%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM713_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:16:40 PM UTC 2026
% Result : Theorem 2.72s 1.35s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 19 !; 1 ?; 20 :)
% 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(func_def_4,type,
ts: ( nat * nat ) > nat ).
tff(func_def_7,type,
sK0: nat ).
tff(f1,axiom,
~ ! [X0: nat] : ( x != pl(y,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(f3,axiom,
! [X0: nat,X1: nat] : ( ts(X0,X1) = ts(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] : ( ts(X0,pl(X1,X2)) = pl(ts(X0,X1),ts(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz30) ).
tff(f5,conjecture,
~ ! [X0: nat] : ( ts(x,z) != pl(ts(y,z),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz32a) ).
tff(f6,negated_conjecture,
~ ~ ! [X0: nat] : ( ts(x,z) != pl(ts(y,z),X0) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f9,plain,
! [X0: nat] : ( ts(x,z) != pl(ts(y,z),X0) ),
inference(flattening,[],[f6]) ).
tff(f10,plain,
? [X0: nat] : ( x = pl(y,X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f11,plain,
x = pl(y,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
tff(f12,plain,
! [X0: nat] : ( ts(x,z) != pl(ts(y,z),X0) ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
x = pl(y,sK0),
inference(cnf_transformation,[],[f11]) ).
tff(f14,plain,
! [X2: nat,X0: nat,X1: nat] : ( ts(X0,pl(X1,X2)) = pl(ts(X0,X1),ts(X0,X2)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f15,plain,
! [X0: nat,X1: nat] : ( ts(X0,X1) = ts(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
tff(f16,plain,
! [X2: nat,X0: nat,X1: nat] : ( ts(X1,pl(X0,X2)) = pl(ts(X0,X1),ts(X1,X2)) ),
inference(superposition,[],[f14,f15]) ).
tff(f25,plain,
! [X0: nat] : ( ts(x,z) != ts(z,pl(y,X0)) ),
inference(superposition,[],[f12,f16]) ).
tff(f26,plain,
ts(x,z) != ts(z,x),
inference(superposition,[],[f25,f13]) ).
tff(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM713_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.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 21:12:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.72/1.35 % (2757404)Detected formulas, will run a generic FOF schedule.
% 2.72/1.35 % (2757413)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1016927247:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.35 % (2757413)First to succeed.
% 2.72/1.35 % (2757413)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2757404"
% 2.72/1.35 % (2757415)dis-21_1_sil=8000:lcm=predicate:random_seed=214537963: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)
% 2.72/1.35 % (2757412)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2071127473:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.35 % (2757410)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=2796989321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.35 % (2757409)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=1272599941:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.35 % (2757411)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=1891279528:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.35 % (2757414)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3121156485:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.35 % (2757412)Refutation not found, incomplete strategy
% 2.72/1.35 % (2757412)------------------------------
% 2.72/1.35 % (2757412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (2757415)Refutation not found, incomplete strategy
% 2.72/1.35 % (2757415)------------------------------
% 2.72/1.35 % (2757415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (2757415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (2757412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (2757415)CaDiCaL version: 2.1.3
% 2.72/1.35 % (2757412)CaDiCaL version: 2.1.3
% 2.72/1.35 % (2757415)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.35 % (2757415)Time elapsed: 0.001 s
% 2.72/1.35 % (2757412)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.35 % (2757412)Time elapsed: 0.001 s
% 2.72/1.35 % (2757415)Peak memory usage: 88 MB
% 2.72/1.35 % (2757412)Peak memory usage: 88 MB
% 2.72/1.35 % (2757414)Also succeeded, but the first one will report.
% 2.72/1.35 % (2757413)Refutation found. Thanks to Tanya!
% 2.72/1.35 % SZS status Theorem for theBenchmark
% 2.72/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.35 % (2757413)------------------------------
% 2.72/1.35 % (2757413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (2757413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (2757413)CaDiCaL version: 2.1.3
% 2.72/1.35 % (2757413)Termination reason: Refutation
% 2.72/1.35 % (2757413)Time elapsed: 0.001 s
% 2.72/1.35 % (2757413)Peak memory usage: 88 MB
% 2.72/1.35 % (2757413)Instructions burned: 1 (million)
% 2.72/1.35 % (2757413)------------------------------
% 2.72/1.35 % (2757413)------------------------------
% 2.72/1.35 % (2757404)Success in time 0.297 s
% 2.72/1.35 % Vampire exiting
%------------------------------------------------------------------------------