%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV416+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:09:09 PM UTC 2026
% Result : Theorem 2.67s 1.05s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 56 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 15 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X0,X1] :
( pi_sharp_remove(X0,X1)
<=> contains_pq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f57,axiom,
! [X0,X1] :
( pi_remove(X0,X1)
<=> pi_sharp_remove(i(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f64,axiom,
! [X0,X1,X2,X3] :
( contains_pq(i(triple(X0,X1,X2)),X3)
=> i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main3_li34) ).
fof(f65,conjecture,
! [X0,X1,X2,X3] :
( pi_remove(triple(X0,X1,X2),X3)
=> ( phi(remove_cpq(triple(X0,X1,X2),X3))
=> ( pi_sharp_remove(i(triple(X0,X1,X2)),X3)
& i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co3) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( pi_remove(triple(X0,X1,X2),X3)
=> ( phi(remove_cpq(triple(X0,X1,X2),X3))
=> ( pi_sharp_remove(i(triple(X0,X1,X2)),X3)
& i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f72,plain,
! [X0,X1] :
( pi_remove(X0,X1)
=> pi_sharp_remove(i(X0),X1) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f75,plain,
? [X0,X1,X2,X3] :
( ( ~ pi_sharp_remove(i(triple(X0,X1,X2)),X3)
| i(remove_cpq(triple(X0,X1,X2),X3)) != remove_pq(i(triple(X0,X1,X2)),X3) )
& phi(remove_cpq(triple(X0,X1,X2),X3))
& pi_remove(triple(X0,X1,X2),X3) ),
inference(ennf_transformation,[],[f66]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ( ~ pi_sharp_remove(i(triple(X0,X1,X2)),X3)
| i(remove_cpq(triple(X0,X1,X2),X3)) != remove_pq(i(triple(X0,X1,X2)),X3) )
& phi(remove_cpq(triple(X0,X1,X2),X3))
& pi_remove(triple(X0,X1,X2),X3) ),
inference(flattening,[],[f75]) ).
fof(f80,plain,
! [X0,X1] :
( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(ennf_transformation,[],[f72]) ).
fof(f93,plain,
( ( ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3)
| i(remove_cpq(triple(sK0,sK1,sK2),sK3)) != remove_pq(i(triple(sK0,sK1,sK2)),sK3) )
& phi(remove_cpq(triple(sK0,sK1,sK2),sK3))
& pi_remove(triple(sK0,sK1,sK2),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f76]) ).
fof(f94,plain,
! [X0,X1] :
( ( pi_sharp_remove(X0,X1)
| ~ contains_pq(X0,X1) )
& ( contains_pq(X0,X1)
| ~ pi_sharp_remove(X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
pi_remove(triple(sK0,sK1,sK2),sK3),
inference(cnf_transformation,[],[f93]) ).
fof(f105,plain,
( i(remove_cpq(triple(sK0,sK1,sK2),sK3)) != remove_pq(i(triple(sK0,sK1,sK2)),sK3)
| ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3) ),
inference(cnf_transformation,[],[f93]) ).
fof(f109,plain,
! [X0,X1] :
( contains_pq(X0,X1)
| ~ pi_sharp_remove(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f110,plain,
! [X0,X1] :
( pi_sharp_remove(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f111,plain,
! [X0,X1] :
( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f255,plain,
( remove_pq(i(triple(sK0,sK1,sK2)),sK3) != remove_pq(i(triple(sK0,sK1,sK2)),sK3)
| ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3)
| ~ contains_pq(i(triple(sK0,sK1,sK2)),sK3) ),
inference(superposition,[],[f105,f102]) ).
fof(f257,plain,
( ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3)
| ~ contains_pq(i(triple(sK0,sK1,sK2)),sK3) ),
inference(trivial_inequality_removal,[],[f255]) ).
fof(f258,plain,
~ contains_pq(i(triple(sK0,sK1,sK2)),sK3),
inference(forward_subsumption_resolution,[],[f257,f110]) ).
fof(f259,plain,
~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3),
inference(resolution,[],[f258,f109]) ).
fof(f268,plain,
~ pi_remove(triple(sK0,sK1,sK2),sK3),
inference(resolution,[],[f259,f111]) ).
fof(f272,plain,
$false,
inference(forward_subsumption_resolution,[],[f268,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV416+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n013.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 10:51:06 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 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
% 2.67/1.05 % (1092133)Detected formulas, will run a generic FOF schedule.
% 2.67/1.05 % (1092142)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1580573793:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.05 % (1092142)First to succeed.
% 2.67/1.05 % (1092142)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1092133"
% 2.67/1.05 % (1092138)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=1127200410:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.05 % (1092141)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=765825255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.05 % (1092139)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=3946691719:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.05 % (1092140)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=895356972:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.05 % (1092141)Also succeeded, but the first one will report.
% 2.67/1.05 % (1092143)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3692296653:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.05 % (1092144)dis-21_1_sil=8000:lcm=predicate:random_seed=1667453402: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)
% 2.67/1.05 % (1092144)Also succeeded, but the first one will report.
% 2.67/1.05 % (1092143)Also succeeded, but the first one will report.
% 2.67/1.05 % (1092142)Refutation found. Thanks to Tanya!
% 2.67/1.05 % SZS status Theorem for theBenchmark
% 2.67/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.05 % (1092142)------------------------------
% 2.67/1.05 % (1092142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.05 % (1092142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.05 % (1092142)CaDiCaL version: 2.1.3
% 2.67/1.05 % (1092142)Termination reason: Refutation
% 2.67/1.05 % (1092142)Time elapsed: 0.004 s
% 2.67/1.05 % (1092142)Peak memory usage: 88 MB
% 2.67/1.05 % (1092142)Instructions burned: 10 (million)
% 2.67/1.05 % (1092142)------------------------------
% 2.67/1.05 % (1092142)------------------------------
% 2.67/1.05 % (1092133)Success in time 0.304 s
% 2.67/1.05 % Vampire exiting
%------------------------------------------------------------------------------