ~ r(X0)
| ~ r(X0)
| ~ s(X0) )
& ( r(X0)
| ( r(X0)
& s(X0) ) ) ) )
& ( ! [X1] :
( ( ( r(X1)
& s(X1) )
| ~ r(X1) )
& ( r(X1)
| ~ r(X1)
| ~ s(X1) ) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( sP0
| ( ( ~ r(sK1)
| ~ r(sK1)
| ~ s(sK1) )
& ( r(sK1)
| ( r(sK1)
& s(sK1) ) ) ) )
& ( ! [X1] :
( ( ( r(X1)
& s(X1) )
| ~ r(X1) )
& ( r(X1)
| ~ r(X1)
| ~ s(X1) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f9]) ).
fof(f11,plain,
( ( ~ sP0
| ? [X0] :
( ~ s(X0)
& r(X0) ) )
& ( sP0
| ! [X0] :
( s(X0)
| ~ r(X0) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ( ~ sP0
| ? [X0] :
( ~ s(X0)
& r(X0) ) )
& ( sP0
| ! [X1] :
( s(X1)
| ~ r(X1) ) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( ~ sP0
| ( ~ s(sK2)
& r(sK2) ) )
& ( sP0
| ! [X1] :
( s(X1)
| ~ r(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f15,plain,
! [X1] :
( ~ r(X1)
| s(X1)
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
( sP0
| r(sK1)
| r(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( sP0
| ~ r(sK1)
| ~ r(sK1)
| ~ s(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X1] :
( sP0
| s(X1)
| ~ r(X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
( ~ sP0
| r(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
( ~ sP0
| ~ s(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
( ~ s(sK1)
| ~ r(sK1)
| sP0 ),
inference(duplicate_literal_removal,[],[f19]) ).
fof(f24,plain,
( r(sK1)
| sP0 ),
inference(duplicate_literal_removal,[],[f18]) ).
fof(f25,plain,
! [X1] :
( ~ r(X1)
| s(X1) ),
inference(forward_subsumption_resolution,[],[f20,f15]) ).
fof(f27,definition,
( spl3_1
<=> r(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f29,plain,
( r(sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f31,definition,
( spl3_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f33,plain,
( ~ sP0
| spl3_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f21,f31,f27]) ).
fof(f36,definition,
( spl3_3
<=> s(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f38,plain,
( ~ s(sK2)
| spl3_3 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
( ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f22,f31,f36]) ).
fof(f40,plain,
( s(sK1)
| sP0 ),
inference(resolution,[],[f25,f24]) ).
fof(f41,plain,
( s(sK1)
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f40,f33]) ).
fof(f42,plain,
( ~ r(sK1)
| sP0
| spl3_2 ),
inference(resolution,[],[f41,f23]) ).
fof(f43,plain,
( sP0
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f42,f24]) ).
fof(f44,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f43,f33]) ).
fof(f45,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f46,plain,
( s(sK2)
| ~ spl3_1 ),
inference(resolution,[],[f29,f25]) ).
fof(f49,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f46,f38]) ).
fof(f50,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f49]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
~ spl3_3,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
~ spl3_1,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s3,s7]) ).
fof(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n017.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 16:44:36 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
% 2.68/1.18 % (3698641)Detected formulas, will run a generic FOF schedule.
% 2.68/1.18 % (3698725)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3207833982:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.18 % (3698725)First to succeed.
% 2.68/1.18 % (3698725)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3698641"
% 2.68/1.18 % (3698730)dis-21_1_sil=8000:lcm=predicate:random_seed=1389026835: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)
% 2.68/1.18 % (3698723)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=1039232371:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.18 % (3698722)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=2625181838:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.18 % (3698727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1398636104:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.18 % (3698721)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=916757194:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.18 % (3698728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3109709116:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.18 % (3698727)Also succeeded, but the first one will report.
% 2.68/1.18 % (3698730)Also succeeded, but the first one will report.
% 2.68/1.18 % (3698728)Also succeeded, but the first one will report.
% 2.68/1.18 % (3698725)Refutation found. Thanks to Tanya!
% 2.68/1.18 % SZS status Theorem for theBenchmark
% 2.68/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.18 % (3698725)------------------------------
% 2.68/1.18 % (3698725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.18 % (3698725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.18 % (3698725)CaDiCaL version: 2.1.3
% 2.68/1.18 % (3698725)Termination reason: Refutation
% 2.68/1.18 % (3698725)Time elapsed: 0.001 s
% 2.68/1.18 % (3698725)Peak memory usage: 89 MB
% 2.68/1.18 % (3698725)Instructions burned: 1 (million)
% 2.68/1.18 % (3698725)------------------------------
% 2.68/1.18 % (3698725)------------------------------
% 2.68/1.18 % (3698641)Success in time 0.296 s
% 2.68/1.18 % Vampire exiting
%------------------------------------------------------------------------------