%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM613+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:15:59 PM UTC 2026
% Result : Theorem 3.98s 1.47s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 57 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 55 ( 22 ~; 18 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f109,axiom,
( sbrdtbr0(xQ) = szszuzczcdt0(xk)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5255) ).
fof(f110,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f111,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f110]) ).
fof(f134,plain,
xk != sbrdtbr0(xP),
inference(flattening,[],[f111]) ).
fof(f165,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f166,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f165]) ).
fof(f263,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f506,plain,
! [X0,X1] :
( szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f654,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f655,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f849,plain,
xK = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f263]) ).
fof(f880,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cnf_transformation,[],[f109]) ).
fof(f881,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)),
inference(cnf_transformation,[],[f109]) ).
fof(f883,plain,
xk != sbrdtbr0(xP),
inference(cnf_transformation,[],[f134]) ).
fof(f972,plain,
xK = szszuzczcdt0(sbrdtbr0(xP)),
inference(forward_demodulation,[],[f881,f849]) ).
fof(f1496,plain,
! [X0] :
( szszuzczcdt0(X0) != xK
| xk = X0
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f506,f654]) ).
fof(f1503,plain,
! [X0] :
( szszuzczcdt0(X0) != xK
| xk = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1496,f655]) ).
fof(f2530,plain,
( xK != xK
| xk = sbrdtbr0(xP)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[],[f1503,f972]) ).
fof(f2532,plain,
( xk = sbrdtbr0(xP)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(trivial_inequality_removal,[],[f2530]) ).
fof(f2534,plain,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(forward_subsumption_resolution,[],[f2532,f883]) ).
fof(f2536,plain,
$false,
inference(forward_subsumption_resolution,[],[f2534,f880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n013.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:45:06 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 3.98/1.47 % (535259)Detected formulas, will run a generic FOF schedule.
% 3.98/1.47 % (535267)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=909675486:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.98/1.47 % (535267)Instruction limit reached!
% 3.98/1.47 % (535267)------------------------------
% 3.98/1.47 % (535267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535267)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535267)Termination reason: Instruction limit
% 3.98/1.47 % (535267)Termination phase: Saturation
% 3.98/1.47 % (535267)Time elapsed: 0.037 s
% 3.98/1.47 % (535267)Peak memory usage: 90 MB
% 3.98/1.47 % (535267)Instructions burned: 112 (million)
% 3.98/1.47 % (535264)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=3538365875:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.98/1.47 % (535266)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=3671885600:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.98/1.47 % (535269)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2779043129:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.98/1.47 % (535268)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=89456355:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.98/1.47 % (535265)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=1081461998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.98/1.47 % (535270)dis-21_1_sil=8000:lcm=predicate:random_seed=4119580728: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)
% 3.98/1.47 % (535269)First to succeed.
% 3.98/1.47 % (535269)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-535259"
% 3.98/1.47 % (535268)Instruction limit reached!
% 3.98/1.47 % (535268)------------------------------
% 3.98/1.47 % (535268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535268)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535268)Termination reason: Instruction limit
% 3.98/1.47 % (535268)Termination phase: Saturation
% 3.98/1.47 % (535268)Time elapsed: 0.078 s
% 3.98/1.47 % (535268)Peak memory usage: 89 MB
% 3.98/1.47 % (535268)Instructions burned: 122 (million)
% 3.98/1.47 % (535270)Instruction limit reached!
% 3.98/1.47 % (535270)------------------------------
% 3.98/1.47 % (535270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535270)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535270)Termination reason: Instruction limit
% 3.98/1.47 % (535270)Termination phase: Saturation
% 3.98/1.47 % (535270)Time elapsed: 0.068 s
% 3.98/1.47 % (535270)Peak memory usage: 90 MB
% 3.98/1.47 % (535270)Instructions burned: 129 (million)
% 3.98/1.47 % (535272)lrs+10_1_sil=8000:sp=occurrence:random_seed=2754321513:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.98/1.47 % (535272)Instruction limit reached!
% 3.98/1.47 % (535272)------------------------------
% 3.98/1.47 % (535272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535272)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535272)Termination reason: Instruction limit
% 3.98/1.47 % (535272)Termination phase: Saturation
% 3.98/1.47 % (535272)Time elapsed: 0.095 s
% 3.98/1.47 % (535272)Peak memory usage: 92 MB
% 3.98/1.47 % (535272)Instructions burned: 287 (million)
% 3.98/1.47 % (535280)lrs+1011_1_sil=32000:sp=occurrence:random_seed=333252813:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.98/1.47 % (535279)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1593270000:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.98/1.47 % (535279)Refutation not found, incomplete strategy
% 3.98/1.47 % (535279)------------------------------
% 3.98/1.47 % (535279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535279)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535279)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.47 % (535279)Time elapsed: 0.003 s
% 3.98/1.47 % (535279)Peak memory usage: 88 MB
% 3.98/1.47 % (535279)Instructions burned: 3 (million)
% 3.98/1.47 % (535269)Refutation found. Thanks to Tanya!
% 3.98/1.47 % SZS status Theorem for theBenchmark
% 3.98/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.47 % (535269)------------------------------
% 3.98/1.47 % (535269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.47 % (535269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.47 % (535269)CaDiCaL version: 2.1.3
% 3.98/1.47 % (535269)Termination reason: Refutation
% 3.98/1.47 % (535269)Time elapsed: 0.062 s
% 3.98/1.47 % (535269)Peak memory usage: 90 MB
% 3.98/1.47 % (535269)Instructions burned: 87 (million)
% 3.98/1.47 % (535269)------------------------------
% 3.98/1.47 % (535269)------------------------------
% 3.98/1.47 % (535259)Success in time 0.495 s
% 3.98/1.47 % Vampire exiting
%------------------------------------------------------------------------------