%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN918+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 : n016.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 02:22:51 PM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 5 unt; 7 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 278 ( 112 ~; 109 |; 36 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 66 ( 0 sgn 59 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [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) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ( ! [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(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X5] :
( ~ f(X5)
| ~ g(X5)
| h(X5) )
& ! [X4] :
( g(X4)
| ~ f(X4)
| ~ h(X4) )
& ! [X0] :
( ? [X1] :
( f(X1)
& ~ g(X1) )
| ( ~ h(X0)
& f(X0)
& g(X0) ) )
& ( ! [X2] :
( g(X2)
| ~ f(X2) )
| ! [X3] :
( h(X3)
| ~ f(X3) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X5] :
( ~ f(X5)
| ~ g(X5)
| h(X5) )
& ! [X4] :
( g(X4)
| ~ f(X4)
| ~ h(X4) )
& ! [X0] :
( ? [X1] :
( f(X1)
& ~ g(X1) )
| ( ~ h(X0)
& f(X0)
& g(X0) ) )
& ( ! [X2] :
( g(X2)
| ~ f(X2) )
| ! [X3] :
( h(X3)
| ~ f(X3) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0)
| h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) )
& ! [X2] :
( ? [X3] :
( f(X3)
& ~ g(X3) )
| ( ~ h(X2)
& f(X2)
& g(X2) ) )
& ( ! [X4] :
( g(X4)
| ~ f(X4) )
| ! [X5] :
( h(X5)
| ~ f(X5) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0)
| h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) )
& ! [X2] :
( ( f(sK0)
& ~ g(sK0) )
| ( ~ h(X2)
& f(X2)
& g(X2) ) )
& ( ! [X4] :
( g(X4)
| ~ f(X4) )
| ! [X5] :
( h(X5)
| ~ f(X5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0)],[f5]) ).
fof(f7,plain,
! [X4,X5] :
( g(X4)
| ~ f(X4)
| h(X5)
| ~ f(X5) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X2] :
( ~ g(sK0)
| g(X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2] :
( ~ g(sK0)
| f(X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2] :
( ~ g(sK0)
| ~ h(X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X2] :
( f(sK0)
| g(X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X2] :
( f(sK0)
| f(X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f15,plain,
! [X0] :
( ~ f(X0)
| ~ g(X0)
| h(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ h(X0)
| g(X0)
| ~ f(X0) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f17,plain,
! [X1] :
( h(X1)
| ~ f(X1)
| ~ g(X1) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f19,plain,
! [X2] :
( f(sK0)
| ~ g(X2) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f20,plain,
! [X2] :
( g(sK0)
| h(X2) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f21,plain,
! [X2] :
( g(sK0)
| f(X2) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f22,plain,
! [X2] :
( g(sK0)
| ~ g(X2) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f23,plain,
! [X4,X5] :
( ~ g(X4)
| ~ f(X4)
| ~ h(X5)
| ~ f(X5) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f25,definition,
( spl1_1
<=> ! [X5] :
( ~ h(X5)
| ~ f(X5) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f26,plain,
( ! [X5] :
( ~ h(X5)
| ~ f(X5) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,definition,
( spl1_2
<=> ! [X4] :
( ~ g(X4)
| ~ f(X4) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f29,plain,
( ! [X4] :
( ~ g(X4)
| ~ f(X4) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f23,f28,f25]) ).
fof(f32,definition,
( spl1_3
<=> ! [X2] : ~ g(X2) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f33,plain,
( ! [X2] : ~ g(X2)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,definition,
( spl1_4
<=> g(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f37,plain,
( g(sK0)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f22,f35,f32]) ).
fof(f40,definition,
( spl1_5
<=> ! [X2] : f(X2) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f41,plain,
( ! [X2] : f(X2)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl1_5
| spl1_4 ),
inference(avatar_split_clause,[],[f21,f35,f40]) ).
fof(f44,definition,
( spl1_6
<=> ! [X2] : h(X2) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f45,plain,
( ! [X2] : h(X2)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( spl1_6
| spl1_4 ),
inference(avatar_split_clause,[],[f20,f35,f44]) ).
fof(f48,definition,
( spl1_7
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f49,plain,
( ~ f(sK0)
| spl1_7 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl1_3
| spl1_7 ),
inference(avatar_split_clause,[],[f19,f48,f32]) ).
fof(f52,plain,
( spl1_5
| spl1_7 ),
inference(avatar_split_clause,[],[f12,f48,f40]) ).
fof(f54,plain,
( $false
| ~ spl1_5
| spl1_7 ),
inference(resolution,[],[f49,f41]) ).
fof(f55,plain,
( ~ spl1_5
| spl1_7 ),
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f56,plain,
( ! [X0] :
( g(X0)
| ~ f(X0) )
| ~ spl1_6 ),
inference(resolution,[],[f16,f45]) ).
fof(f57,plain,
( ! [X0] : ~ f(X0)
| ~ spl1_3
| ~ spl1_6 ),
inference(resolution,[],[f56,f33]) ).
fof(f58,plain,
( $false
| ~ spl1_3
| ~ spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f57,f41]) ).
fof(f59,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( ~ f(sK0)
| ~ spl1_2
| ~ spl1_4 ),
inference(resolution,[],[f29,f37]) ).
fof(f61,plain,
( ~ spl1_7
| ~ spl1_2
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f60,f35,f28,f48]) ).
fof(f66,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0)
| ~ f(X0) )
| ~ spl1_1 ),
inference(resolution,[],[f17,f26]) ).
fof(f67,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0) )
| ~ spl1_1 ),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f69,plain,
( spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f67,f25,f28]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s4,plain,
( spl1_4
| spl1_6 ),
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
( spl1_3
| spl1_7 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( spl1_5
| spl1_7 ),
inference(sat_conversion,[],[f52]) ).
cnf(s8,plain,
( ~ spl1_5
| spl1_7 ),
inference(sat_conversion,[],[f55]) ).
cnf(s9,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f59]) ).
cnf(s10,plain,
( ~ spl1_2
| ~ spl1_4
| ~ spl1_7 ),
inference(sat_conversion,[],[f61]) ).
cnf(s12,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s13,plain,
( spl1_3
| ~ spl1_2 ),
inference(rat,[],[s10,s2,s5]) ).
cnf(s14,plain,
spl1_7,
inference(rat,[],[s6,s8]) ).
cnf(s15,plain,
~ spl1_2,
inference(rat,[],[s9,s3,s4,s10,s13,s14]) ).
cnf(s16,plain,
~ spl1_1,
inference(rat,[],[s12,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s15,s16]) ).
fof(f70,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 17:17:34 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 0.09/0.24 % (3770759)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (3770770)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=586449945:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.24 % (3770765)% WARNING: option uhcvi not known.
% 0.09/0.24 % (3770770) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3770759-3770770"...
% 0.09/0.24 % (3770770)...printing done.
% 0.09/0.24 % (3770770)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (3770770)------------------------------
% 0.09/0.24 % (3770770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (3770770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (3770770)CaDiCaL version: 2.1.3
% 0.09/0.24 % (3770770)Termination reason: Refutation
% 0.09/0.24 % (3770770)Time elapsed: 0.001 s
% 0.09/0.24 % (3770770)Peak memory usage: 12 MB
% 0.09/0.24 % (3770770)Instructions burned: 2 (million)
% 0.09/0.24 % (3770759)Success in time 0.036 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------