%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI680_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 : n007.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 7.81s 2.12s
% Output : Refutation 7.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 62 ( 16 atm; 19 fun; 27 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 : 11 ( 3 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $int ).
tff(func_def_1,type,
y: $int ).
tff(func_def_2,type,
a: $int ).
tff(f1,axiom,
$greater(4,$sum($product($product(3,x),y),$product(7,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$less(3,$product(2,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,axiom,
$less(1,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,conjecture,
$greater(0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_003) ).
tff(f5,negated_conjecture,
~ $greater(0,a),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
$less($sum($product($product(3,x),y),$product(7,a)),4),
inference(theory_normalization,[],[f1]) ).
tff(f7,plain,
~ $less(a,0),
inference(theory_normalization,[],[f5]) ).
tff(f8,plain,
~ $less(a,0),
inference(flattening,[],[f7]) ).
tff(f9,plain,
$less(1,y),
inference(cnf_transformation,[],[f3]) ).
tff(f10,plain,
~ $less(a,0),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
$less(3,$product(2,x)),
inference(cnf_transformation,[],[f2]) ).
tff(f12,plain,
$less($sum($product($product(3,x),y),$product(7,a)),4),
inference(cnf_transformation,[],[f6]) ).
tff(f14,definition,
( spl0_1
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f17,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f14]) ).
tff(f19,definition,
( spl0_2
<=> $less($sum($product($product(3,x),y),$product(7,a)),4) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f22,plain,
spl0_2,
inference(avatar_split_clause,[],[f12,f19]) ).
tff(f24,definition,
( spl0_3
<=> $less(3,$product(2,x)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f27,plain,
spl0_3,
inference(avatar_split_clause,[],[f11,f24]) ).
tff(f29,definition,
( spl0_4
<=> $less(1,y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f32,plain,
spl0_4,
inference(avatar_split_clause,[],[f9,f29]) ).
tff(f33,plain,
$false,
inference(avatar_smt_refutation,[],[f32,f27,f22,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI680_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n007.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 20:53:55 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running first-order theorem proving
% 0.24/0.31 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
% 5.90/1.77 % (2812897)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.90/1.77 % (2812914)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3012776242:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.90/1.77 % (2812916)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2256587176:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.90/1.77 % (2812916)Instruction limit reached!
% 5.90/1.77 % (2812916)------------------------------
% 5.90/1.77 % (2812916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.77 % (2812916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.77 % (2812916)CaDiCaL version: 2.1.3
% 5.90/1.77 % (2812916)Termination reason: Instruction limit
% 5.90/1.77 % (2812916)Termination phase: Saturation
% 5.90/1.77 % (2812916)Time elapsed: 0.006 s
% 5.90/1.77 % (2812916)Peak memory usage: 89 MB
% 5.90/1.77 % (2812916)Instructions burned: 4 (million)
% 5.90/1.77 % (2812913)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1054920293:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.90/1.77 % (2812912)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2729615964:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.90/1.77 % (2812915)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2784721979:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.90/1.77 % (2812918)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1895367806:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.90/1.77 % (2812917)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3548541720:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.90/1.77 % (2812915)Instruction limit reached!
% 5.90/1.77 % (2812915)------------------------------
% 5.90/1.77 % (2812915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.77 % (2812915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.77 % (2812915)CaDiCaL version: 2.1.3
% 5.90/1.77 % (2812915)Termination reason: Instruction limit
% 5.90/1.77 % (2812915)Termination phase: Saturation
% 5.90/1.77 % (2812915)Time elapsed: 0.007 s
% 5.90/1.77 % (2812915)Peak memory usage: 88 MB
% 5.90/1.77 % (2812915)Instructions burned: 8 (million)
% 5.90/1.77 % (2812913)First to succeed.
% 5.90/1.77 % (2812913)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2812897"
% 5.90/1.77 % (2812917)Also succeeded, but the first one will report.
% 5.90/1.77 % (2812918)Also succeeded, but the first one will report.
% 5.90/1.77 % (2812912)Refutation not found, incomplete strategy
% 5.90/1.77 % (2812912)------------------------------
% 5.90/1.77 % (2812912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.77 % (2812912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.77 % (2812912)CaDiCaL version: 2.1.3
% 5.90/1.77 % (2812912)Termination reason: Refutation not found, incomplete strategy
% 5.90/1.77 % (2812912)Time elapsed: 0.048 s
% 5.90/1.77 % (2812912)Peak memory usage: 116 MB
% 5.90/1.77 % (2812912)Instructions burned: 12 (million)
% 5.90/1.77 % (2812914)Instruction limit reached!
% 5.90/1.77 % (2812914)------------------------------
% 5.90/1.77 % (2812914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.77 % (2812914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.77 % (2812914)CaDiCaL version: 2.1.3
% 5.90/1.77 % (2812914)Termination reason: Instruction limit
% 5.90/1.77 % (2812914)Termination phase: Saturation
% 5.90/1.77 % (2812914)Time elapsed: 0.150 s
% 5.90/1.77 % (2812914)Peak memory usage: 117 MB
% 5.90/1.77 % (2812914)Instructions burned: 202 (million)
% 5.90/1.77 % (2812923)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2399745125:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.90/1.77 % (2812923)Refutation not found, incomplete strategy
% 5.90/1.77 % (2812923)------------------------------
% 5.90/1.77 % (2812923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.77 % (2812923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.77 % (2812923)CaDiCaL version: 2.1.3
% 5.90/1.77 % (2812923)Termination reason: Refutation not found, incomplete strategy
% 7.81/2.12 % (2812923)Time elapsed: 0.002 s
% 7.81/2.12 % (2812923)Peak memory usage: 88 MB
% 7.81/2.12 % (2812932)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2852106148:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 7.81/2.12 % (2812931)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=1012115507:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 7.81/2.12 % (2812932)Instruction limit reached!
% 7.81/2.12 % (2812932)------------------------------
% 7.81/2.12 % (2812932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812932)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812932)Termination reason: Instruction limit
% 7.81/2.12 % (2812932)Termination phase: Saturation
% 7.81/2.12 % (2812932)Time elapsed: 0.007 s
% 7.81/2.12 % (2812932)Peak memory usage: 90 MB
% 7.81/2.12 % (2812932)Instructions burned: 16 (million)
% 7.81/2.12 % (2812931)Instruction limit reached!
% 7.81/2.12 % (2812931)------------------------------
% 7.81/2.12 % (2812931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812931)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812931)Termination reason: Instruction limit
% 7.81/2.12 % (2812931)Termination phase: Saturation
% 7.81/2.12 % (2812931)Time elapsed: 0.031 s
% 7.81/2.12 % (2812931)Peak memory usage: 88 MB
% 7.81/2.12 % (2812931)Instructions burned: 29 (million)
% 7.81/2.12 % (2812912)------------------------------
% 7.81/2.12 % (2812912)------------------------------
% 7.81/2.12 % (2812938)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=513670165:i=24:canc=force:rtra=on_2994 on theBenchmark for (2994ds/24Mi)
% 7.81/2.12 % (2812938)Instruction limit reached!
% 7.81/2.12 % (2812938)------------------------------
% 7.81/2.12 % (2812938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812938)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812938)Termination reason: Instruction limit
% 7.81/2.12 % (2812938)Termination phase: Saturation
% 7.81/2.12 % (2812938)Time elapsed: 0.017 s
% 7.81/2.12 % (2812938)Peak memory usage: 89 MB
% 7.81/2.12 % (2812938)Instructions burned: 25 (million)
% 7.81/2.12 % (2812923)------------------------------
% 7.81/2.12 % (2812923)------------------------------
% 7.81/2.12 % (2812940)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=2769271528:i=27:canc=cautious:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/27Mi)
% 7.81/2.12 % (2812940)Instruction limit reached!
% 7.81/2.12 % (2812940)------------------------------
% 7.81/2.12 % (2812940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812940)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812940)Termination reason: Instruction limit
% 7.81/2.12 % (2812940)Termination phase: Saturation
% 7.81/2.12 % (2812940)Time elapsed: 0.020 s
% 7.81/2.12 % (2812940)Peak memory usage: 89 MB
% 7.81/2.12 % (2812940)Instructions burned: 27 (million)
% 7.81/2.12 % (2812944)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1761508351:i=85:gtgl=4:rtra=on:gtg=exists_sym_2993 on theBenchmark for (2993ds/85Mi)
% 7.81/2.12 % (2812945)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=2277506048:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2992 on theBenchmark for (2992ds/2Mi)
% 7.81/2.12 % (2812946)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2396396161:i=181:rtra=on:ss=axioms:ev=cautious_2992 on theBenchmark for (2992ds/181Mi)
% 7.81/2.12 % (2812946)Refutation not found, incomplete strategy
% 7.81/2.12 % (2812946)------------------------------
% 7.81/2.12 % (2812946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812946)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812946)Termination reason: Refutation not found, incomplete strategy
% 7.81/2.12 % (2812946)Time elapsed: 0.002 s
% 7.81/2.12 % (2812946)Peak memory usage: 88 MB
% 7.81/2.12 % (2812945)Instruction limit reached!
% 7.81/2.12 % (2812945)------------------------------
% 7.81/2.12 % (2812945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812945)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812945)Termination reason: Instruction limit
% 7.81/2.12 % (2812945)Termination phase: Saturation
% 7.81/2.12 % (2812945)Time elapsed: 0.004 s
% 7.81/2.12 % (2812945)Peak memory usage: 88 MB
% 7.81/2.12 % (2812945)Instructions burned: 2 (million)
% 7.81/2.12 % (2812949)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2882539168:i=4:ep=RST:ins=2:rtra=on_2992 on theBenchmark for (2992ds/4Mi)
% 7.81/2.12 % (2812949)Instruction limit reached!
% 7.81/2.12 % (2812949)------------------------------
% 7.81/2.12 % (2812949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812949)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812949)Termination reason: Instruction limit
% 7.81/2.12 % (2812949)Termination phase: Saturation
% 7.81/2.12 % (2812949)Time elapsed: 0.003 s
% 7.81/2.12 % (2812949)Peak memory usage: 88 MB
% 7.81/2.12 % (2812949)Instructions burned: 4 (million)
% 7.81/2.12 % (2812944)Instruction limit reached!
% 7.81/2.12 % (2812944)------------------------------
% 7.81/2.12 % (2812944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812944)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812944)Termination reason: Instruction limit
% 7.81/2.12 % (2812944)Termination phase: Saturation
% 7.81/2.12 % (2812944)Time elapsed: 0.095 s
% 7.81/2.12 % (2812944)Peak memory usage: 89 MB
% 7.81/2.12 % (2812944)Instructions burned: 85 (million)
% 7.81/2.12 % (2812913)Refutation found. Thanks to Tanya!
% 7.81/2.12 % SZS status Theorem for theBenchmark
% 7.81/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 7.81/2.12 % (2812913)------------------------------
% 7.81/2.12 % (2812913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.12 % (2812913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.12 % (2812913)CaDiCaL version: 2.1.3
% 7.81/2.12 % (2812913)Termination reason: Refutation
% 7.81/2.12 % (2812913)Time elapsed: 0.045 s
% 7.81/2.12 % (2812913)Peak memory usage: 116 MB
% 7.81/2.12 % (2812913)Instructions burned: 9 (million)
% 7.81/2.12 % (2812913)------------------------------
% 7.81/2.12 % (2812913)------------------------------
% 7.81/2.12 % (2812897)Success in time 1.038 s
% 7.81/2.12 % Vampire exiting
%------------------------------------------------------------------------------