%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN728+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 02:01:21 PM UTC 2026
% Result : Theorem 0.64s 1.02s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 7 unt; 4 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 130 ( 53 ~; 43 |; 24 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
( ? [X1] : p(X0,X1)
=> ! [X2] : p(X2,X2) )
& ! [X3] :
? [X4] :
( p(X3,X4)
| ( m(X3)
& q(f(X3,X4)) ) )
& ! [X5] :
( q(X5)
=> ~ m(g(X5)) ) )
=> ! [X6] :
? [X7] :
( p(g(X6),X7)
& p(X6,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm69) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( ? [X1] : p(X0,X1)
=> ! [X2] : p(X2,X2) )
& ! [X3] :
? [X4] :
( p(X3,X4)
| ( m(X3)
& q(f(X3,X4)) ) )
& ! [X5] :
( q(X5)
=> ~ m(g(X5)) ) )
=> ! [X6] :
? [X7] :
( p(g(X6),X7)
& p(X6,X6) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X6] :
! [X7] :
( ~ p(g(X6),X7)
| ~ p(X6,X6) )
& ! [X0] :
( ! [X2] : p(X2,X2)
| ! [X1] : ~ p(X0,X1) )
& ! [X3] :
? [X4] :
( p(X3,X4)
| ( m(X3)
& q(f(X3,X4)) ) )
& ! [X5] :
( ~ m(g(X5))
| ~ q(X5) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ? [X6] :
! [X7] :
( ~ p(g(X6),X7)
| ~ p(X6,X6) )
& ! [X0] :
( ! [X2] : p(X2,X2)
| ! [X1] : ~ p(X0,X1) )
& ! [X3] :
? [X4] :
( p(X3,X4)
| ( m(X3)
& q(f(X3,X4)) ) )
& ! [X5] :
( ~ m(g(X5))
| ~ q(X5) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ? [X0] :
! [X1] :
( ~ p(g(X0),X1)
| ~ p(X0,X0) )
& ! [X2] :
( ! [X3] : p(X3,X3)
| ! [X4] : ~ p(X2,X4) )
& ! [X5] :
? [X6] :
( p(X5,X6)
| ( m(X5)
& q(f(X5,X6)) ) )
& ! [X7] :
( ~ m(g(X7))
| ~ q(X7) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X1] :
( ~ p(g(sK0),X1)
| ~ p(sK0,sK0) )
& ! [X2] :
( ! [X3] : p(X3,X3)
| ! [X4] : ~ p(X2,X4) )
& ! [X5] :
( p(X5,sK1(X5))
| ( m(X5)
& q(f(X5,sK1(X5))) ) )
& ! [X7] :
( ~ m(g(X7))
| ~ q(X7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X6,sK1(X5))],[f5]) ).
fof(f7,plain,
! [X7] :
( ~ q(X7)
| ~ m(g(X7)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X5] :
( q(f(X5,sK1(X5)))
| p(X5,sK1(X5)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X5] :
( m(X5)
| p(X5,sK1(X5)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X3,X4] :
( p(X3,X3)
| ~ p(X2,X4) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X1] :
( ~ p(g(sK0),X1)
| ~ p(sK0,sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,definition,
( spl2_1
<=> ! [X4,X2] : ~ p(X2,X4) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f14,plain,
( ! [X2,X4] : ~ p(X2,X4)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,definition,
( spl2_2
<=> ! [X3] : p(X3,X3) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f17,plain,
( ! [X3] : p(X3,X3)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f10,f16,f13]) ).
fof(f20,definition,
( spl2_3
<=> p(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f21,plain,
( ~ p(sK0,sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,definition,
( spl2_4
<=> ! [X1] : ~ p(g(sK0),X1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f24,plain,
( ! [X1] : ~ p(g(sK0),X1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f11,f23,f20]) ).
fof(f26,plain,
( $false
| ~ spl2_2
| spl2_3 ),
inference(resolution,[],[f21,f17]) ).
fof(f27,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ~ m(g(f(X0,sK1(X0))))
| p(X0,sK1(X0)) ),
inference(resolution,[],[f8,f7]) ).
fof(f29,plain,
! [X0] :
( p(g(f(X0,sK1(X0))),sK1(g(f(X0,sK1(X0)))))
| p(X0,sK1(X0)) ),
inference(resolution,[],[f28,f9]) ).
fof(f30,plain,
( ! [X0] : p(X0,sK1(X0))
| ~ spl2_1 ),
inference(resolution,[],[f29,f14]) ).
fof(f31,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f30,f14]) ).
fof(f32,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f31]) ).
fof(f33,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f24,f17]) ).
fof(f34,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f33]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s6,plain,
spl2_2,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
~ spl2_4,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl2_3,
inference(rat,[],[s3,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
fof(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN728+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n026.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 16:52:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/1.02 % (4013930)Detected formulas, will run a generic FOF schedule.
% 0.64/1.02 % (4013941)dis-21_1_sil=8000:lcm=predicate:random_seed=2598758549: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)
% 0.64/1.02 % (4013941)First to succeed.
% 0.64/1.02 % (4013941)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4013930"
% 0.64/1.02 % (4013940)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3321958810:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/1.02 % (4013940)Also succeeded, but the first one will report.
% 0.64/1.02 % (4013939)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1458073869:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/1.02 % (4013936)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=53672704:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/1.02 % (4013938)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2865157345:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/1.02 % (4013935)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=2826539119:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/1.02 % (4013937)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=487359395:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/1.02 % (4013939)Also succeeded, but the first one will report.
% 0.64/1.02 % (4013938)Also succeeded, but the first one will report.
% 0.64/1.02 % (4013941)Refutation found. Thanks to Tanya!
% 0.64/1.02 % SZS status Theorem for theBenchmark
% 0.64/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/1.02 % (4013941)------------------------------
% 0.64/1.02 % (4013941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.02 % (4013941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.02 % (4013941)CaDiCaL version: 2.1.3
% 0.64/1.02 % (4013941)Termination reason: Refutation
% 0.64/1.02 % (4013941)Time elapsed: 0.001 s
% 0.64/1.02 % (4013941)Peak memory usage: 89 MB
% 0.64/1.02 % (4013941)Instructions burned: 1 (million)
% 0.64/1.02 % (4013941)------------------------------
% 0.64/1.02 % (4013941)------------------------------
% 0.64/1.02 % (4013930)Success in time 0.274 s
% 0.64/1.02 % Vampire exiting
%------------------------------------------------------------------------------