%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI602_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:33:27 AM UTC 2026
% Result : Theorem 2.90s 1.19s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 6 unt; 0 typ; 3 def)
% Number of atoms : 45 ( 7 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 39 ( 16 ~; 14 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 63 ( 25 atm; 0 fun; 24 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 : 6 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 2 usr; 3 con; 0-1 aty)
% Number of variables : 14 ( 11 !; 3 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_7,type,
sF0: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ? [X1: $int] :
( $less(X1,f(5))
& $less(4,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_exist_ineq) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ? [X1: $int] :
( $less(X1,f(5))
& $less(4,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ? [X1: $int] :
( $less(X1,f(5))
& $less(4,X1) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f16,plain,
( ! [X0: $int] : $less(X0,f(X0))
& ! [X1: $int] :
( ~ $less(X1,f(5))
| ~ $less(4,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
! [X1: $int] :
( ~ $less(X1,f(5))
| ~ $less(4,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f16]) ).
tff(f19,definition,
sF0 = f(5),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f20,plain,
f(5) = sF0,
inference(reorient_equations,[],[f19]) ).
tff(f21,plain,
! [X1: $int] :
( ~ $less(4,X1)
| ~ $less(X1,sF0) ),
inference(definition_folding,[],[f17,f20]) ).
tff(f23,definition,
( spl1_1
<=> ( f(5) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f25,plain,
( ( f(5) = sF0 )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f23]) ).
tff(f26,plain,
spl1_1,
inference(avatar_split_clause,[],[f20,f23]) ).
tff(f33,plain,
( $less(5,sF0)
| ~ spl1_1 ),
inference(superposition,[],[f18,f25]) ).
tff(f35,definition,
( spl1_3
<=> $less(5,sF0) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f37,plain,
( $less(5,sF0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f38,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f33,f23,f35]) ).
tff(f61,plain,
! [X0: $int] :
( ~ $less(X0,sF0)
| $less(X0,4)
| ( 4 = X0 ) ),
inference(resolution,[],[f11,f21]) ).
tff(f148,plain,
( ( 4 = 5 )
| $less(5,4)
| ~ spl1_3 ),
inference(resolution,[],[f61,f37]) ).
tff(f149,plain,
( $false
| ~ spl1_3 ),
inference(evaluation,[],[f148]) ).
tff(f150,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f149]) ).
tff(f151,plain,
$false,
inference(avatar_smt_refutation,[],[f150,f38,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI602_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:53:15 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 2.90/1.19 % (3461585)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.90/1.19 % (3461596)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=941018445:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.90/1.19 % (3461596)First to succeed.
% 2.90/1.19 % (3461596)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3461585"
% 2.90/1.19 % (3461592)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=128552163:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.90/1.19 % (3461593)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3640563112:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.90/1.19 % (3461594)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2867417950:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.90/1.19 % (3461590)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1640305884:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.90/1.19 % (3461591)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=455389870:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.90/1.19 % (3461595)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2103020436:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.90/1.19 % (3461594)Also succeeded, but the first one will report.
% 2.90/1.19 % (3461593)Also succeeded, but the first one will report.
% 2.90/1.19 % (3461595)Also succeeded, but the first one will report.
% 2.90/1.19 % (3461592)Also succeeded, but the first one will report.
% 2.90/1.19 % (3461591)Refutation not found, incomplete strategy
% 2.90/1.19 % (3461591)------------------------------
% 2.90/1.19 % (3461591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.19 % (3461591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.19 % (3461591)CaDiCaL version: 2.1.3
% 2.90/1.19 % (3461591)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.19 % (3461591)Time elapsed: 0.030 s
% 2.90/1.19 % (3461591)Peak memory usage: 115 MB
% 2.90/1.19 % (3461591)Instructions burned: 7 (million)
% 2.90/1.19 % (3461590)Refutation not found, incomplete strategy
% 2.90/1.19 % (3461590)------------------------------
% 2.90/1.19 % (3461590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.19 % (3461590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.19 % (3461590)CaDiCaL version: 2.1.3
% 2.90/1.19 % (3461590)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.19 % (3461590)Time elapsed: 0.032 s
% 2.90/1.19 % (3461590)Peak memory usage: 116 MB
% 2.90/1.19 % (3461590)Instructions burned: 9 (million)
% 2.90/1.19 % (3461596)Refutation found. Thanks to Tanya!
% 2.90/1.19 % SZS status Theorem for theBenchmark
% 2.90/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.90/1.19 % (3461596)------------------------------
% 2.90/1.19 % (3461596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.19 % (3461596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.19 % (3461596)CaDiCaL version: 2.1.3
% 2.90/1.19 % (3461596)Termination reason: Refutation
% 2.90/1.19 % (3461596)Time elapsed: 0.024 s
% 2.90/1.19 % (3461596)Peak memory usage: 116 MB
% 2.90/1.19 % (3461596)Instructions burned: 16 (million)
% 2.90/1.19 % (3461596)------------------------------
% 2.90/1.19 % (3461596)------------------------------
% 2.90/1.19 % (3461585)Success in time 0.323 s
% 2.90/1.19 % Vampire exiting
%------------------------------------------------------------------------------