%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI608_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:33:28 AM UTC 2026
% Result : Theorem 3.92s 1.53s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 6 |; 14 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 55 ( 41 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 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
b: $int ).
tff(func_def_3,type,
c: $int ).
tff(f1,conjecture,
( ( $less(b,c)
& $lesseq(a,b)
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(f(a),f(c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_trans) ).
tff(f2,negated_conjecture,
~ ( ( $less(b,c)
& $lesseq(a,b)
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(f(a),f(c)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( $less(b,c)
& ~ $less(b,a)
& ! [X1: $int,X0: $int] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) ) )
=> ~ $less(f(c),f(a)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
~ ( ( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
=> ~ $less(f(X0),f(X1)) )
& $less(b,c)
& ~ $less(b,a) )
=> ~ $less(f(c),f(a)) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( $less(f(c),f(a))
& ! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) )
& $less(b,c)
& ~ $less(b,a) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( $less(b,c)
& ! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) )
& $less(f(c),f(a))
& ~ $less(b,a) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
~ $less(b,a),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
$less(f(c),f(a)),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tff(f10,plain,
$less(b,c),
inference(cnf_transformation,[],[f6]) ).
tff(f12,definition,
( spl0_1
<=> $less(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f15,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f7,f12]) ).
tff(f17,definition,
( spl0_2
<=> $less(b,c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f20,plain,
spl0_2,
inference(avatar_split_clause,[],[f10,f17]) ).
tff(f22,definition,
( spl0_3
<=> $less(f(c),f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f24,plain,
( $less(f(c),f(a))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f22]) ).
tff(f25,plain,
spl0_3,
inference(avatar_split_clause,[],[f8,f22]) ).
tff(f26,plain,
( $less(c,a)
| ~ spl0_3 ),
inference(resolution,[],[f9,f24]) ).
tff(f28,definition,
( spl0_4
<=> $less(c,a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f31,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f26,f22,f28]) ).
tff(f32,plain,
$false,
inference(avatar_smt_refutation,[],[f31,f25,f20,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI608_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.28 % Computer : n002.cluster.edu
% 0.22/0.28 % Model : x86_64 x86_64
% 0.22/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.28 % Memory : 8046.5625MB
% 0.22/0.28 % OS : Linux 6.8.0-71-generic
% 0.22/0.28 % CPULimit : 300
% 0.22/0.28 % WCLimit : 300
% 0.22/0.28 % DateTime : Mon Sep 28 20:56:07 UTC 2026
% 0.22/0.28 % CPUTime :
% 0.22/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.33 Running first-order theorem proving
% 0.22/0.33 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
% 3.92/1.53 % (749259)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.92/1.53 % (749269)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=61996111:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.92/1.53 % (749266)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1745879356:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.92/1.53 % (749269)First to succeed.
% 3.92/1.53 % (749269)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-749259"
% 3.92/1.53 % (749266)Also succeeded, but the first one will report.
% 3.92/1.53 % (749265)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3101137717:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.92/1.53 % (749264)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1107622963:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.92/1.53 % (749270)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2080672375:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.92/1.53 % (749267)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=219178918:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.92/1.53 % (749268)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3415842371:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.92/1.53 % (749268)Instruction limit reached!
% 3.92/1.53 % (749268)------------------------------
% 3.92/1.53 % (749268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (749268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (749268)CaDiCaL version: 2.1.3
% 3.92/1.53 % (749268)Termination reason: Instruction limit
% 3.92/1.53 % (749268)Termination phase: Saturation
% 3.92/1.53 % (749268)Time elapsed: 0.006 s
% 3.92/1.53 % (749268)Peak memory usage: 88 MB
% 3.92/1.53 % (749268)Instructions burned: 4 (million)
% 3.92/1.53 % (749267)Instruction limit reached!
% 3.92/1.53 % (749267)------------------------------
% 3.92/1.53 % (749267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (749267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (749267)CaDiCaL version: 2.1.3
% 3.92/1.53 % (749267)Termination reason: Instruction limit
% 3.92/1.53 % (749267)Termination phase: Saturation
% 3.92/1.53 % (749267)Time elapsed: 0.010 s
% 3.92/1.53 % (749267)Peak memory usage: 88 MB
% 3.92/1.53 % (749267)Instructions burned: 7 (million)
% 3.92/1.53 % (749264)Refutation not found, incomplete strategy
% 3.92/1.53 % (749264)------------------------------
% 3.92/1.53 % (749264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (749264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (749264)CaDiCaL version: 2.1.3
% 3.92/1.53 % (749264)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.53 % (749264)Time elapsed: 0.046 s
% 3.92/1.53 % (749264)Peak memory usage: 116 MB
% 3.92/1.53 % (749264)Instructions burned: 11 (million)
% 3.92/1.53 % (749265)Also succeeded, but the first one will report.
% 3.92/1.53 % (749270)Also succeeded, but the first one will report.
% 3.92/1.53 % (749269)Refutation found. Thanks to Tanya!
% 3.92/1.53 % SZS status Theorem for theBenchmark
% 3.92/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.53 % (749269)------------------------------
% 3.92/1.53 % (749269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (749269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (749269)CaDiCaL version: 2.1.3
% 3.92/1.53 % (749269)Termination reason: Refutation
% 3.92/1.53 % (749269)Time elapsed: 0.026 s
% 3.92/1.53 % (749269)Peak memory usage: 116 MB
% 3.92/1.53 % (749269)Instructions burned: 10 (million)
% 3.92/1.53 % (749269)------------------------------
% 3.92/1.53 % (749269)------------------------------
% 3.92/1.53 % (749259)Success in time 0.428 s
% 3.92/1.53 % Vampire exiting
%------------------------------------------------------------------------------