%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM383+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 : n009.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 12:15:02 PM UTC 2026
% Result : Theorem 0.17s 1.40s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 38 ~; 29 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 61 ( 59 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f21,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f24,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f27,conjecture,
! [X0,X1] :
~ ( in(X0,X1)
& subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
~ ( in(X0,X1)
& subset(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f32,plain,
? [X0,X1] :
( in(X0,X1)
& subset(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f38,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f42,plain,
( in(sK0,sK1)
& subset(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
fof(f46,plain,
subset(sK1,sK0),
inference(cnf_transformation,[],[f42]) ).
fof(f47,plain,
in(sK0,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f49,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| ~ empty(X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f61,plain,
! [X0] : ~ in(X0,X0),
inference(factoring,[],[f49]) ).
fof(f64,plain,
! [X0] :
( ~ element(X0,X0)
| empty(X0) ),
inference(resolution,[],[f56,f61]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f54,f50]) ).
fof(f74,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ subset(X1,X2) ),
inference(resolution,[],[f55,f50]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ subset(X1,X0)
| empty(X0) ),
inference(resolution,[],[f74,f64]) ).
fof(f94,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f89,f70]) ).
fof(f98,plain,
~ in(sK0,sK1),
inference(resolution,[],[f94,f46]) ).
fof(f100,plain,
$false,
inference(forward_subsumption_resolution,[],[f98,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.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 : Sun Sep 27 19:45:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.17/1.40 % (2357733)Detected formulas, will run a generic FOF schedule.
% 0.17/1.40 % (2357738)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=1760634661:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.40 % (2357742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4267002618:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.40 % (2357743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1118070714:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.40 % (2357741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2348429669:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.40 % (2357739)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=1672317140:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.40 % (2357740)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=4177776814:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.40 % (2357741)Refutation not found, incomplete strategy
% 0.17/1.40 % (2357741)------------------------------
% 0.17/1.40 % (2357741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (2357741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (2357741)CaDiCaL version: 2.1.3
% 0.17/1.40 % (2357741)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.40 % (2357741)Time elapsed: 0.001 s
% 0.17/1.40 % (2357741)Peak memory usage: 88 MB
% 0.17/1.40 % (2357742)First to succeed.
% 0.17/1.40 % (2357742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2357733"
% 0.17/1.40 % (2357743)Also succeeded, but the first one will report.
% 0.17/1.40 % (2357744)dis-21_1_sil=8000:lcm=predicate:random_seed=2804071094: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)
% 0.17/1.40 % (2357744)Also succeeded, but the first one will report.
% 0.17/1.40 % (2357741)------------------------------
% 0.17/1.40 % (2357741)------------------------------
% 0.17/1.40 % (2357742)Refutation found. Thanks to Tanya!
% 0.17/1.40 % SZS status Theorem for theBenchmark
% 0.17/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (2357742)------------------------------
% 0.17/1.40 % (2357742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (2357742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (2357742)CaDiCaL version: 2.1.3
% 0.17/1.40 % (2357742)Termination reason: Refutation
% 0.17/1.40 % (2357742)Time elapsed: 0.003 s
% 0.17/1.40 % (2357742)Peak memory usage: 88 MB
% 0.17/1.40 % (2357742)Instructions burned: 2 (million)
% 0.17/1.40 % (2357742)------------------------------
% 0.17/1.40 % (2357742)------------------------------
% 0.17/1.40 % (2357733)Success in time 0.436 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------