%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM647_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:16:11 PM UTC 2026
% Result : Theorem 3.35s 1.23s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 20 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(func_def_2,type,
z: nat ).
tff(func_def_3,type,
pl: ( nat * nat ) > nat ).
tff(pred_def_1,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(pred_def_2,type,
sQ1_eqProxy: ( nat * nat ) > $o ).
tff(f1,axiom,
pl(x,y) = pl(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i) ).
tff(f3,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( pl(X0,X1) != pl(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8) ).
tff(f4,conjecture,
y = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8a) ).
tff(f5,negated_conjecture,
( ( ~ y ) = z ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f9,plain,
y != z,
inference(flattening,[],[f5]) ).
tff(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl(X0,X1) != pl(X0,X2) )
| ( X1 = X2 ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f12,plain,
pl(x,y) = pl(x,z),
inference(cnf_transformation,[],[f1]) ).
tff(f14,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl(X0,X1) != pl(X0,X2) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f15,plain,
y != z,
inference(cnf_transformation,[],[f9]) ).
tff(f22,definition,
! [X0: nat,X1: nat] :
( sQ1_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f23,plain,
sQ1_eqProxy(pl(x,y),pl(x,z)),
inference(equality_proxy_replacement,[],[f12,f22]) ).
tff(f25,plain,
! [X2: nat,X0: nat,X1: nat] :
( ~ sQ1_eqProxy(pl(X0,X1),pl(X0,X2))
| sQ1_eqProxy(X1,X2) ),
inference(equality_proxy_replacement,[],[f14,f22,f22]) ).
tff(f26,plain,
~ sQ1_eqProxy(y,z),
inference(equality_proxy_replacement,[],[f15,f22]) ).
tff(f36,plain,
sQ1_eqProxy(y,z),
inference(resolution,[],[f25,f23]) ).
tff(f39,plain,
$false,
inference(resolution,[],[f36,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM647_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.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 20:58:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.35/1.23 % (2714318)Detected formulas, will run a generic FOF schedule.
% 3.35/1.23 % (2714327)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1489037659:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.23 % (2714326)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3458598319:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.23 % (2714325)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=2992960965:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.23 % (2714323)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=2046074286:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.23 % (2714328)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2138335995:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.23 % (2714329)dis-21_1_sil=8000:lcm=predicate:random_seed=979372244: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)
% 3.35/1.23 % (2714324)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=4202637605:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.23 % (2714326)Refutation not found, incomplete strategy
% 3.35/1.23 % (2714326)------------------------------
% 3.35/1.23 % (2714326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.23 % (2714327)Refutation not found, incomplete strategy
% 3.35/1.23 % (2714327)------------------------------
% 3.35/1.23 % (2714327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.23 % (2714327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.23 % (2714326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.23 % (2714327)CaDiCaL version: 2.1.3
% 3.35/1.23 % (2714326)CaDiCaL version: 2.1.3
% 3.35/1.23 % (2714327)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.23 % (2714327)Time elapsed: 0.001 s
% 3.35/1.23 % (2714326)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.23 % (2714326)Time elapsed: 0.001 s
% 3.35/1.23 % (2714326)Peak memory usage: 87 MB
% 3.35/1.23 % (2714327)Peak memory usage: 87 MB
% 3.35/1.23 % (2714329)First to succeed.
% 3.35/1.23 % (2714328)Also succeeded, but the first one will report.
% 3.35/1.23 % (2714329)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2714318"
% 3.35/1.23 % (2714326)------------------------------
% 3.35/1.23 % (2714326)------------------------------
% 3.35/1.23 % (2714327)------------------------------
% 3.35/1.23 % (2714327)------------------------------
% 3.35/1.23 % (2714329)Refutation found. Thanks to Tanya!
% 3.35/1.23 % SZS status Theorem for theBenchmark
% 3.35/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.23 % (2714329)------------------------------
% 3.35/1.23 % (2714329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.23 % (2714329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.23 % (2714329)CaDiCaL version: 2.1.3
% 3.35/1.23 % (2714329)Termination reason: Refutation
% 3.35/1.23 % (2714329)Time elapsed: 0.002 s
% 3.35/1.23 % (2714329)Peak memory usage: 88 MB
% 3.35/1.23 % (2714329)Instructions burned: 1 (million)
% 3.35/1.23 % (2714329)------------------------------
% 3.35/1.23 % (2714329)------------------------------
% 3.35/1.23 % (2714318)Success in time 0.417 s
% 3.35/1.23 % Vampire exiting
%------------------------------------------------------------------------------