%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM667_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 : 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 12:16:21 PM UTC 2026
% Result : Theorem 3.22s 1.24s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 22 ~; 15 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 13 ( 13 !; 0 ?; 13 :)
% 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(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(f1,axiom,
( ~ less(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
( ~ less(y,z)
=> ( y = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
tff(f5,axiom,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X1)
=> ( ( ~ less(X1,X2)
=> ( X1 = X2 ) )
=> less(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16b) ).
tff(f6,conjecture,
( ~ less(x,z)
=> ( x = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz17) ).
tff(f7,negated_conjecture,
~ ( ~ less(x,z)
=> ( x = z ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f10,plain,
( ( x != z )
& ~ less(x,z) ),
inference(ennf_transformation,[],[f7]) ).
tff(f11,plain,
( ( x = y )
| less(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ( ( X1 != X2 )
& ~ less(X1,X2) )
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ( ( X1 != X2 )
& ~ less(X1,X2) )
| ~ less(X0,X1) ),
inference(flattening,[],[f12]) ).
tff(f16,plain,
( ( y = z )
| less(y,z) ),
inference(ennf_transformation,[],[f2]) ).
tff(f17,plain,
~ less(x,z),
inference(cnf_transformation,[],[f10]) ).
tff(f18,plain,
x != z,
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
( less(x,y)
| ( x = y ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tff(f24,plain,
( less(y,z)
| ( y = z ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
! [X0: nat] :
( ~ less(x,X0)
| ~ less(X0,z) ),
inference(resolution,[],[f20,f17]) ).
tff(f28,plain,
( ~ less(y,z)
| ( x = y ) ),
inference(resolution,[],[f27,f19]) ).
tff(f30,plain,
( ( y = z )
| ( x = y ) ),
inference(resolution,[],[f28,f24]) ).
tff(f38,plain,
( ~ less(x,y)
| ( x = y ) ),
inference(superposition,[],[f17,f30]) ).
tff(f40,plain,
x = y,
inference(forward_subsumption_resolution,[],[f38,f19]) ).
tff(f41,plain,
( less(x,z)
| ( x = z ) ),
inference(superposition,[],[f24,f40]) ).
tff(f42,plain,
x = z,
inference(forward_subsumption_resolution,[],[f41,f17]) ).
tff(f43,plain,
$false,
inference(forward_subsumption_resolution,[],[f42,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM667_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n014.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 21:01:17 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.22/1.24 % (1157053)Detected formulas, will run a generic FOF schedule.
% 3.22/1.24 % (1157063)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1523144932:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.22/1.24 % (1157058)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=3749600683:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.22/1.24 % (1157062)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3249411451:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.22/1.24 % (1157059)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=969783703:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.22/1.24 % (1157060)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=3158040073:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.22/1.24 % (1157064)dis-21_1_sil=8000:lcm=predicate:random_seed=2054528866:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 3.22/1.24 % (1157061)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3382359412:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.22/1.24 % (1157061)Refutation not found, incomplete strategy
% 3.22/1.24 % (1157061)------------------------------
% 3.22/1.24 % (1157061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.24 % (1157061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.24 % (1157061)CaDiCaL version: 2.1.3
% 3.22/1.24 % (1157061)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.24 % (1157061)Time elapsed: 0.001 s
% 3.22/1.24 % (1157061)Peak memory usage: 88 MB
% 3.22/1.24 % (1157062)First to succeed.
% 3.22/1.24 % (1157062)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1157053"
% 3.22/1.24 % (1157063)Also succeeded, but the first one will report.
% 3.22/1.24 % (1157064)Instruction limit reached!
% 3.22/1.24 % (1157064)------------------------------
% 3.22/1.24 % (1157064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.24 % (1157064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.24 % (1157064)CaDiCaL version: 2.1.3
% 3.22/1.24 % (1157064)Termination reason: Instruction limit
% 3.22/1.24 % (1157064)Termination phase: Saturation
% 3.22/1.24 % (1157064)Time elapsed: 0.047 s
% 3.22/1.24 % (1157064)Peak memory usage: 88 MB
% 3.22/1.24 % (1157064)Instructions burned: 131 (million)
% 3.22/1.24 % (1157072)lrs+10_1_sil=8000:sp=occurrence:random_seed=1920798431:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.22/1.24 % (1157072)Also succeeded, but the first one will report.
% 3.22/1.24 % (1157061)------------------------------
% 3.22/1.24 % (1157061)------------------------------
% 3.22/1.24 % (1157062)Refutation found. Thanks to Tanya!
% 3.22/1.24 % SZS status Theorem for theBenchmark
% 3.22/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.22/1.24 % (1157062)------------------------------
% 3.22/1.24 % (1157062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.24 % (1157062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.24 % (1157062)CaDiCaL version: 2.1.3
% 3.22/1.24 % (1157062)Termination reason: Refutation
% 3.22/1.24 % (1157062)Time elapsed: 0.002 s
% 3.22/1.24 % (1157062)Peak memory usage: 88 MB
% 3.22/1.24 % (1157062)Instructions burned: 1 (million)
% 3.22/1.24 % (1157062)------------------------------
% 3.22/1.24 % (1157062)------------------------------
% 3.22/1.24 % (1157053)Success in time 0.39 s
% 3.22/1.24 % Vampire exiting
%------------------------------------------------------------------------------