%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM654_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 : n005.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 12:16:14 PM UTC 2026
% Result : Theorem 2.65s 1.37s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 52 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 15 |; 1 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(pred_def_1,type,
more: ( nat * nat ) > $o ).
tff(pred_def_2,type,
less: ( nat * nat ) > $o ).
tff(pred_def_3,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(pred_def_4,type,
sQ1_eqProxy: ( nat * nat ) > $o ).
tff(f1,axiom,
~ more(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
tff(f3,axiom,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ more(X0,X1)
=> less(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a) ).
tff(f4,conjecture,
( ~ less(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10e) ).
tff(f5,negated_conjecture,
~ ( ~ less(x,y)
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f10,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f11,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ( x != y )
& ~ less(x,y) ),
inference(ennf_transformation,[],[f5]) ).
tff(f13,plain,
~ more(x,y),
inference(cnf_transformation,[],[f1]) ).
tff(f15,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f16,plain,
~ less(x,y),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
x != y,
inference(cnf_transformation,[],[f12]) ).
tff(f25,definition,
! [X0: nat,X1: nat] :
( sQ1_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f26,plain,
! [X0: nat,X1: nat] :
( sQ1_eqProxy(X0,X1)
| more(X0,X1)
| less(X0,X1) ),
inference(equality_proxy_replacement,[],[f15,f25]) ).
tff(f27,plain,
~ sQ1_eqProxy(x,y),
inference(equality_proxy_replacement,[],[f17,f25]) ).
tff(f36,plain,
( more(x,y)
| less(x,y) ),
inference(resolution,[],[f26,f27]) ).
tff(f46,definition,
( spl2_3
<=> less(x,y) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f47,plain,
( less(x,y)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f49,definition,
( spl2_4
<=> more(x,y) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f50,plain,
( more(x,y)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f51,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f36,f49,f46]) ).
tff(f52,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f47,f16]) ).
tff(f53,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f52]) ).
tff(f54,plain,
( $false
| ~ spl2_4 ),
inference(resolution,[],[f50,f13]) ).
tff(f55,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
tff(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM654_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n005.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:57:47 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 2.65/1.37 % (153043)Detected formulas, will run a generic FOF schedule.
% 2.65/1.37 % (153054)dis-21_1_sil=8000:lcm=predicate:random_seed=670953893: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)
% 2.65/1.37 % (153054)First to succeed.
% 2.65/1.37 % (153054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-153043"
% 2.65/1.37 % (153048)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=1635440531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.37 % (153051)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2544798909:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.37 % (153050)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=5032100:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.37 % (153049)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=3851562039:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.37 % (153052)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=720634321:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.37 % (153053)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2114254290:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.37 % (153052)Also succeeded, but the first one will report.
% 2.65/1.37 % (153051)Also succeeded, but the first one will report.
% 2.65/1.37 % (153053)Also succeeded, but the first one will report.
% 2.65/1.37 % (153054)Refutation found. Thanks to Tanya!
% 2.65/1.37 % SZS status Theorem for theBenchmark
% 2.65/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.37 % (153054)------------------------------
% 2.65/1.37 % (153054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (153054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (153054)CaDiCaL version: 2.1.3
% 2.65/1.37 % (153054)Termination reason: Refutation
% 2.65/1.37 % (153054)Time elapsed: 0.001 s
% 2.65/1.37 % (153054)Peak memory usage: 89 MB
% 2.65/1.37 % (153054)Instructions burned: 1 (million)
% 2.65/1.37 % (153054)------------------------------
% 2.65/1.37 % (153054)------------------------------
% 2.65/1.37 % (153043)Success in time 0.294 s
% 2.65/1.37 % Vampire exiting
%------------------------------------------------------------------------------