%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:44:57 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 13 unt; 5 def)
% Number of atoms : 191 ( 57 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 198 ( 82 ~; 97 |; 9 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f9,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f2]) ).
fof(f10,plain,
? [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<~> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
( sK2 != unordered_pair(sK3,sK4)
| ~ subset(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
( sK2 != singleton(sK4)
| ~ subset(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( sK2 != singleton(sK3)
| ~ subset(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
( empty_set != sK2
| ~ subset(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
( sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2
| subset(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| unordered_pair(X1,X2) = X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X2,X0,X1] :
( singleton(X2) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X2,X0,X1] :
( singleton(X1) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X2,X0,X1] :
( empty_set != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f26]) ).
fof(f28,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f25]) ).
fof(f29,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f24]) ).
fof(f35,definition,
( spl5_1
<=> subset(sK2,unordered_pair(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f36,plain,
( subset(sK2,unordered_pair(sK3,sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| spl5_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl5_2
<=> sK2 = unordered_pair(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f40,plain,
( sK2 = unordered_pair(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( sK2 != unordered_pair(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f17,f39,f35]) ).
fof(f44,definition,
( spl5_3
<=> sK2 = singleton(sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f45,plain,
( sK2 = singleton(sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( sK2 != singleton(sK4)
| spl5_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f18,f44,f35]) ).
fof(f49,definition,
( spl5_4
<=> sK2 = singleton(sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f50,plain,
( sK2 = singleton(sK3)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( sK2 != singleton(sK3)
| spl5_4 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f19,f49,f35]) ).
fof(f54,definition,
( spl5_5
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f55,plain,
( empty_set = sK2
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( empty_set != sK2
| spl5_5 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f20,f54,f35]) ).
fof(f58,plain,
( spl5_1
| spl5_5
| spl5_4
| spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f21,f39,f44,f49,f54,f35]) ).
fof(f59,plain,
( ~ subset(sK2,sK2)
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f37,f40]) ).
fof(f60,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f59,f13]) ).
fof(f61,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f63,plain,
( ! [X0] : subset(sK2,unordered_pair(X0,sK4))
| ~ spl5_3 ),
inference(superposition,[],[f29,f45]) ).
fof(f79,plain,
( $false
| spl5_1
| ~ spl5_3 ),
inference(backward_subsumption_resolution,[],[f37,f63]) ).
fof(f83,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f84,plain,
( ! [X0,X1] : subset(sK2,unordered_pair(X0,X1))
| ~ spl5_5 ),
inference(superposition,[],[f27,f55]) ).
fof(f86,plain,
( $false
| spl5_1
| ~ spl5_5 ),
inference(backward_subsumption_resolution,[],[f37,f84]) ).
fof(f90,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f92,plain,
( ! [X0] : subset(sK2,unordered_pair(sK3,X0))
| ~ spl5_4 ),
inference(superposition,[],[f28,f50]) ).
fof(f96,plain,
( $false
| spl5_1
| ~ spl5_4 ),
inference(backward_subsumption_resolution,[],[f37,f92]) ).
fof(f100,plain,
( spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f101,plain,
( sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2
| sK2 = unordered_pair(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f36,f22]) ).
fof(f102,plain,
( sK2 = singleton(sK3)
| empty_set = sK2
| sK2 = unordered_pair(sK3,sK4)
| ~ spl5_1
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f101,f46]) ).
fof(f103,plain,
( empty_set = sK2
| sK2 = unordered_pair(sK3,sK4)
| ~ spl5_1
| spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f102,f51]) ).
fof(f104,plain,
( sK2 = unordered_pair(sK3,sK4)
| ~ spl5_1
| spl5_3
| spl5_4
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f103,f56]) ).
fof(f105,plain,
( $false
| ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f104,f41]) ).
fof(f106,plain,
( ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
( spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f58]) ).
cnf(s6,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f83]) ).
cnf(s8,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f90]) ).
cnf(s9,plain,
( spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f100]) ).
cnf(s10,plain,
( ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s11,plain,
spl5_1,
inference(rat,[],[s5,s6,s7,s8,s9]) ).
cnf(s12,plain,
~ spl5_5,
inference(rat,[],[s4,s11]) ).
cnf(s13,plain,
~ spl5_4,
inference(rat,[],[s3,s11]) ).
cnf(s14,plain,
~ spl5_3,
inference(rat,[],[s2,s11]) ).
cnf(s15,plain,
~ spl5_2,
inference(rat,[],[s1,s11]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s12,s13,s14,s11,s15]) ).
fof(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:07:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43 % (769158)Will run a generic schedule for satisfiability detection.
% 0.14/0.43 % (769164)% WARNING: option uhcvi not known.
% 0.14/0.43 % (769164)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=539141068:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.43 % (769164) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-769158-769164"...
% 0.14/0.43 % (769164)...printing done.
% 0.14/0.43 % (769164)Refutation found. Thanks to Tanya!
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.43 % (769164)------------------------------
% 0.14/0.43 % (769164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.43 % (769164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.43 % (769164)CaDiCaL version: 2.1.3
% 0.14/0.43 % (769164)Termination reason: Refutation
% 0.14/0.43 % (769164)Time elapsed: 0.003 s
% 0.14/0.43 % (769164)Peak memory usage: 12 MB
% 0.14/0.43 % (769164)Instructions burned: 4 (million)
% 0.14/0.43 % (769158)Success in time 0.032 s
% 0.14/0.43 % Vampire exiting
%------------------------------------------------------------------------------