%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV165+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:08:17 PM UTC 2026
% Result : Theorem 3.44s 1.17s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 93 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 37 ~; 29 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f42,axiom,
! [X0,X1] :
( leq(succ(X0),succ(X1))
<=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
fof(f53,conjecture,
! [X0] :
( ( leq(n0,X0)
& leq(X0,tptp_minus_1) )
=> uninit = init ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0001) ).
fof(f54,negated_conjecture,
~ ! [X0] :
( ( leq(n0,X0)
& leq(X0,tptp_minus_1) )
=> uninit = init ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f58,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f78,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f87,plain,
? [X0] :
( uninit != init
& leq(n0,X0)
& leq(X0,tptp_minus_1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f88,plain,
? [X0] :
( uninit != init
& leq(n0,X0)
& leq(X0,tptp_minus_1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f90,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f92,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f110,plain,
( uninit != init
& leq(n0,sK0)
& leq(sK0,tptp_minus_1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
fof(f111,plain,
! [X0,X1] :
( ( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) )
& ( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f112,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f113,plain,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f110]) ).
fof(f114,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f110]) ).
fof(f116,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f117,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f122,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f125,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f127,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f128,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f160,plain,
! [X0,X1] :
( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f161,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f171,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f173,plain,
n0 = plus(n1,tptp_minus_1),
inference(definition_unfolding,[],[f125,f171]) ).
fof(f182,plain,
! [X0,X1] :
( leq(plus(n1,X0),plus(n1,X1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f160,f171,f171]) ).
fof(f185,plain,
! [X0,X1] :
( gt(plus(n1,X1),X0)
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f161,f171]) ).
fof(f221,plain,
! [X0] : ~ leq(plus(n1,X0),X0),
inference(resolution,[],[f185,f128]) ).
fof(f237,plain,
( ~ leq(sK0,n0)
| n0 = sK0 ),
inference(resolution,[],[f116,f114]) ).
fof(f246,plain,
! [X0] :
( ~ leq(sK0,X0)
| ~ leq(X0,n0)
| n0 = sK0 ),
inference(resolution,[],[f117,f237]) ).
fof(f247,plain,
( ~ leq(tptp_minus_1,n0)
| n0 = sK0 ),
inference(resolution,[],[f246,f113]) ).
fof(f257,plain,
( n0 = sK0
| ~ gt(n0,tptp_minus_1) ),
inference(resolution,[],[f247,f127]) ).
fof(f258,plain,
n0 = sK0,
inference(forward_subsumption_resolution,[],[f257,f122]) ).
fof(f323,plain,
! [X0] :
( leq(plus(n1,X0),n0)
| ~ leq(X0,tptp_minus_1) ),
inference(superposition,[],[f182,f173]) ).
fof(f327,plain,
! [X0] :
( leq(plus(n1,X0),sK0)
| ~ leq(X0,tptp_minus_1) ),
inference(forward_demodulation,[],[f323,f258]) ).
fof(f353,plain,
~ leq(sK0,tptp_minus_1),
inference(resolution,[],[f327,f221]) ).
fof(f361,plain,
$false,
inference(forward_subsumption_resolution,[],[f353,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV165+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/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 10:02:51 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.44/1.17 % (1070816)Detected formulas, will run a generic FOF schedule.
% 3.44/1.17 % (1070823)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=4006764064:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.17 % (1070826)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=438502055:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.17 % (1070824)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=891207872:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.17 % (1070825)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4259650183:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.17 % (1070822)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=3803934930:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.17 % (1070827)dis-21_1_sil=8000:lcm=predicate:random_seed=836787007: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)
% 3.44/1.17 % (1070821)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=3538783709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.17 % (1070824)Refutation not found, incomplete strategy
% 3.44/1.17 % (1070824)------------------------------
% 3.44/1.17 % (1070824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.17 % (1070824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.17 % (1070824)CaDiCaL version: 2.1.3
% 3.44/1.17 % (1070824)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.17 % (1070824)Time elapsed: 0.002 s
% 3.44/1.17 % (1070824)Peak memory usage: 88 MB
% 3.44/1.17 % (1070824)Instructions burned: 1 (million)
% 3.44/1.17 % (1070825)First to succeed.
% 3.44/1.17 % (1070825)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1070816"
% 3.44/1.17 % (1070826)Also succeeded, but the first one will report.
% 3.44/1.17 % (1070827)Instruction limit reached!
% 3.44/1.17 % (1070827)------------------------------
% 3.44/1.17 % (1070827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.17 % (1070827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.17 % (1070827)CaDiCaL version: 2.1.3
% 3.44/1.17 % (1070827)Termination reason: Instruction limit
% 3.44/1.17 % (1070827)Termination phase: Saturation
% 3.44/1.17 % (1070827)Time elapsed: 0.081 s
% 3.44/1.17 % (1070827)Peak memory usage: 89 MB
% 3.44/1.17 % (1070827)Instructions burned: 129 (million)
% 3.44/1.17 % (1070835)lrs+10_1_sil=8000:sp=occurrence:random_seed=3922478406:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.44/1.17 % (1070835)Also succeeded, but the first one will report.
% 3.44/1.17 % (1070824)------------------------------
% 3.44/1.17 % (1070824)------------------------------
% 3.44/1.17 % (1070825)Refutation found. Thanks to Tanya!
% 3.44/1.17 % SZS status Theorem for theBenchmark
% 3.44/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.17 % (1070825)------------------------------
% 3.44/1.17 % (1070825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.17 % (1070825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.17 % (1070825)CaDiCaL version: 2.1.3
% 3.44/1.17 % (1070825)Termination reason: Refutation
% 3.44/1.17 % (1070825)Time elapsed: 0.007 s
% 3.44/1.17 % (1070825)Peak memory usage: 88 MB
% 3.44/1.17 % (1070825)Instructions burned: 9 (million)
% 3.44/1.17 % (1070825)------------------------------
% 3.44/1.17 % (1070825)------------------------------
% 3.44/1.17 % (1070816)Success in time 0.414 s
% 3.44/1.17 % Vampire exiting
%------------------------------------------------------------------------------