%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV411+1 : 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 : n004.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 0.20s 1.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 77 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 83 ( 31 ~; 27 |; 17 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 68 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( contains_slb(X0,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l47_co) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X3,X4,X5] :
( ! [X6] : ~ pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6)
& contains_slb(insert_slb(X0,pair(X4,X5)),X3) )
& ! [X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
? [X0] :
( ? [X1,X2,X3] :
( ! [X4] : ~ pair_in_list(insert_slb(X0,pair(X2,X3)),X1,X4)
& contains_slb(insert_slb(X0,pair(X2,X3)),X1) )
& ! [X5] :
( ? [X6] : pair_in_list(X0,X5,X6)
| ~ contains_slb(X0,X5) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
( ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4)
& contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1)
& ! [X5] :
( pair_in_list(sK0,X5,sK4(X5))
| ~ contains_slb(sK0,X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4(X5))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( ~ contains_slb(X0,X2)
& X1 != X2 ) )
& ( contains_slb(X0,X2)
| X1 = X2
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( ~ contains_slb(X0,X2)
& X1 != X2 ) )
& ( contains_slb(X0,X2)
| X1 = X2
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ~ pair_in_list(X0,X2,X4)
& ( X1 != X2
| X3 != X4 ) ) )
& ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X5] :
( pair_in_list(sK0,X5,sK4(X5))
| ~ contains_slb(sK0,X5) ),
inference(cnf_transformation,[],[f23]) ).
fof(f29,plain,
contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(cnf_transformation,[],[f27]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X2,X3,X0,X4] :
( pair_in_list(insert_slb(X0,pair(X2,X3)),X2,X4)
| X3 != X4 ),
inference(equality_resolution,[],[f36]) ).
fof(f42,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f41]) ).
fof(f43,plain,
! [X0] : ~ pair_in_list(sK0,sK1,X0),
inference(resolution,[],[f37,f30]) ).
fof(f44,plain,
~ contains_slb(sK0,sK1),
inference(resolution,[],[f43,f28]) ).
fof(f45,plain,
( sK1 = sK2
| contains_slb(sK0,sK1) ),
inference(resolution,[],[f31,f29]) ).
fof(f48,plain,
sK1 = sK2,
inference(forward_subsumption_resolution,[],[f45,f44]) ).
fof(f49,plain,
! [X0] : ~ pair_in_list(insert_slb(sK0,pair(sK1,sK3)),sK1,X0),
inference(superposition,[],[f30,f48]) ).
fof(f53,plain,
$false,
inference(resolution,[],[f49,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 10:51:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.20/1.30 % (281044)Detected formulas, will run a generic FOF schedule.
% 0.20/1.30 % (281049)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=2012257702:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.30 % (281052)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2112586321:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.30 % (281055)dis-21_1_sil=8000:lcm=predicate:random_seed=1235946592: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)
% 0.20/1.30 % (281050)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=743651125:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.30 % (281051)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=1647445179:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.30 % (281054)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1173790932:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.30 % (281053)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=579426873:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.30 % (281055)Refutation not found, incomplete strategy
% 0.20/1.30 % (281055)------------------------------
% 0.20/1.30 % (281055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (281053)First to succeed.
% 0.20/1.30 % (281055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (281055)CaDiCaL version: 2.1.3
% 0.20/1.30 % (281055)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.30 % (281055)Time elapsed: 0.002 s
% 0.20/1.30 % (281055)Peak memory usage: 88 MB
% 0.20/1.30 % (281055)Instructions burned: 1 (million)
% 0.20/1.30 % (281052)Also succeeded, but the first one will report.
% 0.20/1.30 % (281053)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-281044"
% 0.20/1.30 % (281054)Also succeeded, but the first one will report.
% 0.20/1.30 % (281055)------------------------------
% 0.20/1.30 % (281055)------------------------------
% 0.20/1.30 % (281053)Refutation found. Thanks to Tanya!
% 0.20/1.30 % SZS status Theorem for theBenchmark
% 0.20/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.30 % (281053)------------------------------
% 0.20/1.30 % (281053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (281053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (281053)CaDiCaL version: 2.1.3
% 0.20/1.30 % (281053)Termination reason: Refutation
% 0.20/1.30 % (281053)Time elapsed: 0.003 s
% 0.20/1.30 % (281053)Peak memory usage: 88 MB
% 0.20/1.30 % (281053)Instructions burned: 2 (million)
% 0.20/1.30 % (281053)------------------------------
% 0.20/1.30 % (281053)------------------------------
% 0.20/1.30 % (281044)Success in time 0.433 s
% 0.20/1.30 % Vampire exiting
%------------------------------------------------------------------------------