%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI679_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:33:38 AM UTC 2026
% Result : Theorem 3.09s 0.91s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 5 |; 1 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 139 ( 26 atm; 62 fun; 51 num; 0 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 : 10 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
d: $int ).
tff(func_def_1,type,
c: $int ).
tff(f1,axiom,
$lesseq(3,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(2,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
( $lesseq($product(2,3),$product(c,d))
<=> $lesseq($product(2,$difference(d,3)),$product(c,$difference(d,3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ ( $lesseq($product(2,3),$product(c,d))
<=> $lesseq($product(2,$difference(d,3)),$product(c,$difference(d,3))) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ $less(d,3),
inference(theory_normalization,[],[f1]) ).
tff(f6,plain,
~ ( ~ $less($product(c,$sum(d,$uminus(3))),$product(2,$sum(d,$uminus(3))))
<=> ~ $less($product(c,d),$product(2,3)) ),
inference(theory_normalization,[],[f4]) ).
tff(f7,plain,
~ $less(c,2),
inference(theory_normalization,[],[f2]) ).
tff(f8,plain,
( ~ $less($product(c,$sum(d,$uminus(3))),$product(2,$sum(d,$uminus(3))))
<~> ~ $less($product(c,d),$product(2,3)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f9,plain,
( ( $less($product(c,d),$product(2,3))
| $less($product(c,$sum(d,$uminus(3))),$product(2,$sum(d,$uminus(3)))) )
& ( ~ $less($product(c,d),$product(2,3))
| ~ $less($product(c,$sum(d,$uminus(3))),$product(2,$sum(d,$uminus(3)))) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f11,plain,
( $less($product(c,d),$product(2,3))
| $less($product(c,$sum(d,$uminus(3))),$product(2,$sum(d,$uminus(3)))) ),
inference(cnf_transformation,[],[f9]) ).
tff(f12,plain,
~ $less(c,2),
inference(cnf_transformation,[],[f7]) ).
tff(f13,plain,
~ $less(d,3),
inference(cnf_transformation,[],[f5]) ).
tff(f14,plain,
( $less($product(c,$sum(d,-3)),$product(2,$sum(d,-3)))
| $less($product(c,d),6) ),
inference(evaluation,[],[f11]) ).
tff(f17,definition,
( spl0_1
<=> $less($product(c,d),6) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f21,definition,
( spl0_2
<=> $less($product(c,$sum(d,-3)),$product(2,$sum(d,-3))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f24,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f21,f17]) ).
tff(f27,definition,
( spl0_3
<=> $less(d,3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f30,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f13,f27]) ).
tff(f32,definition,
( spl0_4
<=> $less(c,2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f35,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f12,f32]) ).
tff(f36,plain,
$false,
inference(avatar_smt_refutation,[],[f35,f30,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI679_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n010.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 20:56:18 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 3.09/0.91 % (2325441)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.09/0.91 % (2325451)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1658399397:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.09/0.91 % (2325451)First to succeed.
% 3.09/0.91 % (2325451)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2325441"
% 3.09/0.91 % (2325450)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=130951589:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.09/0.91 % (2325446)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=750729448:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.09/0.91 % (2325452)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1044628808:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.09/0.91 % (2325448)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2267429460:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.09/0.91 % (2325449)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3902595979:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.09/0.91 % (2325447)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3995101232:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.09/0.91 % (2325450)Instruction limit reached!
% 3.09/0.91 % (2325450)------------------------------
% 3.09/0.91 % (2325450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325450)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325450)Termination reason: Instruction limit
% 3.09/0.91 % (2325450)Termination phase: Saturation
% 3.09/0.91 % (2325450)Time elapsed: 0.004 s
% 3.09/0.91 % (2325450)Peak memory usage: 89 MB
% 3.09/0.91 % (2325450)Instructions burned: 4 (million)
% 3.09/0.91 % (2325449)Instruction limit reached!
% 3.09/0.91 % (2325449)------------------------------
% 3.09/0.91 % (2325449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325449)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325449)Termination reason: Instruction limit
% 3.09/0.91 % (2325449)Termination phase: Saturation
% 3.09/0.91 % (2325449)Time elapsed: 0.005 s
% 3.09/0.91 % (2325449)Peak memory usage: 88 MB
% 3.09/0.91 % (2325449)Instructions burned: 7 (million)
% 3.09/0.91 % (2325446)Instruction limit reached!
% 3.09/0.91 % (2325446)------------------------------
% 3.09/0.91 % (2325446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325446)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325446)Termination reason: Instruction limit
% 3.09/0.91 % (2325446)Termination phase: Saturation
% 3.09/0.91 % (2325446)Time elapsed: 0.031 s
% 3.09/0.91 % (2325446)Peak memory usage: 117 MB
% 3.09/0.91 % (2325446)Instructions burned: 12 (million)
% 3.09/0.91 % (2325447)Also succeeded, but the first one will report.
% 3.09/0.91 % (2325452)Also succeeded, but the first one will report.
% 3.09/0.91 % (2325461)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=3746599117:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.09/0.91 % (2325461)Instruction limit reached!
% 3.09/0.91 % (2325461)------------------------------
% 3.09/0.91 % (2325461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325461)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325461)Termination reason: Instruction limit
% 3.09/0.91 % (2325461)Termination phase: Saturation
% 3.09/0.91 % (2325461)Time elapsed: 0.012 s
% 3.09/0.91 % (2325461)Peak memory usage: 88 MB
% 3.09/0.91 % (2325461)Instructions burned: 30 (million)
% 3.09/0.91 % (2325460)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2084048376:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.09/0.91 % (2325460)Refutation not found, incomplete strategy
% 3.09/0.91 % (2325460)------------------------------
% 3.09/0.91 % (2325460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325460)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325460)Termination reason: Refutation not found, incomplete strategy
% 3.09/0.91 % (2325460)Time elapsed: 0.001 s
% 3.09/0.91 % (2325460)Peak memory usage: 88 MB
% 3.09/0.91 % (2325448)Instruction limit reached!
% 3.09/0.91 % (2325448)------------------------------
% 3.09/0.91 % (2325448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325448)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325448)Termination reason: Instruction limit
% 3.09/0.91 % (2325448)Termination phase: Saturation
% 3.09/0.91 % (2325448)Time elapsed: 0.168 s
% 3.09/0.91 % (2325448)Peak memory usage: 117 MB
% 3.09/0.91 % (2325448)Instructions burned: 201 (million)
% 3.09/0.91 % (2325462)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2403557394:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.09/0.91 % (2325462)Instruction limit reached!
% 3.09/0.91 % (2325462)------------------------------
% 3.09/0.91 % (2325462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325462)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325462)Termination reason: Instruction limit
% 3.09/0.91 % (2325462)Termination phase: Saturation
% 3.09/0.91 % (2325462)Time elapsed: 0.010 s
% 3.09/0.91 % (2325462)Peak memory usage: 90 MB
% 3.09/0.91 % (2325462)Instructions burned: 17 (million)
% 3.09/0.91 % (2325464)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2203560314:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.09/0.91 % (2325464)Instruction limit reached!
% 3.09/0.91 % (2325464)------------------------------
% 3.09/0.91 % (2325464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325464)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325464)Termination reason: Instruction limit
% 3.09/0.91 % (2325464)Termination phase: Saturation
% 3.09/0.91 % (2325464)Time elapsed: 0.011 s
% 3.09/0.91 % (2325464)Peak memory usage: 89 MB
% 3.09/0.91 % (2325464)Instructions burned: 26 (million)
% 3.09/0.91 % (2325451)Refutation found. Thanks to Tanya!
% 3.09/0.91 % SZS status Theorem for theBenchmark
% 3.09/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 3.09/0.91 % (2325451)------------------------------
% 3.09/0.91 % (2325451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/0.91 % (2325451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/0.91 % (2325451)CaDiCaL version: 2.1.3
% 3.09/0.91 % (2325451)Termination reason: Refutation
% 3.09/0.91 % (2325451)Time elapsed: 0.021 s
% 3.09/0.91 % (2325451)Peak memory usage: 117 MB
% 3.09/0.91 % (2325451)Instructions burned: 11 (million)
% 3.09/0.91 % (2325451)------------------------------
% 3.09/0.91 % (2325451)------------------------------
% 3.09/0.91 % (2325441)Success in time 0.392 s
% 3.09/0.91 % Vampire exiting
%------------------------------------------------------------------------------