%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:00:57 PM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 42 unt; 0 def)
% Number of atoms : 90 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 27 ~; 22 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 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 : 98 ( 97 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] : '>='(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f6,axiom,
! [X0,X1] :
( ( '>='(X0,X1)
& '>='(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
<=> '>='(X1,'==>'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0] : '>='(X0,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f9,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('+'(X0,X2),'+'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(f12,axiom,
! [X0] : '+'(X0,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(f13,axiom,
! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(f14,conjecture,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
file('/export/starexec/sandbox/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(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] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,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,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : '1' = '+'(X0,'1'),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0] : '0' = '==>'('==>'('==>'(X0,'1'),X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0] : '1' = '+'('1',X0),
inference(superposition,[],[f27,f38]) ).
fof(f122,plain,
! [X0] :
( ~ '>='('0',X0)
| '0' = X0 ),
inference(resolution,[],[f31,f34]) ).
fof(f212,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[],[f32,f29]) ).
fof(f214,plain,
! [X0,X1] :
( '>='('0','==>'(X0,X1))
| ~ '>='(X0,X1) ),
inference(superposition,[],[f32,f28]) ).
fof(f262,plain,
! [X0] : '0' = '==>'(X0,'+'(X0,'0')),
inference(resolution,[],[f212,f122]) ).
fof(f266,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X0,X1))),
inference(superposition,[],[f212,f27]) ).
fof(f270,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_demodulation,[],[f262,f28]) ).
fof(f314,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| '0' = '==>'(X0,X1) ),
inference(resolution,[],[f214,f122]) ).
fof(f616,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[],[f33,f29]) ).
fof(f623,plain,
! [X0,X1] :
( ~ '>='(X0,'0')
| '>='('+'(X1,X0),X1) ),
inference(superposition,[],[f33,f270]) ).
fof(f636,plain,
! [X0,X1] : '>='('+'(X1,X0),X1),
inference(forward_subsumption_resolution,[],[f623,f34]) ).
fof(f729,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),X0),
inference(resolution,[],[f636,f314]) ).
fof(f735,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(superposition,[],[f636,f27]) ).
fof(f740,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[],[f735,f32]) ).
fof(f904,plain,
! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
inference(superposition,[],[f616,f39]) ).
fof(f911,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(forward_demodulation,[],[f904,f28]) ).
fof(f980,plain,
! [X0] :
( ~ '>='(X0,'==>'('==>'(X0,'1'),X0))
| '==>'('==>'(X0,'1'),X0) = X0 ),
inference(resolution,[],[f911,f31]) ).
fof(f993,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
inference(forward_subsumption_resolution,[],[f980,f740]) ).
fof(f1046,plain,
! [X2,X0,X1] :
( ~ '>='(X0,'0')
| '>='('+'('+'(X1,X2),X0),X1) ),
inference(superposition,[],[f33,f729]) ).
fof(f1061,plain,
! [X2,X0,X1] : '>='('+'('+'(X1,X2),X0),X1),
inference(forward_subsumption_resolution,[],[f1046,f34]) ).
fof(f1154,plain,
! [X0,X1] : '>='('+'('1',X1),X0),
inference(superposition,[],[f1061,f38]) ).
fof(f1162,plain,
! [X0] : '>='('1',X0),
inference(forward_demodulation,[],[f1154,f42]) ).
fof(f1209,plain,
! [X0,X1] :
( '>='('1','+'(X1,X0))
| ~ '>='('1',X1) ),
inference(superposition,[],[f35,f42]) ).
fof(f1304,plain,
! [X0,X1] : '>='('1','+'(X1,X0)),
inference(global_subsumption,[],[f1209,f1162]) ).
fof(f1311,plain,
! [X0] : '>='('1',X0),
inference(superposition,[],[f1304,f28]) ).
fof(f1316,plain,
! [X0] :
( ~ '>='(X0,'1')
| '1' = X0 ),
inference(resolution,[],[f1311,f31]) ).
fof(f1323,plain,
! [X0] : '1' = '+'(X0,'==>'(X0,'1')),
inference(resolution,[],[f1316,f616]) ).
fof(f1353,plain,
! [X0,X1] :
( ~ '>='('1',X1)
| '>='('==>'(X0,'1'),'==>'(X0,X1)) ),
inference(superposition,[],[f32,f1323]) ).
fof(f1357,plain,
! [X0] : '>='(X0,'==>'('==>'(X0,'1'),'1')),
inference(superposition,[],[f266,f1323]) ).
fof(f1372,plain,
! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(forward_subsumption_resolution,[],[f1353,f1311]) ).
fof(f1421,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
inference(superposition,[],[f1372,f993]) ).
fof(f1431,plain,
! [X0] :
( ~ '>='(X0,'==>'('==>'(X0,'1'),'1'))
| '==>'('==>'(X0,'1'),'1') = X0 ),
inference(resolution,[],[f1421,f31]) ).
fof(f1451,plain,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(forward_subsumption_resolution,[],[f1431,f1357]) ).
fof(f1459,plain,
sK0 != sK0,
inference(superposition,[],[f40,f1451]) ).
fof(f1480,plain,
$false,
inference(trivial_inequality_removal,[],[f1459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 17:05:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 % (1015935)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (1015942)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2299651261:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (1015941)% WARNING: option uhcvi not known.
% 0.13/0.46 % (1015940)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2877018994_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % (1015943)dis+10_1_sil=32000:sp=arity:random_seed=1446704171:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (1015941)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1687765796:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (1015944)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3275938239:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (1015945)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4083139027:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.46 % (1015946)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1145845556:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % TRYING [1]
% 0.13/0.46 % TRYING [2]
% 0.13/0.46 % TRYING [3]
% 0.13/0.46 % TRYING [4]
% 0.13/0.46 % (1015942) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1015935-1015942"...
% 0.13/0.46 % (1015942)...printing done.
% 0.13/0.46 % (1015942)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (1015942)------------------------------
% 0.13/0.46 % (1015942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (1015942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (1015942)CaDiCaL version: 2.1.3
% 0.13/0.46 % (1015942)Termination reason: Refutation
% 0.13/0.46 % (1015942)Time elapsed: 0.015 s
% 0.13/0.46 % (1015942)Peak memory usage: 12 MB
% 0.13/0.46 % (1015942)Instructions burned: 36 (million)
% 0.13/0.46 % (1015935)Success in time 0.045 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------