%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM390+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 12:15:03 PM UTC 2026
% Result : Theorem 2.65s 1.27s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 13 unt; 3 def)
% Number of atoms : 191 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 205 ( 79 ~; 76 |; 29 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 65 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f28,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f29,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f30,conjecture,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f38,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
& X0 != X1 )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f52,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& in(X1,X2)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& in(X1,X2)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(flattening,[],[f66]) ).
fof(f75,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f78]) ).
fof(f92,plain,
( ~ in(sK13,sK15)
& subset(sK13,sK14)
& in(sK14,sK15)
& ordinal(sK15)
& ordinal(sK14)
& epsilon_transitive(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f67]) ).
fof(f98,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f103,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f106,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f137,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f138,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f139,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
in(sK14,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f143,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f144,plain,
~ in(sK13,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f159,plain,
~ subset(sK15,sK14),
inference(resolution,[],[f152,f142]) ).
fof(f163,plain,
( subset(sK14,sK15)
| ~ epsilon_transitive(sK15) ),
inference(resolution,[],[f103,f142]) ).
fof(f165,definition,
( spl16_1
<=> epsilon_transitive(sK15) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f167,plain,
( ~ epsilon_transitive(sK15)
| spl16_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl16_2
<=> subset(sK14,sK15) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f171,plain,
( subset(sK14,sK15)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f163,f169,f165]) ).
fof(f174,plain,
( ~ ordinal(sK15)
| spl16_1 ),
inference(resolution,[],[f167,f98]) ).
fof(f175,plain,
( $false
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f174,f141]) ).
fof(f176,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ordinal(X1)
| in(X0,X1)
| ~ epsilon_transitive(X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[],[f138,f106]) ).
fof(f256,plain,
! [X0] :
( ~ subset(X0,sK15)
| ~ epsilon_transitive(X0)
| in(X0,sK15)
| sK15 = X0 ),
inference(resolution,[],[f185,f141]) ).
fof(f278,plain,
! [X0,X1] :
( ~ subset(X1,sK15)
| in(X0,sK15)
| sK15 = X0
| ~ subset(X0,X1)
| ~ epsilon_transitive(X0) ),
inference(resolution,[],[f256,f137]) ).
fof(f487,plain,
( ! [X0] :
( in(X0,sK15)
| sK15 = X0
| ~ subset(X0,sK14)
| ~ epsilon_transitive(X0) )
| ~ spl16_2 ),
inference(resolution,[],[f278,f171]) ).
fof(f495,definition,
( spl16_28
<=> ! [X0] :
( in(X0,sK15)
| ~ epsilon_transitive(X0)
| ~ subset(X0,sK14)
| sK15 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl16_28])],[avatar_definition]) ).
fof(f496,plain,
( ! [X0] :
( ~ subset(X0,sK14)
| ~ epsilon_transitive(X0)
| in(X0,sK15)
| sK15 = X0 )
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f498,plain,
( spl16_28
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f487,f169,f495]) ).
fof(f825,plain,
( ~ epsilon_transitive(sK13)
| in(sK13,sK15)
| sK13 = sK15
| ~ spl16_28 ),
inference(resolution,[],[f496,f143]) ).
fof(f827,plain,
( in(sK13,sK15)
| sK13 = sK15
| ~ spl16_28 ),
inference(forward_subsumption_resolution,[],[f825,f139]) ).
fof(f828,plain,
( sK13 = sK15
| ~ spl16_28 ),
inference(forward_subsumption_resolution,[],[f827,f144]) ).
fof(f833,plain,
( ~ subset(sK13,sK14)
| ~ spl16_28 ),
inference(superposition,[],[f159,f828]) ).
fof(f882,plain,
( $false
| ~ spl16_28 ),
inference(forward_subsumption_resolution,[],[f833,f143]) ).
fof(f883,plain,
~ spl16_28,
inference(avatar_contradiction_clause,[],[f882]) ).
cnf(s1,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s2,plain,
spl16_1,
inference(sat_conversion,[],[f176]) ).
cnf(s15,plain,
( ~ spl16_2
| spl16_28 ),
inference(sat_conversion,[],[f498]) ).
cnf(s43,plain,
~ spl16_28,
inference(sat_conversion,[],[f883]) ).
cnf(s47,plain,
~ spl16_2,
inference(rat,[],[s15,s43]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s1,s47,s2]) ).
fof(f888,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:48:37 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 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
% 2.65/1.27 % (3835484)Detected formulas, will run a generic FOF schedule.
% 2.65/1.27 % (3835489)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=3024066739:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.27 % (3835490)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=3347050764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.27 % (3835493)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2998861949:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.27 % (3835491)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=1771409292:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.27 % (3835494)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4008458411:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.27 % (3835495)dis-21_1_sil=8000:lcm=predicate:random_seed=1889734460: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)
% 2.65/1.27 % (3835492)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2746218175:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.27 % (3835492)Refutation not found, incomplete strategy
% 2.65/1.27 % (3835492)------------------------------
% 2.65/1.27 % (3835492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (3835492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (3835492)CaDiCaL version: 2.1.3
% 2.65/1.27 % (3835492)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.27 % (3835492)Time elapsed: 0.001 s
% 2.65/1.27 % (3835492)Peak memory usage: 88 MB
% 2.65/1.27 % (3835494)First to succeed.
% 2.65/1.27 % (3835494)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3835484"
% 2.65/1.27 % (3835493)Instruction limit reached!
% 2.65/1.27 % (3835493)------------------------------
% 2.65/1.27 % (3835493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (3835493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (3835493)CaDiCaL version: 2.1.3
% 2.65/1.27 % (3835493)Termination reason: Instruction limit
% 2.65/1.27 % (3835493)Termination phase: Saturation
% 2.65/1.27 % (3835493)Time elapsed: 0.055 s
% 2.65/1.27 % (3835493)Peak memory usage: 87 MB
% 2.65/1.27 % (3835493)Instructions burned: 121 (million)
% 2.65/1.27 % (3835495)Instruction limit reached!
% 2.65/1.27 % (3835495)------------------------------
% 2.65/1.27 % (3835495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (3835495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (3835495)CaDiCaL version: 2.1.3
% 2.65/1.27 % (3835495)Termination reason: Instruction limit
% 2.65/1.27 % (3835495)Termination phase: Saturation
% 2.65/1.27 % (3835495)Time elapsed: 0.076 s
% 2.65/1.27 % (3835495)Peak memory usage: 88 MB
% 2.65/1.27 % (3835495)Instructions burned: 129 (million)
% 2.65/1.27 % (3835503)lrs+10_1_sil=8000:sp=occurrence:random_seed=90362441:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.65/1.27 % (3835503)Also succeeded, but the first one will report.
% 2.65/1.27 % (3835504)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1639266264:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.65/1.27 % (3835504)Also succeeded, but the first one will report.
% 2.65/1.27 % (3835492)------------------------------
% 2.65/1.27 % (3835492)------------------------------
% 2.65/1.27 % (3835494)Refutation found. Thanks to Tanya!
% 2.65/1.27 % SZS status Theorem for theBenchmark
% 2.65/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.47 % (3835494)------------------------------
% 3.59/1.47 % (3835494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.47 % (3835494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.47 % (3835494)CaDiCaL version: 2.1.3
% 3.59/1.47 % (3835494)Termination reason: Refutation
% 3.59/1.47 % (3835494)Time elapsed: 0.019 s
% 3.59/1.47 % (3835494)Peak memory usage: 89 MB
% 3.59/1.47 % (3835494)Instructions burned: 21 (million)
% 3.59/1.47 % (3835494)------------------------------
% 3.59/1.47 % (3835494)------------------------------
% 3.59/1.47 % (3835484)Success in time 0.428 s
% 3.59/1.47 % Vampire exiting
%------------------------------------------------------------------------------