%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN939+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 : 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 02:06:01 PM UTC 2026
% Result : Theorem 0.20s 0.90s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 11 unt; 7 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 171 ( 73 ~; 70 |; 15 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ! [X2] : q(f(X2))
=> ? [X3,X4] :
( ( p(f(X4))
=> p(X3) )
& ( r(X4)
=> ( r(X1)
& r(X0) ) )
& q(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] : q(f(X2))
=> ? [X3,X4] :
( ( p(f(X4))
=> p(X3) )
& ( r(X4)
=> ( r(X1)
& r(X0) ) )
& q(X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
( ! [X3,X4] :
( ( ~ p(X3)
& p(f(X4)) )
| ( ( ~ r(X1)
| ~ r(X0) )
& r(X4) )
| ~ q(X3) )
& ! [X2] : q(f(X2)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( ! [X2,X3] :
( ( ~ p(X2)
& p(f(X3)) )
| ( ( ~ r(X1)
| ~ r(X0) )
& r(X3) )
| ~ q(X2) )
& ! [X4] : q(f(X4)) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
( ! [X2,X3] :
( ( ~ p(X2)
& p(f(X3)) )
| ( ( ~ r(sK1)
| ~ r(sK0) )
& r(X3) )
| ~ q(X2) )
& ! [X4] : q(f(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f4]) ).
fof(f6,plain,
! [X4] : q(f(X4)),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( p(f(X3))
| r(X3)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
! [X2,X3] :
( p(f(X3))
| ~ r(sK1)
| ~ r(sK0)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2,X3] :
( ~ p(X2)
| r(X3)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X2] :
( ~ p(X2)
| ~ r(sK1)
| ~ r(sK0)
| ~ q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f12,definition,
( spl2_1
<=> ! [X2] : ~ q(X2) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f13,plain,
( ! [X2] : ~ q(X2)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,definition,
( spl2_2
<=> ! [X3] :
( p(f(X3))
| r(X3) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f16,plain,
( ! [X3] :
( p(f(X3))
| r(X3) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f7,f15,f12]) ).
fof(f19,definition,
( spl2_3
<=> r(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f21,plain,
( ~ r(sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl2_4
<=> r(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f25,plain,
( ~ r(sK1)
| spl2_4 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl2_5
<=> ! [X3] : p(f(X3)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f28,plain,
( ! [X3] : p(f(X3))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f8,f27,f23,f19,f12]) ).
fof(f31,definition,
( spl2_6
<=> ! [X3] : r(X3) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f32,plain,
( ! [X3] : r(X3)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,definition,
( spl2_7
<=> ! [X2] :
( ~ p(X2)
| ~ q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f35,plain,
( ! [X2] :
( ~ p(X2)
| ~ q(X2) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( spl2_6
| spl2_7 ),
inference(avatar_split_clause,[],[f9,f34,f31]) ).
fof(f37,plain,
( ~ spl2_3
| ~ spl2_4
| spl2_7 ),
inference(avatar_split_clause,[],[f10,f34,f23,f19]) ).
fof(f38,plain,
( $false
| spl2_3
| ~ spl2_6 ),
inference(resolution,[],[f32,f21]) ).
fof(f39,plain,
( spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f40,plain,
( ! [X0] :
( r(X0)
| ~ q(f(X0)) )
| ~ spl2_2
| ~ spl2_7 ),
inference(resolution,[],[f16,f35]) ).
fof(f41,plain,
( ! [X0] : r(X0)
| ~ spl2_2
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f40,f6]) ).
fof(f42,plain,
( spl2_6
| ~ spl2_2
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f41,f34,f15,f31]) ).
fof(f43,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f13,f6]) ).
fof(f44,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| spl2_4
| ~ spl2_6 ),
inference(resolution,[],[f32,f25]) ).
fof(f46,plain,
( spl2_4
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( ! [X0] : ~ q(f(X0))
| ~ spl2_5
| ~ spl2_7 ),
inference(resolution,[],[f28,f35]) ).
fof(f48,plain,
( $false
| ~ spl2_5
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f47,f6]) ).
fof(f49,plain,
( ~ spl2_5
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[],[f48]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
( spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
( ~ spl2_3
| ~ spl2_4
| spl2_7 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
( spl2_3
| ~ spl2_6 ),
inference(sat_conversion,[],[f39]) ).
cnf(s6,plain,
( ~ spl2_2
| spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
~ spl2_1,
inference(sat_conversion,[],[f44]) ).
cnf(s9,plain,
( spl2_4
| ~ spl2_6 ),
inference(sat_conversion,[],[f46]) ).
cnf(s10,plain,
( ~ spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f49]) ).
cnf(s11,plain,
( ~ spl2_3
| ~ spl2_4
| spl2_5 ),
inference(rat,[],[s2,s7]) ).
cnf(s12,plain,
spl2_2,
inference(rat,[],[s1,s7]) ).
cnf(s13,plain,
spl2_6,
inference(rat,[],[s3,s6,s12]) ).
cnf(s14,plain,
spl2_4,
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
spl2_3,
inference(rat,[],[s5,s13]) ).
cnf(s16,plain,
spl2_7,
inference(rat,[],[s4,s14,s15]) ).
cnf(s17,plain,
spl2_5,
inference(rat,[],[s11,s14,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s16,s17]) ).
fof(f50,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 17:16:57 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.20/0.90 % (4026902)Detected formulas, will run a generic FOF schedule.
% 0.20/0.90 % (4026912)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=807709741:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/0.90 % (4026910)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=735605651:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/0.90 % (4026908)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=3703274857:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/0.90 % (4026909)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=2262824115:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/0.90 % (4026907)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=633076411:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/0.90 % (4026912)First to succeed.
% 0.20/0.90 % (4026912)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4026902"
% 0.20/0.90 % (4026910)Also succeeded, but the first one will report.
% 0.20/0.90 % (4026911)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1019257480:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/0.90 % (4026911)Also succeeded, but the first one will report.
% 0.20/0.90 % (4026913)dis-21_1_sil=8000:lcm=predicate:random_seed=1399541932: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)
% 0.20/0.90 % (4026913)Also succeeded, but the first one will report.
% 0.20/0.90 % (4026912)Refutation found. Thanks to Tanya!
% 0.20/0.90 % SZS status Theorem for theBenchmark
% 0.20/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.91 % (4026912)------------------------------
% 0.20/0.91 % (4026912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/0.91 % (4026912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.91 % (4026912)CaDiCaL version: 2.1.3
% 0.20/0.91 % (4026912)Termination reason: Refutation
% 0.20/0.91 % (4026912)Time elapsed: 0.001 s
% 0.20/0.91 % (4026912)Peak memory usage: 89 MB
% 0.20/0.91 % (4026912)Instructions burned: 1 (million)
% 0.20/0.91 % (4026912)------------------------------
% 0.20/0.91 % (4026912)------------------------------
% 0.20/0.91 % (4026902)Success in time 0.297 s
% 0.20/0.91 % Vampire exiting
%------------------------------------------------------------------------------