%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN403+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:50:31 PM UTC 2026
% Result : Theorem 3.44s 1.24s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 3 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 19 ~; 12 |; 11 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 4 ( 0 sgn 2 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ( f(X0)
=> g(X0) )
& ( g(X0)
=> h(X0) ) )
=> ( f(X0)
=> h(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish234) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ( f(X0)
=> g(X0) )
& ( g(X0)
=> h(X0) ) )
=> ( f(X0)
=> h(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
( ~ h(X0)
& f(X0)
& ( g(X0)
| ~ f(X0) )
& ( h(X0)
| ~ g(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ~ h(X0)
& f(X0)
& ( g(X0)
| ~ f(X0) )
& ( h(X0)
| ~ g(X0) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ~ h(sK0)
& f(sK0)
& ( g(sK0)
| ~ f(sK0) )
& ( h(sK0)
| ~ g(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f4]) ).
fof(f6,plain,
( h(sK0)
| ~ g(sK0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
( g(sK0)
| ~ f(sK0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
f(sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
~ h(sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f11,definition,
( spl1_1
<=> g(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f15,definition,
( spl1_2
<=> h(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f18,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f6,f15,f11]) ).
fof(f20,definition,
( spl1_3
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f23,plain,
( ~ spl1_3
| spl1_1 ),
inference(avatar_split_clause,[],[f7,f11,f20]) ).
fof(f24,plain,
spl1_3,
inference(avatar_split_clause,[],[f8,f20]) ).
fof(f25,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f9,f15]) ).
cnf(s1,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
spl1_3,
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
~ spl1_2,
inference(sat_conversion,[],[f25]) ).
cnf(s5,plain,
spl1_1,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
fof(f26,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN403+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 15:55:20 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.44/1.24 % (269155)Detected formulas, will run a generic FOF schedule.
% 3.44/1.24 % (269162)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=3250688042:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.24 % (269163)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=206515412:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.24 % (269163)First to succeed.
% 3.44/1.24 % (269163)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-269155"
% 3.44/1.24 % (269160)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=3362509422:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.24 % (269161)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=2186487633:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.24 % (269164)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2148720139:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.24 % (269166)dis-21_1_sil=8000:lcm=predicate:random_seed=4095846925: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)
% 3.44/1.24 % (269165)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1222324403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.24 % (269164)Also succeeded, but the first one will report.
% 3.44/1.24 % (269165)Also succeeded, but the first one will report.
% 3.44/1.24 % (269166)Also succeeded, but the first one will report.
% 3.44/1.24 [W928 15:55:20.439749134 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 [W928 15:55:20.439786825 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 [W928 15:55:20.439806548 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 [W928 15:55:20.439812983 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 [W928 15:55:20.439826696 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 [W928 15:55:20.439832503 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.44/1.24 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.44/1.24 % (269163)Refutation found. Thanks to Tanya!
% 3.44/1.24 % SZS status Theorem for theBenchmark
% 3.44/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.24 % (269163)------------------------------
% 3.44/1.24 % (269163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.24 % (269163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.24 % (269163)CaDiCaL version: 2.1.3
% 3.44/1.24 % (269163)Termination reason: Refutation
% 3.44/1.24 % (269163)Time elapsed: 0.002 s
% 3.44/1.24 % (269163)Peak memory usage: 89 MB
% 3.44/1.24 % (269163)------------------------------
% 3.44/1.24 % (269163)------------------------------
% 3.44/1.24 % (269155)Success in time 0.4 s
% 3.44/1.24 % Vampire exiting
%------------------------------------------------------------------------------