%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:46:08 PM UTC 2026
% Result : Theorem 3.86s 1.58s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 16 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] : ~ leqNat(s(X0),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f9,axiom,
! [X0] : merge(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(f13,axiom,
ord(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ord(cons(X0,cons(X1,X2)))
<=> ( leqNat(X0,X1)
& ord(cons(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,conjecture,
? [X0,X1] :
~ ( ord(X0)
=> ( ~ ord(X1)
=> ord(merge(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_016) ).
fof(f17,negated_conjecture,
~ ? [X0,X1] :
~ ( ord(X0)
=> ( ~ ord(X1)
=> ord(merge(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ord(merge(X0,X1))
| ord(X1)
| ~ ord(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ord(merge(X0,X1))
| ord(X1)
| ~ ord(X0) ),
inference(flattening,[],[f20]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ord(cons(X0,cons(X1,X2)))
| ~ leqNat(X0,X1)
| ~ ord(cons(X1,X2)) )
& ( ( leqNat(X0,X1)
& ord(cons(X1,X2)) )
| ~ ord(cons(X0,cons(X1,X2))) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ord(cons(X0,cons(X1,X2)))
| ~ leqNat(X0,X1)
| ~ ord(cons(X1,X2)) )
& ( ( leqNat(X0,X1)
& ord(cons(X1,X2)) )
| ~ ord(cons(X0,cons(X1,X2))) ) ),
inference(flattening,[],[f23]) ).
fof(f31,plain,
! [X0] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0] : merge(nil,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
ord(nil),
inference(cnf_transformation,[],[f13]) ).
fof(f41,plain,
! [X2,X0,X1] :
( leqNat(X0,X1)
| ~ ord(cons(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1] :
( ord(merge(X0,X1))
| ord(X1)
| ~ ord(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0] :
( ord(X0)
| ord(X0)
| ~ ord(nil) ),
inference(superposition,[],[f43,f34]) ).
fof(f45,plain,
! [X0] :
( ord(X0)
| ~ ord(nil) ),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f46,plain,
! [X0] : ord(X0),
inference(forward_subsumption_resolution,[],[f45,f38]) ).
fof(f48,plain,
! [X0,X1] : leqNat(X0,X1),
inference(forward_subsumption_resolution,[],[f41,f46]) ).
fof(f49,plain,
$false,
inference(resolution,[],[f48,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 % Computer : n002.cluster.edu
% 0.26/0.31 % Model : x86_64 x86_64
% 0.26/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.31 % Memory : 8046.5625MB
% 0.26/0.31 % OS : Linux 6.8.0-71-generic
% 0.26/0.31 % CPULimit : 300
% 0.26/0.31 % WCLimit : 300
% 0.26/0.31 % DateTime : Mon Sep 28 15:10:37 UTC 2026
% 0.26/0.31 % CPUTime :
% 0.26/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.37 Running first-order theorem proving
% 0.26/0.37 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
% 3.86/1.58 % (429553)Detected formulas, will run a generic FOF schedule.
% 3.86/1.58 % (429633)dis-21_1_sil=8000:lcm=predicate:random_seed=4288730150: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)
% 3.86/1.58 % (429633)Refutation not found, incomplete strategy
% 3.86/1.58 % (429633)------------------------------
% 3.86/1.58 % (429633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.58 % (429633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.58 % (429633)CaDiCaL version: 2.1.3
% 3.86/1.58 % (429633)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.58 % (429633)Time elapsed: 0.001 s
% 3.86/1.58 % (429633)Peak memory usage: 88 MB
% 3.86/1.58 % (429633)Instructions burned: 1 (million)
% 3.86/1.58 % (429629)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1832276566:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.86/1.58 % (429631)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1771027284:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.86/1.58 % (429627)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=121462293:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.86/1.58 % (429625)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=3821975606:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.86/1.58 % (429628)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=682175048:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.86/1.58 % (429626)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=3863081946:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.86/1.58 % (429631)First to succeed.
% 3.86/1.58 % (429628)Refutation not found, incomplete strategy
% 3.86/1.58 % (429628)------------------------------
% 3.86/1.58 % (429628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.58 % (429628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.58 % (429628)CaDiCaL version: 2.1.3
% 3.86/1.58 % (429628)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.58 % (429628)Time elapsed: 0.002 s
% 3.86/1.58 % (429628)Peak memory usage: 88 MB
% 3.86/1.58 % (429628)Instructions burned: 1 (million)
% 3.86/1.58 % (429631)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-429553"
% 3.86/1.58 % (429629)Instruction limit reached!
% 3.86/1.58 % (429629)------------------------------
% 3.86/1.58 % (429629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.58 % (429629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.58 % (429629)CaDiCaL version: 2.1.3
% 3.86/1.58 % (429629)Termination reason: Instruction limit
% 3.86/1.58 % (429629)Termination phase: Saturation
% 3.86/1.58 % (429629)Time elapsed: 0.062 s
% 3.86/1.58 % (429629)Peak memory usage: 88 MB
% 3.86/1.58 % (429629)Instructions burned: 119 (million)
% 3.86/1.58 % (429633)------------------------------
% 3.86/1.58 % (429633)------------------------------
% 3.86/1.58 % (429709)lrs+10_1_sil=8000:sp=occurrence:random_seed=1152358693:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.86/1.58 % (429709)Also succeeded, but the first one will report.
% 3.86/1.58 % (429725)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3492363998:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.86/1.58 % (429725)Refutation not found, incomplete strategy
% 3.86/1.58 % (429725)------------------------------
% 3.86/1.58 % (429725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.58 % (429725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.58 % (429725)CaDiCaL version: 2.1.3
% 3.86/1.58 % (429725)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.58 % (429725)Time elapsed: 0.001 s
% 3.86/1.58 % (429725)Peak memory usage: 88 MB
% 3.86/1.58 % (429725)Instructions burned: 1 (million)
% 3.86/1.58 % (429628)------------------------------
% 3.86/1.58 % (429628)------------------------------
% 3.86/1.58 % (429631)Refutation found. Thanks to Tanya!
% 3.86/1.58 % SZS status Theorem for theBenchmark
% 3.86/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.59 % (429631)------------------------------
% 3.86/1.59 % (429631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.59 % (429631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.59 % (429631)CaDiCaL version: 2.1.3
% 3.86/1.59 % (429631)Termination reason: Refutation
% 3.86/1.59 % (429631)Time elapsed: 0.002 s
% 3.86/1.59 % (429631)Peak memory usage: 88 MB
% 3.86/1.59 % (429631)Instructions burned: 1 (million)
% 3.86/1.59 % (429631)------------------------------
% 3.86/1.59 % (429631)------------------------------
% 3.86/1.59 % (429553)Success in time 0.428 s
% 3.86/1.59 % Vampire exiting
%------------------------------------------------------------------------------