%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI662_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 : n017.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 09:33:36 AM UTC 2026
% Result : Theorem 3.26s 1.22s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 49 ( 26 unt; 0 typ; 22 def)
% Number of atoms : 74 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 12 ~; 8 |; 1 &)
% ( 15 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number arithmetic : 149 ( 22 atm; 105 fun; 22 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 : 16 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 14 ( 11 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_4,type,
sF0: $int ).
tff(func_def_5,type,
sF1: $int ).
tff(func_def_6,type,
sF2: $int ).
tff(func_def_7,type,
sF3: $int ).
tff(func_def_8,type,
sF4: $int ).
tff(func_def_9,type,
sF5: $int ).
tff(func_def_10,type,
sF6: $int ).
tff(func_def_11,type,
sF7: $int ).
tff(func_def_12,type,
sF8: $int ).
tff(func_def_13,type,
sF9: $int ).
tff(f1,conjecture,
( $less(1,a)
<=> $lesseq(1000,$product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( $less(1,a)
<=> $lesseq(1000,$product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ~ $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000)
<=> $less(1,a) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ~ $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000)
<~> $less(1,a) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ( ~ $less(1,a)
| $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000) )
& ( $less(1,a)
| ~ $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
( $less(1,a)
| ~ $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000) ),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
( ~ $less(1,a)
| $less($product($product($product($product($product($product($product($product($product($product(a,a),a),a),a),a),a),a),a),a),a),1000) ),
inference(cnf_transformation,[],[f5]) ).
tff(f8,definition,
sF0 = $product(a,a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f9,plain,
$product(a,a) = sF0,
inference(reorient_equations,[],[f8]) ).
tff(f10,definition,
sF1 = $product(sF0,a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f11,definition,
sF2 = $product(sF1,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f12,plain,
$product(sF1,a) = sF2,
inference(reorient_equations,[],[f11]) ).
tff(f13,definition,
sF3 = $product(sF2,a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f14,plain,
$product(sF2,a) = sF3,
inference(reorient_equations,[],[f13]) ).
tff(f15,definition,
sF4 = $product(sF3,a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f16,definition,
sF5 = $product(sF4,a),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f17,definition,
sF6 = $product(sF5,a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f18,plain,
$product(sF5,a) = sF6,
inference(reorient_equations,[],[f17]) ).
tff(f19,definition,
sF7 = $product(sF6,a),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f20,definition,
sF8 = $product(sF7,a),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
tff(f21,plain,
$product(sF7,a) = sF8,
inference(reorient_equations,[],[f20]) ).
tff(f22,definition,
sF9 = $product(sF8,a),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
tff(f23,plain,
( $less(sF9,1000)
| ~ $less(1,a) ),
inference(definition_folding,[],[f7,f22,f21,f19,f18,f16,f15,f14,f12,f10,f9]) ).
tff(f24,plain,
( $less(1,a)
| ~ $less(sF9,1000) ),
inference(definition_folding,[],[f6,f22,f21,f19,f18,f16,f15,f14,f12,f10,f9]) ).
tff(f26,definition,
( spl10_1
<=> $less(sF9,1000) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
tff(f30,definition,
( spl10_2
<=> $less(1,a) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
tff(f33,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f24,f30,f26]) ).
tff(f35,definition,
( spl10_3
<=> ( $product(sF7,a) = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
tff(f38,plain,
spl10_3,
inference(avatar_split_clause,[],[f21,f35]) ).
tff(f39,plain,
( ~ spl10_2
| spl10_1 ),
inference(avatar_split_clause,[],[f23,f26,f30]) ).
tff(f41,definition,
( spl10_4
<=> ( $product(sF1,a) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
tff(f44,plain,
spl10_4,
inference(avatar_split_clause,[],[f12,f41]) ).
tff(f46,definition,
( spl10_5
<=> ( sF7 = $product(sF6,a) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
tff(f49,plain,
spl10_5,
inference(avatar_split_clause,[],[f19,f46]) ).
tff(f51,definition,
( spl10_6
<=> ( $product(sF5,a) = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
tff(f54,plain,
spl10_6,
inference(avatar_split_clause,[],[f18,f51]) ).
tff(f56,definition,
( spl10_7
<=> ( $product(sF2,a) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
tff(f59,plain,
spl10_7,
inference(avatar_split_clause,[],[f14,f56]) ).
tff(f61,definition,
( spl10_8
<=> ( sF1 = $product(sF0,a) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
tff(f64,plain,
spl10_8,
inference(avatar_split_clause,[],[f10,f61]) ).
tff(f66,definition,
( spl10_9
<=> ( sF4 = $product(sF3,a) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
tff(f69,plain,
spl10_9,
inference(avatar_split_clause,[],[f15,f66]) ).
tff(f71,definition,
( spl10_10
<=> ( sF5 = $product(sF4,a) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
tff(f74,plain,
spl10_10,
inference(avatar_split_clause,[],[f16,f71]) ).
tff(f76,definition,
( spl10_11
<=> ( $product(a,a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
tff(f79,plain,
spl10_11,
inference(avatar_split_clause,[],[f9,f76]) ).
tff(f81,definition,
( spl10_12
<=> ( sF9 = $product(sF8,a) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
tff(f84,plain,
spl10_12,
inference(avatar_split_clause,[],[f22,f81]) ).
tff(f85,plain,
$false,
inference(avatar_smt_refutation,[],[f84,f79,f74,f69,f64,f59,f54,f49,f44,f39,f38,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI662_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:50:36 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 1.17/1.03 % (4015175)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.17/1.03 % (4015181)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1858894854:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.17/1.03 % (4015186)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2964082272:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.17/1.03 % (4015183)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1631584868:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.17/1.03 % (4015185)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=516863946:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.17/1.03 % (4015184)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2898362010:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.17/1.03 % (4015182)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2525896115:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.17/1.03 % (4015180)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3916268349:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.17/1.03 % (4015184)Instruction limit reached!
% 1.17/1.03 % (4015184)------------------------------
% 1.17/1.03 % (4015184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.17/1.03 % (4015184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.17/1.03 % (4015184)CaDiCaL version: 2.1.3
% 1.17/1.03 % (4015184)Termination reason: Instruction limit
% 1.17/1.03 % (4015184)Termination phase: Saturation
% 1.17/1.03 % (4015184)Time elapsed: 0.004 s
% 1.17/1.03 % (4015184)Peak memory usage: 88 MB
% 1.17/1.03 % (4015184)Instructions burned: 6 (million)
% 1.17/1.03 % (4015183)Instruction limit reached!
% 1.17/1.03 % (4015183)------------------------------
% 1.17/1.03 % (4015183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.17/1.03 % (4015183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.17/1.03 % (4015183)CaDiCaL version: 2.1.3
% 1.17/1.03 % (4015183)Termination reason: Instruction limit
% 1.17/1.03 % (4015183)Termination phase: Saturation
% 1.17/1.03 % (4015183)Time elapsed: 0.005 s
% 1.17/1.03 % (4015183)Peak memory usage: 88 MB
% 1.17/1.03 % (4015183)Instructions burned: 9 (million)
% 1.17/1.03 % (4015181)First to succeed.
% 1.17/1.03 % (4015181)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4015175"
% 1.17/1.03 % (4015180)Also succeeded, but the first one will report.
% 1.17/1.03 % (4015185)Also succeeded, but the first one will report.
% 1.17/1.03 % (4015186)Instruction limit reached!
% 1.17/1.03 % (4015186)------------------------------
% 1.17/1.03 % (4015186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.17/1.03 % (4015186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.17/1.03 % (4015186)CaDiCaL version: 2.1.3
% 1.17/1.03 % (4015186)Termination reason: Instruction limit
% 1.17/1.03 % (4015186)Termination phase: Saturation
% 1.17/1.03 % (4015186)Time elapsed: 0.043 s
% 1.17/1.03 % (4015186)Peak memory usage: 116 MB
% 1.17/1.03 % (4015186)Instructions burned: 35 (million)
% 1.17/1.03 % (4015182)Instruction limit reached!
% 1.17/1.03 % (4015182)------------------------------
% 1.17/1.03 % (4015182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.17/1.03 % (4015182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.17/1.03 % (4015182)CaDiCaL version: 2.1.3
% 1.17/1.03 % (4015182)Termination reason: Instruction limit
% 1.17/1.03 % (4015182)Termination phase: Saturation
% 1.17/1.03 % (4015182)Time elapsed: 0.142 s
% 1.17/1.03 % (4015182)Peak memory usage: 114 MB
% 1.17/1.03 % (4015182)Instructions burned: 202 (million)
% 1.17/1.03 % (4015194)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1583998730:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.17/1.03 % (4015195)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=1991257938:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 1.17/1.03 % (4015194)Refutation not found, incomplete strategy
% 1.17/1.03 % (4015194)------------------------------
% 1.17/1.03 % (4015194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.22 % (4015194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.22 % (4015194)CaDiCaL version: 2.1.3
% 3.26/1.22 % (4015194)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.22 % (4015194)Time elapsed: 0.001 s
% 3.26/1.22 % (4015194)Peak memory usage: 88 MB
% 3.26/1.22 % (4015195)Instruction limit reached!
% 3.26/1.22 % (4015195)------------------------------
% 3.26/1.22 % (4015195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.22 % (4015195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.22 % (4015195)CaDiCaL version: 2.1.3
% 3.26/1.22 % (4015195)Termination reason: Instruction limit
% 3.26/1.22 % (4015195)Termination phase: Saturation
% 3.26/1.22 % (4015195)Time elapsed: 0.022 s
% 3.26/1.22 % (4015195)Peak memory usage: 88 MB
% 3.26/1.22 % (4015195)Instructions burned: 30 (million)
% 3.26/1.22 % (4015181)Refutation found. Thanks to Tanya!
% 3.26/1.22 % SZS status Theorem for theBenchmark
% 3.26/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.26/1.23 % (4015181)------------------------------
% 3.26/1.23 % (4015181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.23 % (4015181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.23 % (4015181)CaDiCaL version: 2.1.3
% 3.26/1.23 % (4015181)Termination reason: Refutation
% 3.26/1.23 % (4015181)Time elapsed: 0.061 s
% 3.26/1.23 % (4015181)Peak memory usage: 118 MB
% 3.26/1.23 % (4015181)Instructions burned: 139 (million)
% 3.26/1.23 % (4015181)------------------------------
% 3.26/1.23 % (4015181)------------------------------
% 3.26/1.23 % (4015175)Success in time 0.368 s
% 3.26/1.23 % Vampire exiting
%------------------------------------------------------------------------------