%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV408+2 : 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 : 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 01:09:08 PM UTC 2026
% Result : Theorem 3.62s 1.29s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 7 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 49 ~; 38 |; 20 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 79 ( 67 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f42,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& strictly_less_than(X2,X3) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( ( pair_in_list(X0,X1,X2)
& less_than(X3,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
fof(f45,conjecture,
! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f46,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(ennf_transformation,[],[f43]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f57,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(flattening,[],[f56]) ).
fof(f69,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f51]) ).
fof(f70,plain,
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
& ! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) )
& contains_slb(sK2,sK4)
& strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f57]) ).
fof(f73,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f74,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f53]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f79,plain,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f70]) ).
fof(f80,plain,
! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f81,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f70]) ).
fof(f90,plain,
! [X0,X1] :
( ~ less_than(X0,X1)
| strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f94,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f134,plain,
! [X0] :
( ~ pair_in_list(sK2,sK4,X0)
| ~ strictly_less_than(X0,findmin_pqp_res(sK1)) ),
inference(resolution,[],[f76,f81]) ).
fof(f144,plain,
! [X0] :
( ~ pair_in_list(sK2,sK4,X0)
| ~ less_than(findmin_pqp_res(sK1),X0)
| ~ less_than(findmin_pqp_res(sK1),X0) ),
inference(resolution,[],[f77,f80]) ).
fof(f148,plain,
! [X0] :
( ~ pair_in_list(sK2,sK4,X0)
| ~ less_than(findmin_pqp_res(sK1),X0) ),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f151,plain,
( ~ strictly_less_than(sK0(sK2,sK4),findmin_pqp_res(sK1))
| ~ contains_slb(sK2,sK4) ),
inference(resolution,[],[f134,f75]) ).
fof(f152,plain,
~ strictly_less_than(sK0(sK2,sK4),findmin_pqp_res(sK1)),
inference(forward_subsumption_resolution,[],[f151,f79]) ).
fof(f153,plain,
( ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4))
| ~ contains_slb(sK2,sK4) ),
inference(resolution,[],[f148,f75]) ).
fof(f154,plain,
~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4)),
inference(forward_subsumption_resolution,[],[f153,f79]) ).
fof(f155,plain,
less_than(sK0(sK2,sK4),findmin_pqp_res(sK1)),
inference(resolution,[],[f154,f94]) ).
fof(f158,plain,
( strictly_less_than(sK0(sK2,sK4),findmin_pqp_res(sK1))
| less_than(findmin_pqp_res(sK1),sK0(sK2,sK4)) ),
inference(resolution,[],[f155,f90]) ).
fof(f159,plain,
less_than(findmin_pqp_res(sK1),sK0(sK2,sK4)),
inference(forward_subsumption_resolution,[],[f158,f152]) ).
fof(f160,plain,
$false,
inference(forward_subsumption_resolution,[],[f159,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 10:51:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 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
% 3.62/1.29 % (2952067)Detected formulas, will run a generic FOF schedule.
% 3.62/1.29 % (2952073)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=3430460636:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.29 % (2952076)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1816717361:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.29 % (2952077)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=429016238:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.29 % (2952072)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=80762614:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.29 % (2952074)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=953085597:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.29 % (2952075)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=425947859:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.29 % (2952078)dis-21_1_sil=8000:lcm=predicate:random_seed=3457818769: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)
% 3.62/1.29 % (2952075)First to succeed.
% 3.62/1.29 % (2952075)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2952067"
% 3.62/1.29 % (2952076)Also succeeded, but the first one will report.
% 3.62/1.29 % (2952077)Also succeeded, but the first one will report.
% 3.62/1.29 % (2952078)Instruction limit reached!
% 3.62/1.29 % (2952078)------------------------------
% 3.62/1.29 % (2952078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.29 % (2952078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.29 % (2952078)CaDiCaL version: 2.1.3
% 3.62/1.29 % (2952078)Termination reason: Instruction limit
% 3.62/1.29 % (2952078)Termination phase: Saturation
% 3.62/1.29 % (2952078)Time elapsed: 0.057 s
% 3.62/1.29 % (2952078)Peak memory usage: 88 MB
% 3.62/1.29 % (2952078)Instructions burned: 129 (million)
% 3.62/1.29 % (2952086)lrs+10_1_sil=8000:sp=occurrence:random_seed=3415704758:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.62/1.29 % (2952075)Refutation found. Thanks to Tanya!
% 3.62/1.29 % SZS status Theorem for theBenchmark
% 3.62/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.29 % (2952075)------------------------------
% 3.62/1.29 % (2952075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.29 % (2952075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.29 % (2952075)CaDiCaL version: 2.1.3
% 3.62/1.29 % (2952075)Termination reason: Refutation
% 3.62/1.29 % (2952075)Time elapsed: 0.005 s
% 3.62/1.29 % (2952075)Peak memory usage: 88 MB
% 3.62/1.29 % (2952075)Instructions burned: 5 (million)
% 3.62/1.29 % (2952075)------------------------------
% 3.62/1.29 % (2952075)------------------------------
% 3.62/1.29 % (2952067)Success in time 0.433 s
% 3.62/1.29 % Vampire exiting
%------------------------------------------------------------------------------