%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:47:14 PM UTC 2026
% Result : Theorem 2.02s 0.88s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 1 def)
% Number of atoms : 116 ( 6 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 133 ( 55 ~; 49 |; 22 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> element(prebool_difference(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ( element(X0,X2)
& element(X1,X2) )
=> element(set_intersection2(X0,X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finsub_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ( element(X0,X2)
& element(X1,X2) )
=> element(set_intersection2(X0,X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f33,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f57]) ).
fof(f65,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
? [X0,X1,X2] :
( ~ element(set_intersection2(X0,X1),X2)
& element(X0,X2)
& element(X1,X2)
& ~ empty(X2)
& preboolean(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f68,plain,
? [X0,X1,X2] :
( ~ element(set_intersection2(X0,X1),X2)
& element(X0,X2)
& element(X1,X2)
& ~ empty(X2)
& preboolean(X2) ),
inference(flattening,[],[f67]) ).
fof(f89,plain,
( ~ element(set_intersection2(sK10,sK11),sK12)
& element(sK10,sK12)
& element(sK11,sK12)
& ~ empty(sK12)
& preboolean(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f68]) ).
fof(f97,plain,
! [X2,X0,X1] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f126,plain,
! [X2,X0,X1] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f128,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f129,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
element(sK11,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f131,plain,
element(sK10,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f132,plain,
~ element(set_intersection2(sK10,sK11),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
fof(f202,plain,
! [X2,X0,X1] :
( element(set_difference(X0,X1),X2)
| empty(X2)
| ~ preboolean(X2)
| ~ element(X0,X2)
| ~ element(X1,X2)
| empty(X2)
| ~ preboolean(X2)
| ~ element(X0,X2)
| ~ element(X1,X2) ),
inference(superposition,[],[f97,f126]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ preboolean(X2)
| empty(X2)
| element(set_difference(X0,X1),X2)
| ~ element(X0,X2)
| ~ element(X1,X2) ),
inference(duplicate_literal_removal,[],[f202]) ).
fof(f232,plain,
! [X0,X1] :
( empty(sK12)
| element(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(resolution,[],[f203,f128]) ).
fof(f236,plain,
! [X0,X1] :
( element(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f232,f129]) ).
fof(f239,plain,
! [X0,X1] :
( element(set_intersection2(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(set_difference(X0,X1),sK12) ),
inference(superposition,[],[f236,f138]) ).
fof(f281,plain,
( ~ element(sK10,sK12)
| ~ element(set_difference(sK10,sK11),sK12) ),
inference(resolution,[],[f239,f132]) ).
fof(f289,plain,
~ element(set_difference(sK10,sK11),sK12),
inference(forward_subsumption_resolution,[],[f281,f131]) ).
fof(f296,definition,
( spl13_8
<=> element(set_difference(sK10,sK11),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f298,plain,
( ~ element(set_difference(sK10,sK11),sK12)
| spl13_8 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f304,plain,
~ spl13_8,
inference(avatar_split_clause,[],[f289,f296]) ).
fof(f320,plain,
( ~ element(sK10,sK12)
| ~ element(sK11,sK12)
| spl13_8 ),
inference(resolution,[],[f298,f236]) ).
fof(f322,plain,
( ~ element(sK11,sK12)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f320,f131]) ).
fof(f323,plain,
( $false
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f322,f130]) ).
fof(f324,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f323]) ).
cnf(s6,plain,
~ spl13_8,
inference(sat_conversion,[],[f304]) ).
cnf(s7,plain,
spl13_8,
inference(sat_conversion,[],[f324]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s6,s7]) ).
fof(f325,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 28 03:33:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.02/0.88 % (2992779)Detected formulas, will run a generic FOF schedule.
% 2.02/0.88 % (2992787)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1628814926:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.02/0.88 % (2992788)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=121826541:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.02/0.88 % (2992789)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1588979974:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.02/0.88 % (2992784)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=3756396986:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.02/0.88 % (2992786)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=464086340:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.02/0.88 % (2992785)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=578274989:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.02/0.88 % (2992787)Refutation not found, incomplete strategy
% 2.02/0.88 % (2992787)------------------------------
% 2.02/0.88 % (2992787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2992787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2992787)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2992787)Termination reason: Refutation not found, incomplete strategy
% 2.02/0.88 % (2992787)Time elapsed: 0.001 s
% 2.02/0.88 % (2992787)Peak memory usage: 88 MB
% 2.02/0.88 % (2992788)Refutation not found, incomplete strategy
% 2.02/0.88 % (2992788)------------------------------
% 2.02/0.88 % (2992788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2992788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2992788)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2992788)Termination reason: Refutation not found, incomplete strategy
% 2.02/0.88 % (2992788)Time elapsed: 0.001 s
% 2.02/0.88 % (2992788)Peak memory usage: 88 MB
% 2.02/0.88 % (2992788)Instructions burned: 2 (million)
% 2.02/0.88 % (2992789)First to succeed.
% 2.02/0.88 % (2992789)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2992779"
% 2.02/0.88 % (2992790)dis-21_1_sil=8000:lcm=predicate:random_seed=2800958324: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)
% 2.02/0.88 % (2992790)Instruction limit reached!
% 2.02/0.88 % (2992790)------------------------------
% 2.02/0.88 % (2992790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2992790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2992790)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2992790)Termination reason: Instruction limit
% 2.02/0.88 % (2992790)Termination phase: Saturation
% 2.02/0.88 % (2992790)Time elapsed: 0.039 s
% 2.02/0.88 % (2992790)Peak memory usage: 91 MB
% 2.02/0.88 % (2992790)Instructions burned: 131 (million)
% 2.02/0.88 % (2992798)lrs+10_1_sil=8000:sp=occurrence:random_seed=2206483172:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.02/0.88 % (2992788)------------------------------
% 2.02/0.88 % (2992788)------------------------------
% 2.02/0.88 % (2992787)------------------------------
% 2.02/0.88 % (2992787)------------------------------
% 2.02/0.88 % (2992789)Refutation found. Thanks to Tanya!
% 2.02/0.88 % SZS status Theorem for theBenchmark
% 2.02/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.88 % (2992789)------------------------------
% 2.02/0.88 % (2992789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2992789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2992789)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2992789)Termination reason: Refutation
% 2.02/0.88 % (2992789)Time elapsed: 0.005 s
% 2.02/0.88 % (2992789)Peak memory usage: 89 MB
% 2.02/0.88 % (2992789)Instructions burned: 10 (million)
% 2.02/0.88 % (2992789)------------------------------
% 2.02/0.88 % (2992789)------------------------------
% 2.02/0.88 % (2992779)Success in time 0.259 s
% 2.02/0.88 % Vampire exiting
%------------------------------------------------------------------------------