%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM490+3 : 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 : n026.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 12:15:25 PM UTC 2026
% Result : Theorem 2.63s 1.35s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 6 unt; 1 def)
% Number of atoms : 14 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 2 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
fof(f47,conjecture,
( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm)
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm)
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f121,plain,
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))
& sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f257,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f46]) ).
fof(f259,plain,
sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f121]) ).
fof(f272,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f345,plain,
sQ13_eqProxy(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))),
inference(equality_proxy_replacement,[],[f257,f272]) ).
fof(f346,plain,
~ sQ13_eqProxy(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))),
inference(equality_proxy_replacement,[],[f259,f272]) ).
fof(f398,plain,
$false,
inference(resolution,[],[f345,f346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM490+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:12:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 2.63/1.35 % (3178508)Detected formulas, will run a generic FOF schedule.
% 2.63/1.35 % (3178519)dis-21_1_sil=8000:lcm=predicate:random_seed=1674751779: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)
% 2.63/1.35 % (3178519)First to succeed.
% 2.63/1.35 % (3178519)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3178508"
% 2.63/1.35 % (3178517)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2412576531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.35 % (3178514)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=3690820016:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.35 % (3178513)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=2553469107:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.35 % (3178516)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1352088400:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.35 % (3178515)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=2983837670:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.35 % (3178518)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1607612869:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.35 % (3178517)Also succeeded, but the first one will report.
% 2.63/1.35 % (3178518)Also succeeded, but the first one will report.
% 2.63/1.35 % (3178516)Also succeeded, but the first one will report.
% 2.63/1.35 % (3178519)Refutation found. Thanks to Tanya!
% 2.63/1.35 % SZS status Theorem for theBenchmark
% 2.63/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.35 % (3178519)------------------------------
% 2.63/1.35 % (3178519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.35 % (3178519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.35 % (3178519)CaDiCaL version: 2.1.3
% 2.63/1.35 % (3178519)Termination reason: Refutation
% 2.63/1.35 % (3178519)Time elapsed: 0.003 s
% 2.63/1.35 % (3178519)Peak memory usage: 89 MB
% 2.63/1.35 % (3178519)Instructions burned: 6 (million)
% 2.63/1.35 % (3178519)------------------------------
% 2.63/1.35 % (3178519)------------------------------
% 2.63/1.35 % (3178508)Success in time 0.287 s
% 2.63/1.35 % Vampire exiting
%------------------------------------------------------------------------------