%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU132+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:47:20 PM UTC 2026
% Result : Theorem 3.64s 1.41s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 12 unt; 2 def)
% Number of atoms : 150 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 173 ( 69 ~; 66 |; 29 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 70 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f83,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f84,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f84]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f92]) ).
fof(f100,plain,
( ~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10))
& subset(sK8,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f65]) ).
fof(f117,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f118,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f93]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f93]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f93]) ).
fof(f156,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f180,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f128]) ).
fof(f181,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f182,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f126]) ).
fof(f237,plain,
in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10)),
inference(resolution,[],[f118,f157]) ).
fof(f238,plain,
~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)),
inference(resolution,[],[f119,f157]) ).
fof(f249,plain,
in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8),
inference(resolution,[],[f181,f237]) ).
fof(f252,plain,
~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10),
inference(resolution,[],[f182,f237]) ).
fof(f288,plain,
! [X0] :
( in(X0,sK9)
| ~ in(X0,sK8) ),
inference(resolution,[],[f117,f156]) ).
fof(f333,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9)
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10) ),
inference(resolution,[],[f180,f238]) ).
fof(f335,definition,
( spl14_4
<=> in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f336,plain,
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f338,definition,
( spl14_5
<=> in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f339,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9)
| spl14_5 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f340,plain,
( spl14_4
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f333,f338,f335]) ).
fof(f341,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8)
| spl14_5 ),
inference(resolution,[],[f339,f288]) ).
fof(f351,plain,
( $false
| spl14_5 ),
inference(resolution,[],[f341,f249]) ).
fof(f352,plain,
spl14_5,
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f353,plain,
( $false
| ~ spl14_4 ),
inference(resolution,[],[f336,f252]) ).
fof(f356,plain,
~ spl14_4,
inference(avatar_contradiction_clause,[],[f353]) ).
cnf(s5,plain,
( spl14_4
| ~ spl14_5 ),
inference(sat_conversion,[],[f340]) ).
cnf(s6,plain,
spl14_5,
inference(sat_conversion,[],[f352]) ).
cnf(s7,plain,
~ spl14_4,
inference(sat_conversion,[],[f356]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s6,s7]) ).
fof(f357,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU132+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:46:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.64/1.41 % (4189351)Detected formulas, will run a generic FOF schedule.
% 3.64/1.41 % (4189356)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=717724413:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.41 % (4189358)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=1038953657:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.41 % (4189362)dis-21_1_sil=8000:lcm=predicate:random_seed=2331690154: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)
% 3.64/1.41 % (4189357)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=1723222732:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.41 % (4189360)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=289155114:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.41 % (4189361)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=599219271:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/1.41 % (4189359)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1357166054:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.41 % (4189362)First to succeed.
% 3.64/1.41 % (4189362)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4189351"
% 3.64/1.41 % (4189359)Instruction limit reached!
% 3.64/1.41 % (4189359)------------------------------
% 3.64/1.41 % (4189359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.41 % (4189359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.41 % (4189359)CaDiCaL version: 2.1.3
% 3.64/1.41 % (4189359)Termination reason: Instruction limit
% 3.64/1.41 % (4189359)Termination phase: Saturation
% 3.64/1.41 % (4189359)Time elapsed: 0.075 s
% 3.64/1.41 % (4189359)Peak memory usage: 89 MB
% 3.64/1.41 % (4189359)Instructions burned: 110 (million)
% 3.64/1.41 % (4189360)Instruction limit reached!
% 3.64/1.41 % (4189360)------------------------------
% 3.64/1.41 % (4189360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.41 % (4189360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.41 % (4189360)CaDiCaL version: 2.1.3
% 3.64/1.41 % (4189360)Termination reason: Instruction limit
% 3.64/1.41 % (4189360)Termination phase: Saturation
% 3.64/1.41 % (4189360)Time elapsed: 0.075 s
% 3.64/1.41 % (4189360)Peak memory usage: 88 MB
% 3.64/1.41 % (4189360)Instructions burned: 119 (million)
% 3.64/1.41 % (4189361)Instruction limit reached!
% 3.64/1.41 % (4189361)------------------------------
% 3.64/1.41 % (4189361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.41 % (4189361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.41 % (4189361)CaDiCaL version: 2.1.3
% 3.64/1.41 % (4189361)Termination reason: Instruction limit
% 3.64/1.41 % (4189361)Termination phase: Saturation
% 3.64/1.41 % (4189361)Time elapsed: 0.097 s
% 3.64/1.41 % (4189361)Peak memory usage: 90 MB
% 3.64/1.41 % (4189361)Instructions burned: 140 (million)
% 3.64/1.41 % (4189371)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3538699856:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.64/1.41 % (4189370)lrs+10_1_sil=8000:sp=occurrence:random_seed=701767184:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.64/1.41 % (4189371)Also succeeded, but the first one will report.
% 3.64/1.41 % (4189362)Refutation found. Thanks to Tanya!
% 3.64/1.41 % SZS status Theorem for theBenchmark
% 3.64/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.41 % (4189362)------------------------------
% 3.64/1.41 % (4189362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.41 % (4189362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.41 % (4189362)CaDiCaL version: 2.1.3
% 3.64/1.41 % (4189362)Termination reason: Refutation
% 3.64/1.41 % (4189362)Time elapsed: 0.006 s
% 3.64/1.41 % (4189362)Peak memory usage: 89 MB
% 3.64/1.41 % (4189362)Instructions burned: 7 (million)
% 3.64/1.41 % (4189362)------------------------------
% 3.64/1.41 % (4189362)------------------------------
% 3.64/1.41 % (4189351)Success in time 0.435 s
% 3.64/1.41 % Vampire exiting
%------------------------------------------------------------------------------