%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM913_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:17:25 PM UTC 2026
% Result : Theorem 3.84s 1.39s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 1 unt; 0 typ; 3 def)
% Number of atoms : 54 ( 14 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 57 ( 21 ~; 22 |; 6 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number arithmetic : 43 ( 29 atm; 0 fun; 0 num; 14 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 14 ( 8 !; 6 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $real ).
tff(func_def_5,type,
sK1: $real ).
tff(f1,conjecture,
! [X1: $real,X0: $real] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_combined_problem_1) ).
tff(f2,negated_conjecture,
~ ! [X1: $real,X0: $real] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> $lesseq(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $real,X0: $real] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f2]) ).
tff(f15,plain,
~ ! [X1: $real,X0: $real] :
( ~ $less(X0,X1)
<=> ( $less(X1,X0)
| ( X0 = X1 ) ) ),
inference(rectify,[],[f3]) ).
tff(f16,plain,
? [X0: $real,X1: $real] :
( ( $less(X1,X0)
| ( X0 = X1 ) )
<~> ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
? [X0: $real,X1: $real] :
( ( $less(X0,X1)
| ( ~ $less(X1,X0)
& ( X0 != X1 ) ) )
& ( ~ $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f18,plain,
? [X0: $real,X1: $real] :
( ( $less(X0,X1)
| ( ~ $less(X1,X0)
& ( X0 != X1 ) ) )
& ( ~ $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ( $less(sK0,sK1)
| ( ~ $less(sK1,sK0)
& ( sK0 != sK1 ) ) )
& ( ~ $less(sK0,sK1)
| $less(sK1,sK0)
| ( sK0 = sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
tff(f20,plain,
( ~ $less(sK0,sK1)
| ( sK0 = sK1 )
| $less(sK1,sK0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
( $less(sK0,sK1)
| ( sK0 != sK1 ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f22,plain,
( $less(sK0,sK1)
| ~ $less(sK1,sK0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f24,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f28,definition,
( spl2_2
<=> $less(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f32,definition,
( spl2_3
<=> $less(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f35,plain,
( spl2_1
| spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f20,f32,f28,f24]) ).
tff(f36,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f22,f28,f32]) ).
tff(f37,plain,
( spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f21,f24,f32]) ).
tff(f38,plain,
$false,
inference(avatar_smt_refutation,[],[f37,f36,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM913_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 % Computer : n012.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sun Sep 27 21:39:04 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 Running first-order theorem proving
% 0.10/0.37 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
% 3.84/1.39 % (2769845)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.84/1.39 % (2769853)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3231010652:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.84/1.39 % (2769853)Instruction limit reached!
% 3.84/1.39 % (2769853)------------------------------
% 3.84/1.39 % (2769853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.39 % (2769853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.39 % (2769853)CaDiCaL version: 2.1.3
% 3.84/1.39 % (2769853)Termination reason: Instruction limit
% 3.84/1.39 % (2769853)Termination phase: Saturation
% 3.84/1.39 % (2769853)Time elapsed: 0.005 s
% 3.84/1.39 % (2769853)Peak memory usage: 88 MB
% 3.84/1.39 % (2769853)Instructions burned: 7 (million)
% 3.84/1.39 % (2769852)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2245395687:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.84/1.39 % (2769855)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3627144391:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.84/1.39 % (2769851)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3149995289:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.84/1.39 % (2769856)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3428643043:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.84/1.39 % (2769850)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2650708007:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.84/1.39 % (2769854)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2728118063:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.84/1.39 % (2769854)Instruction limit reached!
% 3.84/1.39 % (2769854)------------------------------
% 3.84/1.39 % (2769854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.39 % (2769854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.39 % (2769854)CaDiCaL version: 2.1.3
% 3.84/1.39 % (2769854)Termination reason: Instruction limit
% 3.84/1.39 % (2769854)Termination phase: Saturation
% 3.84/1.39 % (2769854)Time elapsed: 0.004 s
% 3.84/1.39 % (2769854)Peak memory usage: 89 MB
% 3.84/1.39 % (2769854)Instructions burned: 6 (million)
% 3.84/1.39 % (2769856)First to succeed.
% 3.84/1.39 % (2769850)Also succeeded, but the first one will report.
% 3.84/1.39 % (2769855)Also succeeded, but the first one will report.
% 3.84/1.39 % (2769852)Also succeeded, but the first one will report.
% 3.84/1.39 % (2769851)Also succeeded, but the first one will report.
% 3.84/1.39 % (2769856)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2769845"
% 3.84/1.39 % (2769858)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2109538655:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.84/1.39 % (2769865)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1886797152:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.84/1.39 % (2769858)Refutation not found, incomplete strategy
% 3.84/1.39 % (2769858)------------------------------
% 3.84/1.39 % (2769858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.39 % (2769858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.39 % (2769858)CaDiCaL version: 2.1.3
% 3.84/1.39 % (2769858)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.39 % (2769858)Time elapsed: 0.001 s
% 3.84/1.39 % (2769858)Peak memory usage: 89 MB
% 3.84/1.39 % (2769865)Also succeeded, but the first one will report.
% 3.84/1.39 % (2769856)Refutation found. Thanks to Tanya!
% 3.84/1.39 % SZS status Theorem for theBenchmark
% 3.84/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.39 % (2769856)------------------------------
% 3.84/1.39 % (2769856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.39 % (2769856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.39 % (2769856)CaDiCaL version: 2.1.3
% 3.84/1.39 % (2769856)Termination reason: Refutation
% 3.84/1.39 % (2769856)Time elapsed: 0.027 s
% 3.84/1.39 % (2769856)Peak memory usage: 116 MB
% 3.84/1.39 % (2769856)Instructions burned: 9 (million)
% 3.84/1.39 % (2769856)------------------------------
% 3.84/1.39 % (2769856)------------------------------
% 3.84/1.39 % (2769845)Success in time 0.478 s
% 3.84/1.39 % Vampire exiting
%------------------------------------------------------------------------------