%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN920+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 : n008.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 02:22:52 PM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 5 unt; 7 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 290 ( 108 ~; 112 |; 42 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 36 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ! [X0] :
( ( f(X0)
& g(X0) )
=> h(X0) )
=> ? [X0] :
( f(X0)
& ~ g(X0) ) )
& ( ! [X1] :
( f(X1)
=> g(X1) )
| ! [X2] :
( f(X2)
=> h(X2) ) ) )
=> ( ! [X3] :
( ( f(X3)
& h(X3) )
=> g(X3) )
=> ? [X4] :
( f(X4)
& g(X4)
& ~ h(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ( ( ! [X0] :
( ( f(X0)
& g(X0) )
=> h(X0) )
=> ? [X0] :
( f(X0)
& ~ g(X0) ) )
& ( ! [X1] :
( f(X1)
=> g(X1) )
| ! [X2] :
( f(X2)
=> h(X2) ) ) )
=> ( ! [X3] :
( ( f(X3)
& h(X3) )
=> g(X3) )
=> ? [X4] :
( f(X4)
& g(X4)
& ~ h(X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ( ! [X0] :
( ( f(X0)
& g(X0) )
=> h(X0) )
=> ? [X1] :
( f(X1)
& ~ g(X1) ) )
& ( ! [X2] :
( f(X2)
=> g(X2) )
| ! [X3] :
( f(X3)
=> h(X3) ) ) )
=> ( ! [X4] :
( ( f(X4)
& h(X4) )
=> g(X4) )
=> ? [X5] :
( f(X5)
& g(X5)
& ~ h(X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X5] :
( ~ f(X5)
| ~ g(X5)
| h(X5) )
& ! [X4] :
( g(X4)
| ~ f(X4)
| ~ h(X4) )
& ( ? [X1] :
( f(X1)
& ~ g(X1) )
| ? [X0] :
( ~ h(X0)
& f(X0)
& g(X0) ) )
& ( ! [X2] :
( g(X2)
| ~ f(X2) )
| ! [X3] :
( h(X3)
| ~ f(X3) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X5] :
( ~ f(X5)
| ~ g(X5)
| h(X5) )
& ! [X4] :
( g(X4)
| ~ f(X4)
| ~ h(X4) )
& ( ? [X1] :
( f(X1)
& ~ g(X1) )
| ? [X0] :
( ~ h(X0)
& f(X0)
& g(X0) ) )
& ( ! [X2] :
( g(X2)
| ~ f(X2) )
| ! [X3] :
( h(X3)
| ~ f(X3) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0)
| h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) )
& ( ? [X2] :
( f(X2)
& ~ g(X2) )
| ? [X3] :
( ~ h(X3)
& f(X3)
& g(X3) ) )
& ( ! [X4] :
( g(X4)
| ~ f(X4) )
| ! [X5] :
( h(X5)
| ~ f(X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0)
| h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) )
& ( ( f(sK0)
& ~ g(sK0) )
| ( ~ h(sK1)
& f(sK1)
& g(sK1) ) )
& ( ! [X4] :
( g(X4)
| ~ f(X4) )
| ! [X5] :
( h(X5)
| ~ f(X5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f6]) ).
fof(f8,plain,
! [X4,X5] :
( g(X4)
| ~ f(X4)
| h(X5)
| ~ f(X5) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
( ~ g(sK0)
| g(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
( ~ g(sK0)
| f(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( ~ g(sK0)
| ~ h(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
( f(sK0)
| g(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
( f(sK0)
| f(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
( f(sK0)
| ~ h(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X1] :
( ~ h(X1)
| ~ f(X1)
| g(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X0] :
( ~ g(X0)
| ~ f(X0)
| h(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,definition,
( spl2_1
<=> h(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f19,plain,
( h(sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f20,plain,
( ~ h(sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f22,definition,
( spl2_2
<=> g(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f24,plain,
( ~ g(sK0)
| spl2_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f11,f22,f18]) ).
fof(f27,definition,
( spl2_3
<=> g(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f29,plain,
( g(sK1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f9,f22,f27]) ).
fof(f32,definition,
( spl2_4
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f33,plain,
( ~ f(sK0)
| spl2_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( f(sK0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f12,f32,f27]) ).
fof(f37,definition,
( spl2_5
<=> f(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f38,plain,
( ~ f(sK1)
| spl2_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
( spl2_5
| spl2_4 ),
inference(avatar_split_clause,[],[f13,f32,f37]) ).
fof(f70,plain,
( ~ f(sK1)
| h(sK1)
| ~ spl2_3 ),
inference(resolution,[],[f16,f29]) ).
fof(f71,plain,
( ~ f(sK1)
| spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f70,f20]) ).
fof(f72,plain,
( ~ spl2_5
| spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f71,f27,f18,f37]) ).
fof(f79,plain,
( ~ g(sK0)
| spl2_5 ),
inference(forward_subsumption_resolution,[],[f10,f38]) ).
fof(f80,plain,
( ~ spl2_2
| spl2_5 ),
inference(avatar_split_clause,[],[f79,f37,f22]) ).
fof(f82,definition,
( spl2_11
<=> ! [X5] :
( h(X5)
| ~ f(X5) ) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f83,plain,
( ! [X5] :
( ~ f(X5)
| h(X5) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl2_12
<=> ! [X4] :
( g(X4)
| ~ f(X4) ) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f86,plain,
( ! [X4] :
( ~ f(X4)
| g(X4) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f8,f85,f82]) ).
fof(f88,plain,
( h(sK0)
| ~ spl2_4
| ~ spl2_11 ),
inference(resolution,[],[f83,f34]) ).
fof(f89,plain,
( ~ f(sK0)
| g(sK0)
| ~ spl2_4
| ~ spl2_11 ),
inference(resolution,[],[f88,f15]) ).
fof(f90,plain,
( g(sK0)
| ~ spl2_4
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f89,f34]) ).
fof(f91,plain,
( $false
| spl2_2
| ~ spl2_4
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f90,f24]) ).
fof(f92,plain,
( spl2_2
| ~ spl2_4
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f93,plain,
( g(sK0)
| ~ spl2_4
| ~ spl2_12 ),
inference(resolution,[],[f86,f34]) ).
fof(f94,plain,
( $false
| spl2_2
| ~ spl2_4
| ~ spl2_12 ),
inference(forward_subsumption_resolution,[],[f93,f24]) ).
fof(f95,plain,
( spl2_2
| ~ spl2_4
| ~ spl2_12 ),
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f97,plain,
( ~ h(sK1)
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f14,f33]) ).
fof(f98,plain,
( $false
| ~ spl2_1
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f97,f19]) ).
fof(f99,plain,
( ~ spl2_1
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f98]) ).
cnf(s11,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s15,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f30]) ).
cnf(s19,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f35]) ).
cnf(s23,plain,
( spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f40]) ).
cnf(s63,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s77,plain,
( ~ spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s81,plain,
( spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f87]) ).
cnf(s86,plain,
( spl2_2
| ~ spl2_4
| ~ spl2_11 ),
inference(sat_conversion,[],[f92]) ).
cnf(s89,plain,
( spl2_2
| ~ spl2_4
| ~ spl2_12 ),
inference(sat_conversion,[],[f95]) ).
cnf(s99,plain,
( ~ spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f99]) ).
cnf(s100,plain,
( ~ spl2_4
| spl2_2 ),
inference(rat,[],[s81,s89,s86]) ).
cnf(s101,plain,
( spl2_4
| spl2_1 ),
inference(rat,[],[s63,s19,s23]) ).
cnf(s102,plain,
spl2_1,
inference(rat,[],[s63,s15,s77,s100,s101]) ).
cnf(s103,plain,
spl2_4,
inference(rat,[],[s99,s102]) ).
cnf(s104,plain,
~ spl2_2,
inference(rat,[],[s11,s102]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s100,s104,s103]) ).
fof(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN920+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n008.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 17:13:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.08/0.26 % (2401923)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (2401930)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3384956820:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (2401930) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2401923-2401930"...
% 0.08/0.26 % (2401930)...printing done.
% 0.08/0.26 % (2401929)% WARNING: option uhcvi not known.
% 0.08/0.26 % (2401930)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (2401930)------------------------------
% 0.08/0.26 % (2401930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2401930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2401930)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2401930)Termination reason: Refutation
% 0.08/0.26 % (2401930)Time elapsed: 0.002 s
% 0.08/0.26 % (2401930)Peak memory usage: 12 MB
% 0.08/0.26 % (2401930)Instructions burned: 3 (million)
% 0.08/0.26 % (2401923)Success in time 0.031 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------