%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM479+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:15:22 PM UTC 2026
% Result : Theorem 3.68s 1.42s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 76 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 83 ( 37 ~; 24 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f36,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
fof(f39,conjecture,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f42,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f43,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
inference(flattening,[],[f42]) ).
fof(f49,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f50,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f52,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f105,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f110,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f111,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f112,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f113,plain,
sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f115,plain,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f122,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f123,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f170,plain,
sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)),
inference(forward_demodulation,[],[f115,f113]) ).
fof(f200,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f170,f123]) ).
fof(f213,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f200,f110]) ).
fof(f221,plain,
sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f213,f105]) ).
fof(f528,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(superposition,[],[f221,f122]) ).
fof(f563,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f528,f110]) ).
fof(f581,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f563,f105]) ).
fof(f592,plain,
sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl))),
inference(forward_subsumption_resolution,[],[f581,f112]) ).
fof(f594,plain,
sdtasdt0(xn,xm) != sdtasdt0(xn,xm),
inference(forward_demodulation,[],[f592,f111]) ).
fof(f595,plain,
$false,
inference(trivial_inequality_removal,[],[f594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM479+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:06:47 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.68/1.42 % (1274317)Detected formulas, will run a generic FOF schedule.
% 3.68/1.42 % (1274324)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=3004300135:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.42 % (1274328)dis-21_1_sil=8000:lcm=predicate:random_seed=74378626: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)
% 3.68/1.42 % (1274325)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1051684861:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.42 % (1274326)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1044671409:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.42 % (1274322)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=2598744081:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.42 % (1274323)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=3023315203:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.42 % (1274327)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=40281951:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.42 % (1274326)First to succeed.
% 3.68/1.42 % (1274325)Also succeeded, but the first one will report.
% 3.68/1.42 % (1274326)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1274317"
% 3.68/1.42 % (1274328)Instruction limit reached!
% 3.68/1.42 % (1274328)------------------------------
% 3.68/1.42 % (1274328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.42 % (1274328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.42 % (1274328)CaDiCaL version: 2.1.3
% 3.68/1.42 % (1274328)Termination reason: Instruction limit
% 3.68/1.42 % (1274328)Termination phase: Saturation
% 3.68/1.42 % (1274328)Time elapsed: 0.081 s
% 3.68/1.42 % (1274328)Peak memory usage: 91 MB
% 3.68/1.42 % (1274328)Instructions burned: 131 (million)
% 3.68/1.42 % (1274327)Instruction limit reached!
% 3.68/1.42 % (1274327)------------------------------
% 3.68/1.42 % (1274327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.42 % (1274327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.42 % (1274327)CaDiCaL version: 2.1.3
% 3.68/1.42 % (1274327)Termination reason: Instruction limit
% 3.68/1.42 % (1274327)Termination phase: Saturation
% 3.68/1.42 % (1274327)Time elapsed: 0.088 s
% 3.68/1.42 % (1274327)Peak memory usage: 90 MB
% 3.68/1.42 % (1274327)Instructions burned: 140 (million)
% 3.68/1.42 % (1274337)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2335243947:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.68/1.42 % (1274336)lrs+10_1_sil=8000:sp=occurrence:random_seed=1014806457:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.68/1.42 % (1274326)Refutation found. Thanks to Tanya!
% 3.68/1.42 % SZS status Theorem for theBenchmark
% 3.68/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.43 % (1274326)------------------------------
% 3.68/1.43 % (1274326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.43 % (1274326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.43 % (1274326)CaDiCaL version: 2.1.3
% 3.68/1.43 % (1274326)Termination reason: Refutation
% 3.68/1.43 % (1274326)Time elapsed: 0.011 s
% 3.68/1.43 % (1274326)Peak memory usage: 88 MB
% 3.68/1.43 % (1274326)Instructions burned: 16 (million)
% 3.68/1.43 % (1274326)------------------------------
% 3.68/1.43 % (1274326)------------------------------
% 3.68/1.43 % (1274317)Success in time 0.447 s
% 3.68/1.43 % Vampire exiting
%------------------------------------------------------------------------------