%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:56:58 AM UTC 2026
% Result : Theorem 2.57s 1.33s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 34 unt; 0 def)
% Number of atoms : 83 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 29 ~; 22 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 81 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] : '>='(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(f6,axiom,
! [X0,X1] :
( ( '>='(X0,X1)
& '>='(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
<=> '>='(X1,'==>'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0] : '>='(X0,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f9,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('+'(X0,X2),'+'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(f11,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('==>'(X2,X0),'==>'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(f12,axiom,
! [X0] : '+'(X0,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f13,axiom,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(f14,conjecture,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f15,negated_conjecture,
~ ! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ '>='(X0,X1)
| ~ '>='(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ~ '>='(X0,X1)
| ~ '>='(X1,X0) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1,X2] :
( '>='('==>'(X2,X0),'==>'(X2,X1))
| ~ '>='(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f23,plain,
? [X0] : '==>'('==>'(X0,'1'),'1') != X0,
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( '>='('+'(X0,X1),X2)
| ~ '>='(X1,'==>'(X0,X2)) )
& ( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f25,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f27,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| X0 = X1
| ~ '>='(X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X2,X0,X1] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( '>='('==>'(X2,X0),'==>'(X2,X1))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0] : '1' = '+'(X0,'1'),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0] : '+'('0',X0) = X0,
inference(superposition,[],[f27,f28]) ).
fof(f42,plain,
! [X0] : '1' = '+'('1',X0),
inference(superposition,[],[f27,f38]) ).
fof(f54,plain,
! [X0] :
( ~ '>='('0',X0)
| '0' = X0 ),
inference(resolution,[],[f31,f34]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ '>='('==>'(X0,X2),X1)
| '==>'(X0,X2) = X1
| ~ '>='('+'(X0,X1),X2) ),
inference(resolution,[],[f32,f31]) ).
fof(f62,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[],[f33,f29]) ).
fof(f88,plain,
sK0 != '==>'('==>'('1',sK0),sK0),
inference(superposition,[],[f40,f39]) ).
fof(f89,plain,
! [X2,X0,X1] :
( '>='(X2,'==>'('==>'(X0,X1),X1))
| ~ '>='('+'('==>'(X1,X0),X2),X0) ),
inference(superposition,[],[f32,f39]) ).
fof(f111,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
inference(resolution,[],[f35,f34]) ).
fof(f115,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_demodulation,[],[f111,f41]) ).
fof(f125,plain,
! [X0] : '>='('1',X0),
inference(superposition,[],[f115,f42]) ).
fof(f137,plain,
! [X0] :
( ~ '>='(X0,'1')
| '1' = X0 ),
inference(resolution,[],[f125,f31]) ).
fof(f304,plain,
! [X0] : '>='('==>'('0',X0),X0),
inference(superposition,[],[f62,f41]) ).
fof(f313,plain,
'1' = '==>'('0','1'),
inference(resolution,[],[f304,f137]) ).
fof(f334,plain,
! [X0] :
( '>='(X0,'==>'('1','1'))
| ~ '>='('+'('==>'('1','0'),X0),'0') ),
inference(superposition,[],[f89,f313]) ).
fof(f337,plain,
! [X0] : '>='(X0,'==>'('1','1')),
inference(forward_subsumption_resolution,[],[f334,f34]) ).
fof(f344,plain,
'0' = '==>'('1','1'),
inference(resolution,[],[f337,f54]) ).
fof(f369,plain,
! [X0] :
( '>='('0','==>'('1',X0))
| ~ '>='('1',X0) ),
inference(superposition,[],[f37,f344]) ).
fof(f374,plain,
! [X0] : '>='('0','==>'('1',X0)),
inference(forward_subsumption_resolution,[],[f369,f125]) ).
fof(f392,plain,
! [X0] : '0' = '==>'('1',X0),
inference(resolution,[],[f374,f54]) ).
fof(f437,plain,
sK0 != '==>'('0',sK0),
inference(superposition,[],[f88,f392]) ).
fof(f552,plain,
! [X0] :
( '==>'('0',X0) = X0
| ~ '>='('+'('0',X0),X0) ),
inference(resolution,[],[f60,f304]) ).
fof(f567,plain,
! [X0] : '==>'('0',X0) = X0,
inference(forward_subsumption_resolution,[],[f552,f115]) ).
fof(f589,plain,
sK0 != sK0,
inference(superposition,[],[f437,f567]) ).
fof(f590,plain,
$false,
inference(trivial_inequality_removal,[],[f589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 17:06:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.57/1.33 % (3611407)Detected formulas, will run a generic FOF schedule.
% 2.57/1.33 % (3611417)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3491289739:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.33 % (3611417)First to succeed.
% 2.57/1.33 % (3611417)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3611407"
% 2.57/1.33 % (3611412)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=757632005:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.33 % (3611415)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1675311519:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.33 % (3611413)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=141094013:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.33 % (3611418)dis-21_1_sil=8000:lcm=predicate:random_seed=19814083: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)
% 2.57/1.33 % (3611414)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=160437428:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.33 % (3611416)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4196736784:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.33 % (3611415)Refutation not found, incomplete strategy
% 2.57/1.33 % (3611415)------------------------------
% 2.57/1.33 % (3611415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.33 % (3611415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.33 % (3611415)CaDiCaL version: 2.1.3
% 2.57/1.33 % (3611415)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.33 % (3611415)Time elapsed: 0.001 s
% 2.57/1.33 % (3611415)Peak memory usage: 88 MB
% 2.57/1.33 % (3611416)Instruction limit reached!
% 2.57/1.33 % (3611416)------------------------------
% 2.57/1.33 % (3611416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.33 % (3611416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.33 % (3611416)CaDiCaL version: 2.1.3
% 2.57/1.33 % (3611416)Termination reason: Instruction limit
% 2.57/1.33 % (3611416)Termination phase: Saturation
% 2.57/1.33 % (3611416)Time elapsed: 0.066 s
% 2.57/1.33 % (3611416)Peak memory usage: 88 MB
% 2.57/1.33 % (3611416)Instructions burned: 120 (million)
% 2.57/1.33 % (3611418)Instruction limit reached!
% 2.57/1.33 % (3611418)------------------------------
% 2.57/1.33 % (3611418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.33 % (3611418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.33 % (3611418)CaDiCaL version: 2.1.3
% 2.57/1.33 % (3611418)Termination reason: Instruction limit
% 2.57/1.33 % (3611418)Termination phase: Saturation
% 2.57/1.33 % (3611418)Time elapsed: 0.083 s
% 2.57/1.33 % (3611418)Peak memory usage: 89 MB
% 2.57/1.33 % (3611418)Instructions burned: 130 (million)
% 2.57/1.33 % (3611417)Refutation found. Thanks to Tanya!
% 2.57/1.33 % SZS status Theorem for theBenchmark
% 2.57/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.33 % (3611417)------------------------------
% 2.57/1.33 % (3611417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.33 % (3611417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.33 % (3611417)CaDiCaL version: 2.1.3
% 2.57/1.33 % (3611417)Termination reason: Refutation
% 2.57/1.33 % (3611417)Time elapsed: 0.008 s
% 2.57/1.33 % (3611417)Peak memory usage: 89 MB
% 2.57/1.33 % (3611417)Instructions burned: 19 (million)
% 2.57/1.33 % (3611417)------------------------------
% 2.57/1.33 % (3611417)------------------------------
% 2.57/1.33 % (3611407)Success in time 0.275 s
% 2.57/1.33 % Vampire exiting
%------------------------------------------------------------------------------