%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI677_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 : n001.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 2.79s 0.98s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 20 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 10 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 44 ( 8 atm; 23 fun; 13 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 : 8 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,axiom,
$greatereq(0,$product($product(a,a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
$product($product($product(a,a),a),a) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
( ( ~ $product($product($product(a,a),a),a) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ $less(0,$product($product(a,a),a)),
inference(theory_normalization,[],[f1]) ).
tff(f6,plain,
~ $less(a,0),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
0 != $product($product($product(a,a),a),a),
inference(flattening,[],[f4]) ).
tff(f8,plain,
0 != $product($product($product(a,a),a),a),
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
~ $less(0,$product($product(a,a),a)),
inference(cnf_transformation,[],[f5]) ).
tff(f10,plain,
~ $less(a,0),
inference(cnf_transformation,[],[f6]) ).
tff(f12,definition,
( spl0_1
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f15,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f12]) ).
tff(f17,definition,
( spl0_2
<=> $less(0,$product($product(a,a),a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f20,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f9,f17]) ).
tff(f22,definition,
( spl0_3
<=> ( 0 = $product($product($product(a,a),a),a) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f25,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f8,f22]) ).
tff(f26,plain,
$false,
inference(avatar_smt_refutation,[],[f25,f20,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI677_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:01:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 2.79/0.98 % (741470)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.79/0.98 % (741491)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4113552621:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.79/0.98 % (741485)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3625433664:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.79/0.98 % (741488)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1343733111:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.79/0.98 % (741492)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3759002692:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.79/0.98 % (741490)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3408427163:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.79/0.98 % (741484)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3107204637:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.79/0.98 % (741487)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1865561106:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.79/0.98 % (741490)Instruction limit reached!
% 2.79/0.98 % (741490)------------------------------
% 2.79/0.98 % (741490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741490)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741490)Termination reason: Instruction limit
% 2.79/0.98 % (741490)Termination phase: Saturation
% 2.79/0.98 % (741490)Time elapsed: 0.004 s
% 2.79/0.98 % (741490)Peak memory usage: 88 MB
% 2.79/0.98 % (741490)Instructions burned: 5 (million)
% 2.79/0.98 % (741488)Instruction limit reached!
% 2.79/0.98 % (741488)------------------------------
% 2.79/0.98 % (741488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741488)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741488)Termination reason: Instruction limit
% 2.79/0.98 % (741488)Termination phase: Saturation
% 2.79/0.98 % (741488)Time elapsed: 0.005 s
% 2.79/0.98 % (741488)Peak memory usage: 88 MB
% 2.79/0.98 % (741488)Instructions burned: 7 (million)
% 2.79/0.98 % (741491)First to succeed.
% 2.79/0.98 % (741491)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-741470"
% 2.79/0.98 % (741484)Also succeeded, but the first one will report.
% 2.79/0.98 % (741485)Also succeeded, but the first one will report.
% 2.79/0.98 % (741492)Also succeeded, but the first one will report.
% 2.79/0.98 % (741487)Instruction limit reached!
% 2.79/0.98 % (741487)------------------------------
% 2.79/0.98 % (741487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741487)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741487)Termination reason: Instruction limit
% 2.79/0.98 % (741487)Termination phase: Saturation
% 2.79/0.98 % (741487)Time elapsed: 0.132 s
% 2.79/0.98 % (741487)Peak memory usage: 117 MB
% 2.79/0.98 % (741487)Instructions burned: 202 (million)
% 2.79/0.98 % (741554)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=3439273600:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.79/0.98 % (741551)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=690026808:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.79/0.98 % (741554)Instruction limit reached!
% 2.79/0.98 % (741554)------------------------------
% 2.79/0.98 % (741554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741554)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741554)Termination reason: Instruction limit
% 2.79/0.98 % (741554)Termination phase: Saturation
% 2.79/0.98 % (741554)Time elapsed: 0.020 s
% 2.79/0.98 % (741554)Peak memory usage: 88 MB
% 2.79/0.98 % (741554)Instructions burned: 30 (million)
% 2.79/0.98 % (741551)Refutation not found, incomplete strategy
% 2.79/0.98 % (741551)------------------------------
% 2.79/0.98 % (741551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741551)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741551)Termination reason: Refutation not found, incomplete strategy
% 2.79/0.98 % (741551)Time elapsed: 0.001 s
% 2.79/0.98 % (741551)Peak memory usage: 88 MB
% 2.79/0.98 % (741491)Refutation found. Thanks to Tanya!
% 2.79/0.98 % SZS status Theorem for theBenchmark
% 2.79/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/0.98 % (741491)------------------------------
% 2.79/0.98 % (741491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/0.98 % (741491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.98 % (741491)CaDiCaL version: 2.1.3
% 2.79/0.98 % (741491)Termination reason: Refutation
% 2.79/0.98 % (741491)Time elapsed: 0.019 s
% 2.79/0.98 % (741491)Peak memory usage: 115 MB
% 2.79/0.98 % (741491)Instructions burned: 8 (million)
% 2.79/0.98 % (741491)------------------------------
% 2.79/0.98 % (741491)------------------------------
% 2.79/0.98 % (741470)Success in time 0.362 s
% 2.79/0.98 % Vampire exiting
%------------------------------------------------------------------------------