%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI707_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 : n004.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 09:33:42 AM UTC 2026
% Result : Theorem 5.98s 1.78s
% Output : Refutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 13 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 30 ( 0 atm; 27 fun; 3 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 2 usr; 3 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,axiom,
$sum($product(d,d),c) = $product($product(2,d),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$product($product(c,d),d) = $product(c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $product($product(c,d),d) ) = $product(c,c) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
$product($product(c,d),d) != $product(c,c),
inference(flattening,[],[f3]) ).
tff(f5,plain,
$sum($product(d,d),c) = $product($product(2,d),d),
inference(cnf_transformation,[],[f1]) ).
tff(f6,plain,
$product($product(c,d),d) != $product(c,c),
inference(cnf_transformation,[],[f4]) ).
tff(f8,definition,
( spl0_1
<=> ( $sum($product(d,d),c) = $product($product(2,d),d) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f11,plain,
spl0_1,
inference(avatar_split_clause,[],[f5,f8]) ).
tff(f13,definition,
( spl0_2
<=> ( $product($product(c,d),d) = $product(c,c) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f16,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f6,f13]) ).
tff(f17,plain,
$false,
inference(avatar_smt_refutation,[],[f16,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI707_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 % Computer : n004.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8046.5625MB
% 0.08/0.24 % OS : Linux 6.8.0-71-generic
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Mon Sep 28 20:57:52 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.30 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
% 5.98/1.78 % (769044)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.98/1.78 % (769049)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3415052246:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.98/1.78 % (769049)Refutation not found, incomplete strategy
% 5.98/1.78 % (769049)------------------------------
% 5.98/1.78 % (769049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769049)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769049)Termination reason: Refutation not found, incomplete strategy
% 5.98/1.78 % (769049)Time elapsed: 0.026 s
% 5.98/1.78 % (769049)Peak memory usage: 117 MB
% 5.98/1.78 % (769049)Instructions burned: 7 (million)
% 5.98/1.78 % (769052)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4213531688:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.98/1.78 % (769050)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=304109770:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.98/1.78 % (769051)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1751261646:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.98/1.78 % (769052)Instruction limit reached!
% 5.98/1.78 % (769052)------------------------------
% 5.98/1.78 % (769052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769052)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769052)Termination reason: Instruction limit
% 5.98/1.78 % (769052)Termination phase: Saturation
% 5.98/1.78 % (769052)Time elapsed: 0.008 s
% 5.98/1.78 % (769052)Peak memory usage: 88 MB
% 5.98/1.78 % (769052)Instructions burned: 7 (million)
% 5.98/1.78 % (769055)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2872577943:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.98/1.78 % (769053)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2776196214:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.98/1.78 % (769054)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3514599127:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.98/1.78 % (769053)Instruction limit reached!
% 5.98/1.78 % (769053)------------------------------
% 5.98/1.78 % (769053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769053)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769053)Termination reason: Instruction limit
% 5.98/1.78 % (769053)Termination phase: Saturation
% 5.98/1.78 % (769053)Time elapsed: 0.009 s
% 5.98/1.78 % (769053)Peak memory usage: 89 MB
% 5.98/1.78 % (769053)Instructions burned: 8 (million)
% 5.98/1.78 % (769054)First to succeed.
% 5.98/1.78 % (769054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-769044"
% 5.98/1.78 % (769050)Also succeeded, but the first one will report.
% 5.98/1.78 % (769055)Also succeeded, but the first one will report.
% 5.98/1.78 % (769049)------------------------------
% 5.98/1.78 % (769049)------------------------------
% 5.98/1.78 % (769063)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3459937683:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.98/1.78 % (769063)Refutation not found, incomplete strategy
% 5.98/1.78 % (769063)------------------------------
% 5.98/1.78 % (769063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769063)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769063)Termination reason: Refutation not found, incomplete strategy
% 5.98/1.78 % (769063)Time elapsed: 0.002 s
% 5.98/1.78 % (769063)Peak memory usage: 88 MB
% 5.98/1.78 % (769051)Instruction limit reached!
% 5.98/1.78 % (769051)------------------------------
% 5.98/1.78 % (769051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769051)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769051)Termination reason: Instruction limit
% 5.98/1.78 % (769051)Termination phase: Saturation
% 5.98/1.78 % (769051)Time elapsed: 0.252 s
% 5.98/1.78 % (769051)Peak memory usage: 118 MB
% 5.98/1.78 % (769051)Instructions burned: 201 (million)
% 5.98/1.78 % (769064)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=2570128856:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.98/1.78 % (769064)Instruction limit reached!
% 5.98/1.78 % (769064)------------------------------
% 5.98/1.78 % (769064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769064)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769064)Termination reason: Instruction limit
% 5.98/1.78 % (769064)Termination phase: Saturation
% 5.98/1.78 % (769064)Time elapsed: 0.022 s
% 5.98/1.78 % (769064)Peak memory usage: 88 MB
% 5.98/1.78 % (769064)Instructions burned: 29 (million)
% 5.98/1.78 % (769065)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=568442258:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/16Mi)
% 5.98/1.78 % (769065)Instruction limit reached!
% 5.98/1.78 % (769065)------------------------------
% 5.98/1.78 % (769065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769065)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769065)Termination reason: Instruction limit
% 5.98/1.78 % (769065)Termination phase: Saturation
% 5.98/1.78 % (769065)Time elapsed: 0.010 s
% 5.98/1.78 % (769065)Peak memory usage: 90 MB
% 5.98/1.78 % (769065)Instructions burned: 17 (million)
% 5.98/1.78 % (769054)Refutation found. Thanks to Tanya!
% 5.98/1.78 % SZS status Theorem for theBenchmark
% 5.98/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.98/1.78 % (769054)------------------------------
% 5.98/1.78 % (769054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.78 % (769054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.78 % (769054)CaDiCaL version: 2.1.3
% 5.98/1.78 % (769054)Termination reason: Refutation
% 5.98/1.78 % (769054)Time elapsed: 0.044 s
% 5.98/1.78 % (769054)Peak memory usage: 116 MB
% 5.98/1.78 % (769054)Instructions burned: 8 (million)
% 5.98/1.78 % (769054)------------------------------
% 5.98/1.78 % (769054)------------------------------
% 5.98/1.78 % (769044)Success in time 0.737 s
% 5.98/1.78 % Vampire exiting
%------------------------------------------------------------------------------