%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI637_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 09:33:33 AM UTC 2026
% Result : Theorem 4.02s 1.39s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 4 def)
% Number of atoms : 32 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 55 ( 17 atm; 15 fun; 17 num; 6 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 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $real ).
tff(func_def_1,type,
b: $real ).
tff(func_def_2,type,
f: $real > $real ).
tff(f1,axiom,
! [X1: $real,X0: $real] : ( f($sum(X0,X1)) = $product(f(X0),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_feature) ).
tff(f2,axiom,
$greater(f(a),2/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$greater(f(b),2/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,conjecture,
$greater(f($sum(a,b)),4/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(f5,negated_conjecture,
~ $greater(f($sum(a,b)),4/1),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
$less(2/1,f(a)),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
~ $less(4/1,f($sum(a,b))),
inference(theory_normalization,[],[f5]) ).
tff(f8,plain,
$less(2/1,f(b)),
inference(theory_normalization,[],[f3]) ).
tff(f9,plain,
! [X0: $real,X1: $real] : ( $product(f(X1),f(X0)) = f($sum(X1,X0)) ),
inference(rectify,[],[f1]) ).
tff(f10,plain,
~ $less(4/1,f($sum(a,b))),
inference(flattening,[],[f7]) ).
tff(f11,plain,
~ $less(4/1,f($sum(a,b))),
inference(cnf_transformation,[],[f10]) ).
tff(f12,plain,
$less(2/1,f(b)),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
$less(2/1,f(a)),
inference(cnf_transformation,[],[f6]) ).
tff(f14,plain,
! [X0: $real,X1: $real] : ( $product(f(X1),f(X0)) = f($sum(X1,X0)) ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,definition,
( spl0_1
<=> $less(2/1,f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f19,plain,
spl0_1,
inference(avatar_split_clause,[],[f13,f16]) ).
tff(f21,definition,
( spl0_2
<=> $less(2/1,f(b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f24,plain,
spl0_2,
inference(avatar_split_clause,[],[f12,f21]) ).
tff(f26,definition,
( spl0_3
<=> $less(4/1,f($sum(a,b))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f28,plain,
( ~ $less(4/1,f($sum(a,b)))
| spl0_3 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f29,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f11,f26]) ).
tff(f30,plain,
( ~ $less(4/1,$product(f(a),f(b)))
| spl0_3 ),
inference(forward_demodulation,[],[f28,f14]) ).
tff(f32,definition,
( spl0_4
<=> $less(4/1,$product(f(a),f(b))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f35,plain,
( ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f30,f26,f32]) ).
tff(f36,plain,
$false,
inference(avatar_smt_refutation,[],[f35,f29,f24,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI637_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n001.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 21:00:18 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 4.02/1.39 % (737843)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.02/1.39 % (737990)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1891682296:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.02/1.39 % (737990)Instruction limit reached!
% 4.02/1.39 % (737990)------------------------------
% 4.02/1.39 % (737990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737990)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737990)Termination reason: Instruction limit
% 4.02/1.39 % (737990)Termination phase: Saturation
% 4.02/1.39 % (737990)Time elapsed: 0.003 s
% 4.02/1.39 % (737990)Peak memory usage: 88 MB
% 4.02/1.39 % (737990)Instructions burned: 7 (million)
% 4.02/1.39 % (737993)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3849399124:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.02/1.39 % (737992)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2766878175:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.02/1.39 % (737991)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3623633789:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.02/1.39 % (737989)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3829225654:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.02/1.39 % (737987)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1052211220:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.02/1.39 % (737988)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4179856676:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.02/1.39 % (737991)Instruction limit reached!
% 4.02/1.39 % (737991)------------------------------
% 4.02/1.39 % (737991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737991)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737991)Termination reason: Instruction limit
% 4.02/1.39 % (737991)Termination phase: Saturation
% 4.02/1.39 % (737991)Time elapsed: 0.022 s
% 4.02/1.39 % (737991)Peak memory usage: 89 MB
% 4.02/1.39 % (737991)Instructions burned: 14 (million)
% 4.02/1.39 % (737987)Instruction limit reached!
% 4.02/1.39 % (737987)------------------------------
% 4.02/1.39 % (737987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737987)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737987)Termination reason: Instruction limit
% 4.02/1.39 % (737987)Termination phase: Saturation
% 4.02/1.39 % (737987)Time elapsed: 0.075 s
% 4.02/1.39 % (737987)Peak memory usage: 116 MB
% 4.02/1.39 % (737987)Instructions burned: 12 (million)
% 4.02/1.39 % (737992)First to succeed.
% 4.02/1.39 % (737992)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-737843"
% 4.02/1.39 % (737995)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2896615753:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.02/1.39 % (737995)Refutation not found, incomplete strategy
% 4.02/1.39 % (737995)------------------------------
% 4.02/1.39 % (737995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737995)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737995)Termination reason: Refutation not found, incomplete strategy
% 4.02/1.39 % (737995)Time elapsed: 0.001 s
% 4.02/1.39 % (737995)Peak memory usage: 88 MB
% 4.02/1.39 % (737993)Instruction limit reached!
% 4.02/1.39 % (737993)------------------------------
% 4.02/1.39 % (737993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737993)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737993)Termination reason: Instruction limit
% 4.02/1.39 % (737993)Termination phase: Saturation
% 4.02/1.39 % (737993)Time elapsed: 0.093 s
% 4.02/1.39 % (737993)Peak memory usage: 116 MB
% 4.02/1.39 % (737993)Instructions burned: 33 (million)
% 4.02/1.39 % (738002)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=4052874057:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.02/1.39 % (737989)Instruction limit reached!
% 4.02/1.39 % (737989)------------------------------
% 4.02/1.39 % (737989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737989)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737989)Termination reason: Instruction limit
% 4.02/1.39 % (737989)Termination phase: Saturation
% 4.02/1.39 % (737989)Time elapsed: 0.189 s
% 4.02/1.39 % (737989)Peak memory usage: 117 MB
% 4.02/1.39 % (737989)Instructions burned: 201 (million)
% 4.02/1.39 % (738002)Instruction limit reached!
% 4.02/1.39 % (738002)------------------------------
% 4.02/1.39 % (738002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (738002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (738002)CaDiCaL version: 2.1.3
% 4.02/1.39 % (738002)Termination reason: Instruction limit
% 4.02/1.39 % (738002)Termination phase: Saturation
% 4.02/1.39 % (738002)Time elapsed: 0.019 s
% 4.02/1.39 % (738002)Peak memory usage: 88 MB
% 4.02/1.39 % (738002)Instructions burned: 30 (million)
% 4.02/1.39 % (737988)Instruction limit reached!
% 4.02/1.39 % (737988)------------------------------
% 4.02/1.39 % (737988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (737988)CaDiCaL version: 2.1.3
% 4.02/1.39 % (737988)Termination reason: Instruction limit
% 4.02/1.39 % (737988)Termination phase: Saturation
% 4.02/1.39 % (737988)Time elapsed: 0.220 s
% 4.02/1.39 % (737988)Peak memory usage: 117 MB
% 4.02/1.39 % (737988)Instructions burned: 309 (million)
% 4.02/1.39 % (737995)------------------------------
% 4.02/1.39 % (737995)------------------------------
% 4.02/1.39 % (738004)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2792434999:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.02/1.39 % (738004)Instruction limit reached!
% 4.02/1.39 % (738004)------------------------------
% 4.02/1.39 % (738004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (738004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (738004)CaDiCaL version: 2.1.3
% 4.02/1.39 % (738004)Termination reason: Instruction limit
% 4.02/1.39 % (738004)Termination phase: Saturation
% 4.02/1.39 % (738004)Time elapsed: 0.010 s
% 4.02/1.39 % (738004)Peak memory usage: 90 MB
% 4.02/1.39 % (738004)Instructions burned: 18 (million)
% 4.02/1.39 % (738005)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=4021696500:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.02/1.39 % (738005)Instruction limit reached!
% 4.02/1.39 % (738005)------------------------------
% 4.02/1.39 % (738005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (738005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (738005)CaDiCaL version: 2.1.3
% 4.02/1.39 % (738005)Termination reason: Instruction limit
% 4.02/1.39 % (738005)Termination phase: Saturation
% 4.02/1.39 % (738005)Time elapsed: 0.019 s
% 4.02/1.39 % (738005)Peak memory usage: 89 MB
% 4.02/1.39 % (738005)Instructions burned: 25 (million)
% 4.02/1.39 % (738008)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=3878334128:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 4.02/1.39 % (738007)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=2287541785:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 4.02/1.39 % (738011)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=94158511:i=181:rtra=on:ss=axioms:ev=cautious_2995 on theBenchmark for (2995ds/181Mi)
% 4.02/1.39 % (738011)Refutation not found, incomplete strategy
% 4.02/1.39 % (738011)------------------------------
% 4.02/1.39 % (738011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (738011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.39 % (738011)CaDiCaL version: 2.1.3
% 4.02/1.39 % (738011)Termination reason: Refutation not found, incomplete strategy
% 4.02/1.39 % (738011)Time elapsed: 0.001 s
% 4.02/1.39 % (738011)Peak memory usage: 89 MB
% 4.02/1.39 % (737992)Refutation found. Thanks to Tanya!
% 4.02/1.39 % SZS status Theorem for theBenchmark
% 4.02/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.39 % (737992)------------------------------
% 4.02/1.39 % (737992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.39 % (737992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.40 % (737992)CaDiCaL version: 2.1.3
% 4.02/1.40 % (737992)Termination reason: Refutation
% 4.02/1.40 % (737992)Time elapsed: 0.077 s
% 4.02/1.40 % (737992)Peak memory usage: 116 MB
% 4.02/1.40 % (737992)Instructions burned: 10 (million)
% 4.02/1.40 % (737992)------------------------------
% 4.02/1.40 % (737992)------------------------------
% 4.02/1.40 % (737843)Success in time 0.522 s
% 4.02/1.40 % Vampire exiting
%------------------------------------------------------------------------------