%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN941+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 : n006.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 02:06:02 PM UTC 2026
% Result : Theorem 2.84s 1.18s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 10 unt; 6 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 51 ~; 43 |; 12 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 22 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( q(f(X0))
=> ? [X2,X3] :
( ( p(f(X3))
=> ( p(X2)
& ( r(X3)
=> ( r(X0)
& r(X1) ) ) ) )
& q(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( q(f(X0))
=> ? [X2,X3] :
( ( p(f(X3))
=> ( p(X2)
& ( r(X3)
=> ( r(X0)
& r(X1) ) ) ) )
& q(X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
( ! [X2,X3] :
( ( ( ~ p(X2)
| ( ( ~ r(X0)
| ~ r(X1) )
& r(X3) ) )
& p(f(X3)) )
| ~ q(X2) )
& q(f(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X2,X3] :
( ( ( ~ p(X2)
| ( ( ~ r(sK0)
| ~ r(sK1) )
& r(X3) ) )
& p(f(X3)) )
| ~ q(X2) )
& q(f(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f5,plain,
q(f(sK0)),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X3] :
( p(f(X3))
| ~ q(X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X2,X3] :
( ~ p(X2)
| r(X3)
| ~ q(X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
! [X2] :
( ~ p(X2)
| ~ r(sK0)
| ~ r(sK1)
| ~ q(X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,definition,
( spl2_1
<=> ! [X2] : ~ q(X2) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f11,plain,
( ! [X2] : ~ q(X2)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,definition,
( spl2_2
<=> ! [X3] : p(f(X3)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f14,plain,
( ! [X3] : p(f(X3))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f15,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f6,f13,f10]) ).
fof(f17,definition,
( spl2_3
<=> ! [X3] : r(X3) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f18,plain,
( ! [X3] : r(X3)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,definition,
( spl2_4
<=> ! [X2] :
( ~ p(X2)
| ~ q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f21,plain,
( ! [X2] :
( ~ p(X2)
| ~ q(X2) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f7,f20,f17]) ).
fof(f24,definition,
( spl2_5
<=> r(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f26,plain,
( ~ r(sK1)
| spl2_5 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl2_6
<=> r(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f30,plain,
( ~ r(sK0)
| spl2_6 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( ~ spl2_5
| ~ spl2_6
| spl2_4 ),
inference(avatar_split_clause,[],[f8,f20,f28,f24]) ).
fof(f32,plain,
( $false
| ~ spl2_3
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f30,f18]) ).
fof(f33,plain,
( ~ spl2_3
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f32]) ).
fof(f34,plain,
( $false
| ~ spl2_3
| spl2_5 ),
inference(forward_subsumption_resolution,[],[f26,f18]) ).
fof(f35,plain,
( ~ spl2_3
| spl2_5 ),
inference(avatar_contradiction_clause,[],[f34]) ).
fof(f36,plain,
( ! [X0] : ~ q(f(X0))
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f21,f14]) ).
fof(f37,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f36,f5]) ).
fof(f38,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f37]) ).
fof(f39,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f11,f5]) ).
fof(f40,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f39]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f15]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f31]) ).
cnf(s4,plain,
( ~ spl2_3
| spl2_6 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
( ~ spl2_3
| spl2_5 ),
inference(sat_conversion,[],[f35]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s7,plain,
~ spl2_1,
inference(sat_conversion,[],[f40]) ).
cnf(s8,plain,
spl2_2,
inference(rat,[],[s1,s7]) ).
cnf(s9,plain,
~ spl2_4,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
spl2_3,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
spl2_5,
inference(rat,[],[s5,s10]) ).
cnf(s12,plain,
spl2_6,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s3,s9,s12,s11]) ).
fof(f41,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 17:14:10 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.84/1.18 % (4120485)Detected formulas, will run a generic FOF schedule.
% 2.84/1.18 % (4120495)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2910729646:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.18 % (4120495)First to succeed.
% 2.84/1.18 % (4120495)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4120485"
% 2.84/1.18 % (4120493)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1539659269:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.18 % (4120490)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=3721512464:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.18 % (4120492)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=3946991039:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.18 % (4120494)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=963183364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.18 % (4120491)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=2890506442:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.18 % (4120496)dis-21_1_sil=8000:lcm=predicate:random_seed=4038666629: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)
% 2.84/1.18 % (4120494)Also succeeded, but the first one will report.
% 2.84/1.18 % (4120496)Also succeeded, but the first one will report.
% 2.84/1.18 % (4120493)Also succeeded, but the first one will report.
% 2.84/1.18 % (4120495)Refutation found. Thanks to Tanya!
% 2.84/1.18 % SZS status Theorem for theBenchmark
% 2.84/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/1.18 % (4120495)------------------------------
% 2.84/1.18 % (4120495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.18 % (4120495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.18 % (4120495)CaDiCaL version: 2.1.3
% 2.84/1.18 % (4120495)Termination reason: Refutation
% 2.84/1.18 % (4120495)Time elapsed: 0.002 s
% 2.84/1.18 % (4120495)Peak memory usage: 89 MB
% 2.84/1.18 % (4120495)Instructions burned: 1 (million)
% 2.84/1.18 % (4120495)------------------------------
% 2.84/1.18 % (4120495)------------------------------
% 2.84/1.18 % (4120485)Success in time 0.31 s
% 2.84/1.18 % Vampire exiting
%------------------------------------------------------------------------------