%------------------------------------------------------------------------------
% File : Vampire---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 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 11:56:58 AM UTC 2026
% Result : Theorem 4.11s 1.55s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 30 unt; 0 def)
% Number of atoms : 75 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 20 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 79 ( 78 !; 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(f11,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('==>'(X2,X0),'==>'(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
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(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] :
( ~ '>='(X0,X1)
| '>='('==>'(X2,X0),'==>'(X2,X1)) ),
inference(cnf_transformation,[],[f22]) ).
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(f41,plain,
! [X0] : '+'('0',X0) = X0,
inference(superposition,[],[f27,f28]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ '>='('==>'(X0,X2),X1)
| '==>'(X0,X2) = X1
| ~ '>='('+'(X0,X1),X2) ),
inference(resolution,[],[f32,f31]) ).
fof(f64,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[],[f33,f29]) ).
fof(f65,plain,
! [X0,X1] :
( ~ '>='(X0,'0')
| '>='('+'('==>'('==>'(X1,'1'),X1),X0),X1) ),
inference(superposition,[],[f33,f39]) ).
fof(f66,plain,
! [X0,X1] : '>='('+'('==>'('==>'(X1,'1'),X1),X0),X1),
inference(forward_subsumption_resolution,[],[f65,f34]) ).
fof(f108,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(superposition,[],[f66,f28]) ).
fof(f109,plain,
! [X0] : '>='('1',X0),
inference(superposition,[],[f66,f38]) ).
fof(f113,plain,
! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(resolution,[],[f109,f37]) ).
fof(f119,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
inference(resolution,[],[f35,f34]) ).
fof(f125,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_demodulation,[],[f119,f41]) ).
fof(f419,plain,
! [X0] :
( '==>'('==>'(X0,'1'),X0) = X0
| ~ '>='('+'('==>'(X0,'1'),X0),X0) ),
inference(resolution,[],[f108,f61]) ).
fof(f430,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
inference(forward_subsumption_resolution,[],[f419,f125]) ).
fof(f906,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
inference(superposition,[],[f113,f430]) ).
fof(f1683,plain,
! [X0] :
( '==>'('==>'(X0,'1'),'1') = X0
| ~ '>='('+'('==>'(X0,'1'),X0),'1') ),
inference(resolution,[],[f906,f61]) ).
fof(f1706,plain,
! [X0] :
( ~ '>='('+'(X0,'==>'(X0,'1')),'1')
| '==>'('==>'(X0,'1'),'1') = X0 ),
inference(forward_demodulation,[],[f1683,f27]) ).
fof(f1707,plain,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(forward_subsumption_resolution,[],[f1706,f64]) ).
fof(f3467,plain,
sK0 != sK0,
inference(superposition,[],[f40,f1707]) ).
fof(f3503,plain,
$false,
inference(trivial_inequality_removal,[],[f3467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:05:06 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.11/1.55 % (422545)Detected formulas, will run a generic FOF schedule.
% 4.11/1.55 % (422550)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=710278001:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.11/1.55 % (422554)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=588635567:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.11/1.55 % (422551)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=3107750482:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.11/1.55 % (422555)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3622519844:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.11/1.55 % (422553)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=707413432:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.11/1.55 % (422556)dis-21_1_sil=8000:lcm=predicate:random_seed=1393082341: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)
% 4.11/1.55 % (422552)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=2222455753:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.11/1.55 % (422553)Refutation not found, incomplete strategy
% 4.11/1.55 % (422553)------------------------------
% 4.11/1.55 % (422553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (422553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (422553)CaDiCaL version: 2.1.3
% 4.11/1.55 % (422553)Termination reason: Refutation not found, incomplete strategy
% 4.11/1.55 % (422553)Time elapsed: 0.001 s
% 4.11/1.55 % (422553)Peak memory usage: 88 MB
% 4.11/1.55 % (422555)First to succeed.
% 4.11/1.55 % (422555)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-422545"
% 4.11/1.55 % (422554)Instruction limit reached!
% 4.11/1.55 % (422554)------------------------------
% 4.11/1.55 % (422554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (422554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (422554)CaDiCaL version: 2.1.3
% 4.11/1.55 % (422554)Termination reason: Instruction limit
% 4.11/1.55 % (422554)Termination phase: Saturation
% 4.11/1.55 % (422554)Time elapsed: 0.069 s
% 4.11/1.55 % (422554)Peak memory usage: 88 MB
% 4.11/1.55 % (422554)Instructions burned: 119 (million)
% 4.11/1.55 % (422556)Instruction limit reached!
% 4.11/1.55 % (422556)------------------------------
% 4.11/1.55 % (422556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (422556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (422556)CaDiCaL version: 2.1.3
% 4.11/1.55 % (422556)Termination reason: Instruction limit
% 4.11/1.55 % (422556)Termination phase: Saturation
% 4.11/1.55 % (422556)Time elapsed: 0.080 s
% 4.11/1.55 % (422556)Peak memory usage: 88 MB
% 4.11/1.55 % (422556)Instructions burned: 130 (million)
% 4.11/1.55 % (422564)lrs+10_1_sil=8000:sp=occurrence:random_seed=2170348317:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.11/1.55 % (422565)lrs+10_1_sil=32000:urr=on:br=off:random_seed=956068618:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.11/1.55 % (422553)------------------------------
% 4.11/1.55 % (422553)------------------------------
% 4.11/1.55 % (422564)Also succeeded, but the first one will report.
% 4.11/1.55 % (422555)Refutation found. Thanks to Tanya!
% 4.11/1.55 % SZS status Theorem for theBenchmark
% 4.11/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.55 % (422555)------------------------------
% 4.11/1.55 % (422555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (422555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (422555)CaDiCaL version: 2.1.3
% 4.11/1.55 % (422555)Termination reason: Refutation
% 4.11/1.55 % (422555)Time elapsed: 0.065 s
% 4.11/1.55 % (422555)Peak memory usage: 89 MB
% 4.11/1.55 % (422555)Instructions burned: 120 (million)
% 4.11/1.55 % (422555)------------------------------
% 4.11/1.55 % (422555)------------------------------
% 4.11/1.55 % (422545)Success in time 0.495 s
% 4.11/1.55 % Vampire exiting
%------------------------------------------------------------------------------