%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 02:22:54 PM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 11 unt; 7 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 174 ( 75 ~; 71 |; 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 : 48 ( 0 sgn 40 !; 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/sandbox2/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
<=> r(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f14,plain,
( ~ r(sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f16,definition,
( spl2_2
<=> r(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f18,plain,
( ~ r(sK1)
| spl2_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl2_3
<=> ! [X2] : ~ q(X2) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f21,plain,
( ! [X2] : ~ q(X2)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f26,definition,
( spl2_5
<=> ! [X2] :
( ~ p(X2)
| ~ q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f27,plain,
( ! [X2] :
( ~ p(X2)
| ~ q(X2) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_5 ),
inference(avatar_split_clause,[],[f10,f26,f16,f12]) ).
fof(f29,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f6,f21]) ).
fof(f30,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f33,definition,
( spl2_6
<=> ! [X3] : r(X3) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f34,plain,
( ! [X3] : r(X3)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( $false
| spl2_1
| ~ spl2_6 ),
inference(resolution,[],[f34,f14]) ).
fof(f37,plain,
( spl2_1
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f36]) ).
fof(f38,plain,
( ! [X2,X3] :
( p(f(X3))
| ~ r(sK0)
| ~ q(X2) )
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f8,f34]) ).
fof(f39,plain,
( ! [X2,X3] :
( p(f(X3))
| ~ q(X2) )
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f38,f34]) ).
fof(f43,definition,
( spl2_7
<=> ! [X3] : p(f(X3)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f44,plain,
( ! [X3] : p(f(X3))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl2_3
| spl2_7
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f39,f33,f43,f20]) ).
fof(f46,plain,
( ! [X0] : ~ q(f(X0))
| ~ spl2_5
| ~ spl2_7 ),
inference(resolution,[],[f44,f27]) ).
fof(f47,plain,
( $false
| ~ spl2_5
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f46,f6]) ).
fof(f48,plain,
( ~ spl2_5
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[],[f47]) ).
fof(f49,plain,
( $false
| spl2_2
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f18,f34]) ).
fof(f50,plain,
( spl2_2
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f51,plain,
( spl2_6
| spl2_5 ),
inference(avatar_split_clause,[],[f9,f26,f33]) ).
fof(f53,definition,
( spl2_8
<=> ! [X3] :
( p(f(X3))
| r(X3) ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f54,plain,
( ! [X3] :
( p(f(X3))
| r(X3) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( spl2_3
| spl2_8 ),
inference(avatar_split_clause,[],[f7,f53,f20]) ).
fof(f56,plain,
( ! [X0] :
( r(X0)
| ~ q(f(X0)) )
| ~ spl2_5
| ~ spl2_8 ),
inference(resolution,[],[f54,f27]) ).
fof(f57,plain,
( ! [X0] : r(X0)
| ~ spl2_5
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f56,f6]) ).
fof(f58,plain,
( spl2_6
| ~ spl2_5
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f57,f53,f26,f33]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f28]) ).
cnf(s14,plain,
~ spl2_3,
inference(sat_conversion,[],[f30]) ).
cnf(s22,plain,
( spl2_1
| ~ spl2_6 ),
inference(sat_conversion,[],[f37]) ).
cnf(s30,plain,
( spl2_3
| ~ spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f45]) ).
cnf(s33,plain,
( ~ spl2_5
| ~ spl2_7 ),
inference(sat_conversion,[],[f48]) ).
cnf(s34,plain,
( spl2_2
| ~ spl2_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s41,plain,
( spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s46,plain,
( spl2_3
| spl2_8 ),
inference(sat_conversion,[],[f55]) ).
cnf(s51,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_8 ),
inference(sat_conversion,[],[f58]) ).
cnf(s52,plain,
spl2_8,
inference(rat,[],[s46,s14]) ).
cnf(s53,plain,
spl2_6,
inference(rat,[],[s41,s51,s52]) ).
cnf(s54,plain,
spl2_2,
inference(rat,[],[s34,s53]) ).
cnf(s55,plain,
spl2_7,
inference(rat,[],[s30,s14,s53]) ).
cnf(s56,plain,
spl2_1,
inference(rat,[],[s22,s53]) ).
cnf(s58,plain,
~ spl2_5,
inference(rat,[],[s33,s55]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s7,s54,s58,s56]) ).
fof(f59,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n007.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 17:12:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.25 % (2570216)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (2570223)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3749312394:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.25 % (2570223) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2570216-2570223"...
% 0.10/0.25 % (2570223)...printing done.
% 0.10/0.25 % (2570223)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (2570223)------------------------------
% 0.10/0.25 % (2570223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2570223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2570223)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2570223)Termination reason: Refutation
% 0.10/0.25 % (2570223)Time elapsed: 0.001 s
% 0.10/0.25 % (2570223)Peak memory usage: 12 MB
% 0.10/0.25 % (2570223)Instructions burned: 1 (million)
% 0.10/0.25 % (2570216)Success in time 0.033 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------