%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:47:15 PM UTC 2026
% Result : Theorem 2.77s 1.27s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 18 unt; 5 def)
% Number of atoms : 204 ( 7 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 221 ( 92 ~; 84 |; 27 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox/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/sandbox/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_intersection2(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_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_intersection2(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/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f49,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_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_intersection2(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_intersection2(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_intersection2(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f83]) ).
fof(f116,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f152,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f155,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f156,plain,
! [X0] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f159,plain,
! [X2,X1] :
( in(set_intersection2(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] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f175,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f224,plain,
in(sK11(sK12),sK12),
inference(resolution,[],[f155,f161]) ).
fof(f227,plain,
in(sK10(sK12),sK12),
inference(resolution,[],[f156,f161]) ).
fof(f311,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK12)
| ~ element(set_intersection2(X0,X1),sK12)
| ~ element(X0,sK12) ),
inference(superposition,[],[f160,f152]) ).
fof(f347,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1)),
inference(forward_demodulation,[],[f175,f116]) ).
fof(f360,plain,
! [X0,X1] :
( in(set_union2(X0,X1),sK12)
| ~ element(symmetric_difference(X0,X1),sK12)
| ~ element(set_intersection2(X0,X1),sK12) ),
inference(superposition,[],[f160,f347]) ).
fof(f378,plain,
( ~ in(set_union2(sK10(sK12),sK11(sK12)),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(resolution,[],[f157,f161]) ).
fof(f380,definition,
( spl13_7
<=> in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f382,plain,
( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
| spl13_7 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f384,definition,
( spl13_8
<=> in(set_union2(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f386,plain,
( ~ in(set_union2(sK10(sK12),sK11(sK12)),sK12)
| spl13_8 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,plain,
( ~ spl13_7
| ~ spl13_8 ),
inference(avatar_split_clause,[],[f378,f384,f380]) ).
fof(f389,plain,
( ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(sK10(sK12),sK12)
| spl13_7 ),
inference(resolution,[],[f382,f311]) ).
fof(f393,definition,
( spl13_9
<=> element(sK10(sK12),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f394,plain,
( element(sK10(sK12),sK12)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f395,plain,
( ~ element(sK10(sK12),sK12)
| spl13_9 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f397,definition,
( spl13_10
<=> element(set_intersection2(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f399,plain,
( ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_10 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f400,plain,
( ~ spl13_9
| ~ spl13_10
| spl13_7 ),
inference(avatar_split_clause,[],[f389,f380,f397,f393]) ).
fof(f402,plain,
( ~ in(sK10(sK12),sK12)
| spl13_9 ),
inference(resolution,[],[f395,f163]) ).
fof(f403,plain,
( $false
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f402,f227]) ).
fof(f404,plain,
spl13_9,
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f426,plain,
( ~ in(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_10 ),
inference(resolution,[],[f399,f163]) ).
fof(f435,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| spl13_10 ),
inference(resolution,[],[f426,f159]) ).
fof(f437,plain,
( ~ element(sK11(sK12),sK12)
| ~ spl13_9
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f435,f394]) ).
fof(f444,plain,
( ~ in(sK11(sK12),sK12)
| ~ spl13_9
| spl13_10 ),
inference(resolution,[],[f437,f163]) ).
fof(f445,plain,
( $false
| ~ spl13_9
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f444,f224]) ).
fof(f446,plain,
( ~ spl13_9
| spl13_10 ),
inference(avatar_contradiction_clause,[],[f445]) ).
fof(f449,plain,
( ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| spl13_8 ),
inference(resolution,[],[f386,f360]) ).
fof(f453,definition,
( spl13_11
<=> element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f455,plain,
( ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| spl13_11 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f456,plain,
( ~ spl13_10
| ~ spl13_11
| spl13_8 ),
inference(avatar_split_clause,[],[f449,f384,f453,f397]) ).
fof(f493,plain,
( ~ in(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| spl13_11 ),
inference(resolution,[],[f455,f163]) ).
fof(f511,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| spl13_11 ),
inference(resolution,[],[f493,f160]) ).
fof(f513,plain,
( ~ element(sK11(sK12),sK12)
| ~ spl13_9
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f511,f394]) ).
fof(f515,plain,
( ~ in(sK11(sK12),sK12)
| ~ spl13_9
| spl13_11 ),
inference(resolution,[],[f513,f163]) ).
fof(f516,plain,
( $false
| ~ spl13_9
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f515,f224]) ).
fof(f517,plain,
( ~ spl13_9
| spl13_11 ),
inference(avatar_contradiction_clause,[],[f516]) ).
cnf(s7,plain,
( ~ spl13_7
| ~ spl13_8 ),
inference(sat_conversion,[],[f387]) ).
cnf(s8,plain,
( spl13_7
| ~ spl13_9
| ~ spl13_10 ),
inference(sat_conversion,[],[f400]) ).
cnf(s9,plain,
spl13_9,
inference(sat_conversion,[],[f404]) ).
cnf(s10,plain,
( ~ spl13_9
| spl13_10 ),
inference(sat_conversion,[],[f446]) ).
cnf(s11,plain,
( spl13_8
| ~ spl13_10
| ~ spl13_11 ),
inference(sat_conversion,[],[f456]) ).
cnf(s12,plain,
( ~ spl13_9
| spl13_11 ),
inference(sat_conversion,[],[f517]) ).
cnf(s13,plain,
spl13_11,
inference(rat,[],[s12,s9]) ).
cnf(s14,plain,
spl13_10,
inference(rat,[],[s10,s9]) ).
cnf(s15,plain,
spl13_8,
inference(rat,[],[s11,s13,s14]) ).
cnf(s16,plain,
spl13_7,
inference(rat,[],[s8,s14,s9]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s7,s15,s16]) ).
fof(f518,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:37:37 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 2.77/1.26 % (4125421)Detected formulas, will run a generic FOF schedule.
% 2.77/1.26 % (4125426)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=551262847:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.26 % (4125431)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=792377403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.26 % (4125429)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3859447042:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.26 % (4125427)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=2314086098:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.26 % (4125430)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2032734764:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.26 % (4125428)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=1382803235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.26 % (4125429)Refutation not found, incomplete strategy
% 2.77/1.26 % (4125429)------------------------------
% 2.77/1.26 % (4125429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.26 % (4125429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.26 % (4125429)CaDiCaL version: 2.1.3
% 2.77/1.26 % (4125429)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.26 % (4125429)Time elapsed: 0.003 s
% 2.77/1.26 % (4125429)Peak memory usage: 88 MB
% 2.77/1.26 % (4125429)Instructions burned: 2 (million)
% 2.77/1.26 % (4125431)First to succeed.
% 2.77/1.26 % (4125431)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4125421"
% 2.77/1.26 % (4125432)dis-21_1_sil=8000:lcm=predicate:random_seed=3546812075: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)
% 2.77/1.26 % (4125432)Also succeeded, but the first one will report.
% 2.77/1.27 % (4125430)Instruction limit reached!
% 2.77/1.27 % (4125430)------------------------------
% 2.77/1.27 % (4125430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.27 % (4125430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.27 % (4125430)CaDiCaL version: 2.1.3
% 2.77/1.27 % (4125430)Termination reason: Instruction limit
% 2.77/1.27 % (4125430)Termination phase: Saturation
% 2.77/1.27 % (4125430)Time elapsed: 0.067 s
% 2.77/1.27 % (4125430)Peak memory usage: 88 MB
% 2.77/1.27 % (4125430)Instructions burned: 120 (million)
% 2.77/1.27 % (4125440)lrs+10_1_sil=8000:sp=occurrence:random_seed=1644391195:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.77/1.27 % (4125440)Also succeeded, but the first one will report.
% 2.77/1.27 % (4125429)------------------------------
% 2.77/1.27 % (4125429)------------------------------
% 2.77/1.27 % (4125431)Refutation found. Thanks to Tanya!
% 2.77/1.27 % SZS status Theorem for theBenchmark
% 2.77/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.46 % (4125431)------------------------------
% 3.54/1.46 % (4125431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.46 % (4125431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.46 % (4125431)CaDiCaL version: 2.1.3
% 3.54/1.46 % (4125431)Termination reason: Refutation
% 3.54/1.46 % (4125431)Time elapsed: 0.014 s
% 3.54/1.46 % (4125431)Peak memory usage: 89 MB
% 3.54/1.46 % (4125431)Instructions burned: 15 (million)
% 3.54/1.46 % (4125431)------------------------------
% 3.54/1.46 % (4125431)------------------------------
% 3.54/1.46 % (4125421)Success in time 0.418 s
% 3.54/1.46 % Vampire exiting
%------------------------------------------------------------------------------