%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI695_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:33:40 AM UTC 2026
% Result : Theorem 0.23s 1.70s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 10 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 6 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 95 ( 0 atm; 59 fun; 36 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 : 3 ( 1 usr; 2 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,conjecture,
$sum($product($product(-1,d),$sum(2,c)),$product(-1,$product(d,$difference($product(-1,2),c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
( ( ~ $sum($product($product(-1,d),$sum(2,c)),$product(-1,$product(d,$difference($product(-1,2),c)))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
( ( ~ 0 ) = $sum($product($product(-1,d),$sum(2,c)),$product(-1,$product(d,$sum($product(-1,2),$uminus(c))))) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
0 != $sum($product($product(-1,d),$sum(2,c)),$product(-1,$product(d,$sum($product(-1,2),$uminus(c))))),
inference(flattening,[],[f3]) ).
tff(f23,plain,
0 != $sum($product($product(-1,d),$sum(2,c)),$product(-1,$product(d,$sum($product(-1,2),$uminus(c))))),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
0 != $sum($product($uminus(d),$sum(2,c)),$uminus($product(d,$sum(-2,$uminus(c))))),
inference(evaluation,[],[f23]) ).
tff(f27,definition,
( spl0_1
<=> ( 0 = $sum($product($uminus(d),$sum(2,c)),$uminus($product(d,$sum(-2,$uminus(c))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f30,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f25,f27]) ).
tff(f31,plain,
$false,
inference(avatar_smt_refutation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI695_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n026.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Mon Sep 28 21:00:42 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/1.70 % (67115)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.23/1.70 % (67227)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3578681160:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.23/1.70 % (67228)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2855174147:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/1.70 % (67228)Instruction limit reached!
% 0.23/1.70 % (67228)------------------------------
% 0.23/1.70 % (67228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67228)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67228)Termination reason: Instruction limit
% 0.23/1.70 % (67228)Termination phase: Saturation
% 0.23/1.70 % (67228)Time elapsed: 0.008 s
% 0.23/1.70 % (67228)Peak memory usage: 88 MB
% 0.23/1.70 % (67228)Instructions burned: 7 (million)
% 0.23/1.70 % (67226)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1465870418:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.23/1.70 % (67225)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2767455437:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/1.70 % (67229)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=346179889:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.23/1.70 % (67231)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3612973015:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.23/1.70 % (67229)Instruction limit reached!
% 0.23/1.70 % (67229)------------------------------
% 0.23/1.70 % (67229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67229)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67229)Termination reason: Instruction limit
% 0.23/1.70 % (67229)Termination phase: Saturation
% 0.23/1.70 % (67229)Time elapsed: 0.006 s
% 0.23/1.70 % (67229)Peak memory usage: 88 MB
% 0.23/1.70 % (67229)Instructions burned: 4 (million)
% 0.23/1.70 % (67232)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3884871063:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.23/1.70 % (67225)First to succeed.
% 0.23/1.70 % (67225)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-67115"
% 0.23/1.70 % (67231)Also succeeded, but the first one will report.
% 0.23/1.70 % (67227)Instruction limit reached!
% 0.23/1.70 % (67227)------------------------------
% 0.23/1.70 % (67227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67227)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67227)Termination reason: Instruction limit
% 0.23/1.70 % (67227)Termination phase: Saturation
% 0.23/1.70 % (67227)Time elapsed: 0.132 s
% 0.23/1.70 % (67227)Peak memory usage: 114 MB
% 0.23/1.70 % (67227)Instructions burned: 202 (million)
% 0.23/1.70 % (67232)Also succeeded, but the first one will report.
% 0.23/1.70 % (67226)Also succeeded, but the first one will report.
% 0.23/1.70 % (67243)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=1792407416:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 0.23/1.70 % (67243)Instruction limit reached!
% 0.23/1.70 % (67243)------------------------------
% 0.23/1.70 % (67243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67243)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67243)Termination reason: Instruction limit
% 0.23/1.70 % (67243)Termination phase: Saturation
% 0.23/1.70 % (67243)Time elapsed: 0.009 s
% 0.23/1.70 % (67243)Peak memory usage: 88 MB
% 0.23/1.70 % (67243)Instructions burned: 33 (million)
% 0.23/1.70 % (67241)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3163615681:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 0.23/1.70 % (67241)Refutation not found, incomplete strategy
% 0.23/1.70 % (67241)------------------------------
% 0.23/1.70 % (67241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67241)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67241)Termination reason: Refutation not found, incomplete strategy
% 0.23/1.70 % (67241)Time elapsed: 0.002 s
% 0.23/1.70 % (67241)Peak memory usage: 88 MB
% 0.23/1.70 % (67244)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1895266898:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.23/1.70 % (67244)Instruction limit reached!
% 0.23/1.70 % (67244)------------------------------
% 0.23/1.70 % (67244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67244)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67244)Termination reason: Instruction limit
% 0.23/1.70 % (67244)Termination phase: Saturation
% 0.23/1.70 % (67244)Time elapsed: 0.016 s
% 0.23/1.70 % (67244)Peak memory usage: 90 MB
% 0.23/1.70 % (67244)Instructions burned: 16 (million)
% 0.23/1.70 % (67251)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=863781966:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 0.23/1.70 % (67251)Instruction limit reached!
% 0.23/1.70 % (67251)------------------------------
% 0.23/1.70 % (67251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67251)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67251)Termination reason: Instruction limit
% 0.23/1.70 % (67251)Termination phase: Saturation
% 0.23/1.70 % (67251)Time elapsed: 0.015 s
% 0.23/1.70 % (67251)Peak memory usage: 89 MB
% 0.23/1.70 % (67251)Instructions burned: 25 (million)
% 0.23/1.70 % (67257)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=1561987533:i=27:canc=cautious:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/27Mi)
% 0.23/1.70 % (67257)Refutation not found, incomplete strategy
% 0.23/1.70 % (67257)------------------------------
% 0.23/1.70 % (67257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67257)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67257)Termination reason: Refutation not found, incomplete strategy
% 0.23/1.70 % (67257)Time elapsed: 0.001 s
% 0.23/1.70 % (67257)Peak memory usage: 89 MB
% 0.23/1.70 % (67225)Refutation found. Thanks to Tanya!
% 0.23/1.70 % SZS status Theorem for theBenchmark
% 0.23/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.70 % (67225)------------------------------
% 0.23/1.70 % (67225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.70 % (67225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.70 % (67225)CaDiCaL version: 2.1.3
% 0.23/1.70 % (67225)Termination reason: Refutation
% 0.23/1.70 % (67225)Time elapsed: 0.043 s
% 0.23/1.70 % (67225)Peak memory usage: 115 MB
% 0.23/1.70 % (67225)Instructions burned: 8 (million)
% 0.23/1.70 % (67225)------------------------------
% 0.23/1.70 % (67225)------------------------------
% 0.23/1.70 % (67115)Success in time 0.675 s
% 0.23/1.70 % Vampire exiting
%------------------------------------------------------------------------------