%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:53:20 PM UTC 2026
% Result : Theorem 0.24s 0.53s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 10 unt; 2 def)
% Number of atoms : 49 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 15 ~; 12 |; 5 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_2) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( k1_funct_5(X2) != k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
| k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) != k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) )
& m2_relset_1(X2,X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) )
| ~ m2_relset_1(X2,X1,X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f78,plain,
( k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))
| k1_funct_5(sK2) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
m2_relset_1(sK2,sK1,sK0),
inference(cnf_transformation,[],[f51]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X1,X0)
| k10_relset_1(X1,X0,X2,X1) = k2_funct_5(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X1,X0)
| k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
~ m2_relset_1(sK2,sK1,sK0),
inference(consistent_polarity_flipping,[],[f79]) ).
fof(f156,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X1,X0)
| k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f157,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X1,X0)
| k10_relset_1(X1,X0,X2,X1) = k2_funct_5(X2) ),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f159,definition,
( spl11_1
<=> k1_funct_5(sK2) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f163,definition,
( spl11_2
<=> k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f165,plain,
( k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))
| spl11_2 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f78,f163,f159]) ).
fof(f291,plain,
k10_relset_1(sK1,sK0,sK2,sK1) = k2_funct_5(sK2),
inference(resolution,[],[f157,f125]) ).
fof(f299,plain,
k1_funct_5(sK2) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0),
inference(resolution,[],[f156,f125]) ).
fof(f303,plain,
spl11_1,
inference(avatar_split_clause,[],[f299,f159]) ).
fof(f324,plain,
( k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))
| spl11_2 ),
inference(forward_demodulation,[],[f165,f291]) ).
fof(f325,plain,
( $false
| spl11_2 ),
inference(trivial_inequality_removal,[],[f324]) ).
fof(f326,plain,
spl11_2,
inference(avatar_contradiction_clause,[],[f325]) ).
cnf(s1,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s11,plain,
spl11_1,
inference(sat_conversion,[],[f303]) ).
cnf(s14,plain,
spl11_2,
inference(sat_conversion,[],[f326]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s14,s11]) ).
fof(f327,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 28 05:34:27 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.49 Running first-order model finding
% 0.24/0.49 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
% 0.24/0.53 % (1255669)Will run a generic schedule for satisfiability detection.
% 0.24/0.53 % (1255675)% WARNING: option uhcvi not known.
% 0.24/0.53 % (1255675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3325829619:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.53 % (1255674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3743901_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.53 % (1255675) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1255669-1255675"...
% 0.24/0.53 % TRYING [1]
% 0.24/0.53 % TRYING [2]
% 0.24/0.53 % (1255675)...printing done.
% 0.24/0.53 % TRYING [3]
% 0.24/0.53 % (1255675)Refutation found. Thanks to Tanya!
% 0.24/0.53 % SZS status Theorem for theBenchmark
% 0.24/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.53 % (1255675)------------------------------
% 0.24/0.53 % (1255675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.53 % (1255675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.53 % (1255675)CaDiCaL version: 2.1.3
% 0.24/0.53 % (1255675)Termination reason: Refutation
% 0.24/0.53 % (1255675)Time elapsed: 0.006 s
% 0.24/0.53 % (1255675)Peak memory usage: 13 MB
% 0.24/0.53 % (1255675)Instructions burned: 7 (million)
% 0.24/0.53 % (1255669)Success in time 0.029 s
% 0.24/0.53 % Vampire exiting
%------------------------------------------------------------------------------