%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:51:56 PM UTC 2026
% Result : Theorem 0.25s 0.46s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 18 unt; 2 def)
% Number of atoms : 173 ( 11 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 189 ( 76 ~; 71 |; 27 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 83 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(f33,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f49,axiom,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
fof(f80,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f104,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f105,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ preboolean(X0) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) )
& in(sK10(X0),X0)
& in(sK11(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ preboolean(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0))],[f105]) ).
fof(f107,plain,
( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),sK12)
& in(set_union2(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f83]) ).
fof(f114,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f152,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f155,plain,
! [X0] :
( in(sK11(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f156,plain,
! [X0] :
( in(sK10(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X0] :
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f159,plain,
! [X2,X1] :
( in(set_union2(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f107]) ).
fof(f160,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f107]) ).
fof(f161,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f107]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f175,plain,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f176,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),
inference(definition_unfolding,[],[f175,f117,f117]) ).
fof(f177,plain,
! [X0,X1] : set_difference(X0,X1) = set_union2(set_difference(X0,set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))))),set_difference(set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),X0)),
inference(definition_unfolding,[],[f152,f117,f176]) ).
fof(f184,plain,
! [X2,X1] :
( in(set_union2(set_difference(X1,X2),set_difference(X2,X1)),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(definition_unfolding,[],[f160,f117]) ).
fof(f260,plain,
! [X0,X1] :
( element(set_union2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(resolution,[],[f163,f159]) ).
fof(f261,plain,
! [X0,X1] :
( element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(resolution,[],[f163,f184]) ).
fof(f264,plain,
! [X0] :
( element(sK11(X0),X0)
| preboolean(X0) ),
inference(resolution,[],[f163,f155]) ).
fof(f265,plain,
! [X0] :
( element(sK10(X0),X0)
| preboolean(X0) ),
inference(resolution,[],[f163,f156]) ).
fof(f730,plain,
! [X0,X1] : set_difference(X0,X1) = set_union2(set_difference(X0,set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)))),set_difference(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),X0)),
inference(forward_demodulation,[],[f177,f114]) ).
fof(f754,plain,
! [X0,X1] :
( ~ element(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),sK12)
| in(set_difference(X0,X1),sK12)
| ~ element(X0,sK12) ),
inference(superposition,[],[f184,f730]) ).
fof(f854,plain,
! [X0,X1] :
( ~ element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(X0,sK12)
| in(set_difference(X0,X1),sK12)
| ~ element(set_union2(X0,X1),sK12) ),
inference(resolution,[],[f754,f261]) ).
fof(f1058,plain,
! [X0,X1] :
( ~ element(X0,sK12)
| in(set_difference(X0,X1),sK12)
| ~ element(set_union2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(resolution,[],[f854,f261]) ).
fof(f1072,plain,
! [X0,X1] :
( ~ element(X0,sK12)
| in(set_difference(X0,X1),sK12)
| ~ element(set_union2(X0,X1),sK12)
| ~ element(X1,sK12) ),
inference(duplicate_literal_removal,[],[f1058]) ).
fof(f1076,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f1072,f260]) ).
fof(f1084,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12)
| ~ in(set_union2(sK10(sK12),sK11(sK12)),sK12)
| preboolean(sK12) ),
inference(resolution,[],[f1076,f157]) ).
fof(f1092,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(forward_subsumption_resolution,[],[f1084,f159]) ).
fof(f1093,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12) ),
inference(forward_subsumption_resolution,[],[f1092,f161]) ).
fof(f1095,definition,
( spl13_8
<=> element(sK11(sK12),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f1097,plain,
( ~ element(sK11(sK12),sK12)
| spl13_8 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1099,definition,
( spl13_9
<=> element(sK10(sK12),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f1101,plain,
( ~ element(sK10(sK12),sK12)
| spl13_9 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1102,plain,
( ~ spl13_8
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f1093,f1099,f1095]) ).
fof(f1109,plain,
( preboolean(sK12)
| spl13_8 ),
inference(resolution,[],[f1097,f264]) ).
fof(f1110,plain,
( $false
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f1109,f161]) ).
fof(f1111,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f1110]) ).
fof(f1122,plain,
( preboolean(sK12)
| spl13_9 ),
inference(resolution,[],[f1101,f265]) ).
fof(f1123,plain,
( $false
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f1122,f161]) ).
fof(f1124,plain,
spl13_9,
inference(avatar_contradiction_clause,[],[f1123]) ).
cnf(s21,plain,
( ~ spl13_8
| ~ spl13_9 ),
inference(sat_conversion,[],[f1102]) ).
cnf(s22,plain,
spl13_8,
inference(sat_conversion,[],[f1111]) ).
cnf(s23,plain,
spl13_9,
inference(sat_conversion,[],[f1124]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s21,s23,s22]) ).
fof(f1125,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:38:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.25/0.46 % (2971437)Will run a generic schedule for satisfiability detection.
% 0.25/0.46 % (2971447)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=77060370:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.46 % (2971443)% WARNING: option uhcvi not known.
% 0.25/0.46 % (2971442)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1569192593_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.46 % (2971444)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4248644474:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.46 % (2971445)dis+10_1_sil=32000:sp=arity:random_seed=2477026825:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.46 % (2971446)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2329523636:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.46 % (2971448)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2837984445:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.46 % (2971443)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=187226395:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.46 % TRYING [1]
% 0.25/0.46 % TRYING [2]
% 0.25/0.46 % TRYING [3]
% 0.25/0.46 % (2971445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2971437-2971445"...
% 0.25/0.46 % (2971445)...printing done.
% 0.25/0.46 % (2971445)Refutation found. Thanks to Tanya!
% 0.25/0.46 % SZS status Theorem for theBenchmark
% 0.25/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.47 % (2971445)------------------------------
% 0.25/0.47 % (2971445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.47 % (2971445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.47 % (2971445)CaDiCaL version: 2.1.3
% 0.25/0.47 % (2971445)Termination reason: Refutation
% 0.25/0.47 % (2971445)Time elapsed: 0.021 s
% 0.25/0.47 % (2971445)Peak memory usage: 13 MB
% 0.25/0.47 % (2971445)Instructions burned: 31 (million)
% 0.25/0.47 % (2971437)Success in time 0.055 s
% 0.25/0.47 % Vampire exiting
%------------------------------------------------------------------------------