%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN922+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:05:59 PM UTC 2026
% Result : Theorem 2.73s 0.97s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 8 unt; 6 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 131 ( 48 ~; 53 |; 20 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 32 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( p(X0)
& q(X0) )
<=> ( ! [X0] : p(X0)
& ! [X0] : q(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( p(X0)
& q(X0) )
<=> ( ! [X0] : p(X0)
& ! [X0] : q(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( p(X0)
& q(X0) )
<=> ( ! [X1] : p(X1)
& ! [X2] : q(X2) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( p(X0)
& q(X0) )
<~> ( ! [X1] : p(X1)
& ! [X2] : q(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X1] : ~ p(X1)
| ? [X2] : ~ q(X2)
| ? [X0] :
( ~ p(X0)
| ~ q(X0) ) )
& ( ( ! [X1] : p(X1)
& ! [X2] : q(X2) )
| ! [X0] :
( p(X0)
& q(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ? [X1] : ~ p(X1)
| ? [X2] : ~ q(X2)
| ? [X0] :
( ~ p(X0)
| ~ q(X0) ) )
& ( ( ! [X1] : p(X1)
& ! [X2] : q(X2) )
| ! [X0] :
( p(X0)
& q(X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ( ? [X0] : ~ p(X0)
| ? [X1] : ~ q(X1)
| ? [X2] :
( ~ p(X2)
| ~ q(X2) ) )
& ( ( ! [X3] : p(X3)
& ! [X4] : q(X4) )
| ! [X5] :
( p(X5)
& q(X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
( ( ~ p(sK0)
| ~ q(sK1)
| ~ p(sK2)
| ~ q(sK2) )
& ( ( ! [X3] : p(X3)
& ! [X4] : q(X4) )
| ! [X5] :
( p(X5)
& q(X5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
fof(f9,plain,
! [X4,X5] :
( q(X4)
| q(X5) ),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
! [X3,X5] :
( p(X3)
| p(X5) ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
( ~ p(sK0)
| ~ q(sK1)
| ~ p(sK2)
| ~ q(sK2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f15,definition,
( spl3_1
<=> ! [X5] : q(X5) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f16,plain,
( ! [X5] : q(X5)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( spl3_1
| spl3_1 ),
inference(avatar_split_clause,[],[f9,f15,f15]) ).
fof(f19,definition,
( spl3_2
<=> ! [X5] : p(X5) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f20,plain,
( ! [X5] : p(X5)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,plain,
( spl3_2
| spl3_2 ),
inference(avatar_split_clause,[],[f12,f19,f19]) ).
fof(f25,definition,
( spl3_3
<=> q(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f27,plain,
( ~ q(sK2)
| spl3_3 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl3_4
<=> p(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f31,plain,
( ~ p(sK2)
| spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl3_5
<=> q(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f35,plain,
( ~ q(sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl3_6
<=> p(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f39,plain,
( ~ p(sK0)
| spl3_6 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f13,f37,f33,f29,f25]) ).
fof(f41,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f27,f16]) ).
fof(f42,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f43,plain,
( $false
| ~ spl3_2
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f31,f20]) ).
fof(f44,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| ~ spl3_1
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f35,f16]) ).
fof(f46,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( $false
| ~ spl3_2
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f39,f20]) ).
fof(f48,plain,
( ~ spl3_2
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f47]) ).
cnf(s1,plain,
( spl3_1
| spl3_1 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
spl3_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl3_2
| spl3_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f40]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s9,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s11,plain,
( ~ spl3_2
| spl3_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s12,plain,
spl3_6,
inference(rat,[],[s11,s6]) ).
cnf(s13,plain,
spl3_4,
inference(rat,[],[s9,s6]) ).
cnf(s14,plain,
spl3_5,
inference(rat,[],[s10,s2]) ).
cnf(s15,plain,
spl3_3,
inference(rat,[],[s8,s2]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s7,s12,s13,s14,s15]) ).
fof(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN922+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 17:10:40 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.73/0.97 % (2565851)Detected formulas, will run a generic FOF schedule.
% 2.73/0.97 % (2565866)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1993911643:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/0.97 % (2565866)First to succeed.
% 2.73/0.97 % (2565866)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2565851"
% 2.73/0.97 % (2565861)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=3236814829:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/0.97 % (2565859)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=291619683:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/0.97 % (2565867)dis-21_1_sil=8000:lcm=predicate:random_seed=971056411: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)
% 2.73/0.97 % (2565865)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=461255653:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/0.97 % (2565863)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2430036604:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/0.97 % (2565862)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=2496531922:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/0.97 % (2565865)Also succeeded, but the first one will report.
% 2.73/0.97 % (2565867)Also succeeded, but the first one will report.
% 2.73/0.97 % (2565863)Also succeeded, but the first one will report.
% 2.73/0.97 % (2565866)Refutation found. Thanks to Tanya!
% 2.73/0.97 % SZS status Theorem for theBenchmark
% 2.73/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/0.97 % (2565866)------------------------------
% 2.73/0.97 % (2565866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/0.97 % (2565866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.97 % (2565866)CaDiCaL version: 2.1.3
% 2.73/0.97 % (2565866)Termination reason: Refutation
% 2.73/0.97 % (2565866)Time elapsed: 0.002 s
% 2.73/0.97 % (2565866)Peak memory usage: 89 MB
% 2.73/0.97 % (2565866)Instructions burned: 1 (million)
% 2.73/0.97 % (2565866)------------------------------
% 2.73/0.97 % (2565866)------------------------------
% 2.73/0.97 % (2565851)Success in time 0.326 s
% 2.73/0.97 % Vampire exiting
%------------------------------------------------------------------------------