%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM670_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 : n014.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 12:16:22 PM UTC 2026
% Result : Theorem 3.66s 1.47s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 18 !; 1 ?; 19 :)
% 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_6,type,
sK0: nat ).
tff(f1,axiom,
~ ! [X0: nat] : ( x != pl(y,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(f3,axiom,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
tff(f5,conjecture,
~ ! [X0: nat] : ( pl(x,z) != pl(pl(y,z),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
tff(f6,negated_conjecture,
~ ~ ! [X0: nat] : ( pl(x,z) != pl(pl(y,z),X0) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f10,plain,
! [X0: nat] : ( pl(x,z) != pl(pl(y,z),X0) ),
inference(flattening,[],[f6]) ).
tff(f11,plain,
? [X0: nat] : ( x = pl(y,X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f13,plain,
x = pl(y,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
tff(f14,plain,
x = pl(y,sK0),
inference(cnf_transformation,[],[f13]) ).
tff(f16,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
tff(f17,plain,
! [X2: nat,X0: nat,X1: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f18,plain,
! [X0: nat] : ( pl(x,z) != pl(pl(y,z),X0) ),
inference(cnf_transformation,[],[f10]) ).
tff(f26,plain,
! [X0: nat] : ( pl(y,pl(sK0,X0)) = pl(x,X0) ),
inference(superposition,[],[f17,f14]) ).
tff(f32,plain,
! [X0: nat] : ( pl(x,z) != pl(y,pl(z,X0)) ),
inference(superposition,[],[f18,f17]) ).
tff(f38,plain,
! [X0: nat] : ( pl(x,z) != pl(y,pl(X0,z)) ),
inference(superposition,[],[f32,f16]) ).
tff(f45,plain,
pl(x,z) != pl(x,z),
inference(superposition,[],[f38,f26]) ).
tff(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM670_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 21:02:31 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.66/1.47 % (1159822)Detected formulas, will run a generic FOF schedule.
% 3.66/1.47 % (1159827)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=1806180578:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.47 % (1159829)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=3594046391:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.47 % (1159831)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1354194371:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.47 % (1159830)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2601206048:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.47 % (1159828)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=3102199565:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.47 % (1159833)dis-21_1_sil=8000:lcm=predicate:random_seed=948660572: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)
% 3.66/1.47 % (1159832)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3233262412:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.47 % (1159833)Refutation not found, incomplete strategy
% 3.66/1.47 % (1159833)------------------------------
% 3.66/1.47 % (1159833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (1159833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (1159833)CaDiCaL version: 2.1.3
% 3.66/1.47 % (1159833)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.47 % (1159833)Time elapsed: 0.001 s
% 3.66/1.47 % (1159833)Peak memory usage: 88 MB
% 3.66/1.47 % (1159832)First to succeed.
% 3.66/1.47 % (1159831)Also succeeded, but the first one will report.
% 3.66/1.47 % (1159832)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1159822"
% 3.66/1.47 % (1159830)Instruction limit reached!
% 3.66/1.47 % (1159830)------------------------------
% 3.66/1.47 % (1159830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (1159830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (1159830)CaDiCaL version: 2.1.3
% 3.66/1.47 % (1159830)Termination reason: Instruction limit
% 3.66/1.47 % (1159830)Termination phase: Saturation
% 3.66/1.47 % (1159830)Time elapsed: 0.053 s
% 3.66/1.47 % (1159830)Peak memory usage: 88 MB
% 3.66/1.47 % (1159830)Instructions burned: 110 (million)
% 3.66/1.47 % (1159841)lrs+10_1_sil=8000:sp=occurrence:random_seed=1011604807:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.47 % (1159841)Also succeeded, but the first one will report.
% 3.66/1.47 % (1159833)------------------------------
% 3.66/1.47 % (1159833)------------------------------
% 3.66/1.47 % (1159832)Refutation found. Thanks to Tanya!
% 3.66/1.47 % SZS status Theorem for theBenchmark
% 3.66/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.47 % (1159832)------------------------------
% 3.66/1.47 % (1159832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (1159832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (1159832)CaDiCaL version: 2.1.3
% 3.66/1.47 % (1159832)Termination reason: Refutation
% 3.66/1.47 % (1159832)Time elapsed: 0.003 s
% 3.66/1.47 % (1159832)Peak memory usage: 88 MB
% 3.66/1.47 % (1159832)Instructions burned: 2 (million)
% 3.66/1.47 % (1159832)------------------------------
% 3.66/1.47 % (1159832)------------------------------
% 3.66/1.47 % (1159822)Success in time 0.438 s
% 3.66/1.47 % Vampire exiting
%------------------------------------------------------------------------------