%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN398+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:50:30 PM UTC 2026
% Result : Theorem 2.91s 1.17s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 4 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 39 ~; 40 |; 18 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( p
& f(X0) )
<=> ( p
& ! [X1] : f(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish215) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( p
& f(X0) )
<=> ( p
& ! [X1] : f(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( p
& f(X0) )
<~> ( p
& ! [X1] : f(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ~ p
| ? [X1] : ~ f(X1)
| ? [X0] :
( ~ p
| ~ f(X0) ) )
& ( ( p
& ! [X1] : f(X1) )
| ! [X0] :
( p
& f(X0) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ~ p
| ? [X1] : ~ f(X1)
| ? [X0] :
( ~ p
| ~ f(X0) ) )
& ( ( p
& ! [X1] : f(X1) )
| ! [X0] :
( p
& f(X0) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ( ~ p
| ? [X0] : ~ f(X0)
| ? [X1] :
( ~ p
| ~ f(X1) ) )
& ( ( p
& ! [X2] : f(X2) )
| ! [X3] :
( p
& f(X3) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ~ p
| ~ f(sK0)
| ~ p
| ~ f(sK1) )
& ( ( p
& ! [X2] : f(X2) )
| ! [X3] :
( p
& f(X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
fof(f8,plain,
! [X2,X3] :
( f(X2)
| f(X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( p
| p ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
( ~ p
| ~ f(sK0)
| ~ p
| ~ f(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
p,
inference(duplicate_literal_removal,[],[f11]) ).
fof(f14,plain,
( ~ p
| ~ f(sK0)
| ~ f(sK1) ),
inference(duplicate_literal_removal,[],[f12]) ).
fof(f16,definition,
( spl2_1
<=> ! [X3] : f(X3) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f17,plain,
( ! [X3] : f(X3)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl2_1
| spl2_1 ),
inference(avatar_split_clause,[],[f8,f16,f16]) ).
fof(f20,definition,
( spl2_2
<=> p ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f25,plain,
spl2_2,
inference(avatar_split_clause,[],[f13,f20]) ).
fof(f27,definition,
( spl2_3
<=> f(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f29,plain,
( ~ f(sK1)
| spl2_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f31,definition,
( spl2_4
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f33,plain,
( ~ f(sK0)
| spl2_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
( ~ spl2_3
| ~ spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f14,f20,f31,f27]) ).
fof(f35,plain,
( $false
| ~ spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f29,f17]) ).
fof(f36,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f37,plain,
( $false
| ~ spl2_1
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f33,f17]) ).
fof(f38,plain,
( ~ spl2_1
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( spl2_1
| spl2_1 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
spl2_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
spl2_2,
inference(sat_conversion,[],[f25]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s9,plain,
spl2_4,
inference(rat,[],[s8,s2]) ).
cnf(s10,plain,
spl2_3,
inference(rat,[],[s7,s2]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s5,s9,s10]) ).
fof(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN398+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n026.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 15:56:56 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running first-order theorem proving
% 0.10/0.19 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
% 2.91/1.17 % (3974284)Detected formulas, will run a generic FOF schedule.
% 2.91/1.17 % (3974381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1806851425:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.17 % (3974381)First to succeed.
% 2.91/1.17 % (3974381)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3974284"
% 2.91/1.17 % (3974372)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=1877482001:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.17 % (3974376)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=1002938831:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.17 % (3974377)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2152556661:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.17 % (3974379)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1011894323:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.17 % (3974379)Also succeeded, but the first one will report.
% 2.91/1.17 % (3974377)Also succeeded, but the first one will report.
% 2.91/1.17 % (3974374)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=4117868689:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.17 % (3974384)dis-21_1_sil=8000:lcm=predicate:random_seed=1657013819: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)
% 2.91/1.17 % (3974384)Also succeeded, but the first one will report.
% 2.91/1.17 % (3974381)Refutation found. Thanks to Tanya!
% 2.91/1.17 % SZS status Theorem for theBenchmark
% 2.91/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.91/1.17 % (3974381)------------------------------
% 2.91/1.17 % (3974381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.17 % (3974381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.17 % (3974381)CaDiCaL version: 2.1.3
% 2.91/1.17 % (3974381)Termination reason: Refutation
% 2.91/1.17 % (3974381)Time elapsed: 0.001 s
% 2.91/1.17 % (3974381)Peak memory usage: 89 MB
% 2.91/1.17 % (3974381)Instructions burned: 1 (million)
% 2.91/1.17 % (3974381)------------------------------
% 2.91/1.17 % (3974381)------------------------------
% 2.91/1.17 % (3974284)Success in time 0.329 s
% 2.91/1.17 % Vampire exiting
%------------------------------------------------------------------------------