%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI708_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 : n006.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 3.93s 1.33s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 21 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 102 ( 0 atm; 80 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
c: $int ).
tff(func_def_2,type,
d: $int ).
tff(func_def_3,type,
b: $int ).
tff(f1,axiom,
$sum(a,$product(-1,$product($sum(c,d),$sum(d,c)))) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(f2,axiom,
$product($difference(c,d),$difference(c,d)) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq2) ).
tff(f3,conjecture,
$sum($sum(a,b),$product(-1,$product(2,$sum($product(c,c),$product(d,d))))) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f4,negated_conjecture,
( ( ~ $sum($sum(a,b),$product(-1,$product(2,$sum($product(c,c),$product(d,d))))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
b = $product($sum(c,$uminus(d)),$sum(c,$uminus(d))),
inference(theory_normalization,[],[f2]) ).
tff(f6,plain,
0 != $sum($sum(a,b),$product(-1,$product(2,$sum($product(c,c),$product(d,d))))),
inference(flattening,[],[f4]) ).
tff(f7,plain,
$sum(a,$product(-1,$product($sum(c,d),$sum(d,c)))) = 0,
inference(cnf_transformation,[],[f1]) ).
tff(f8,plain,
0 != $sum($sum(a,b),$product(-1,$product(2,$sum($product(c,c),$product(d,d))))),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
b = $product($sum(c,$uminus(d)),$sum(c,$uminus(d))),
inference(cnf_transformation,[],[f5]) ).
tff(f10,plain,
0 != $sum($sum(a,b),$uminus($product(2,$sum($product(c,c),$product(d,d))))),
inference(evaluation,[],[f8]) ).
tff(f11,plain,
0 = $sum(a,$uminus($product($sum(c,d),$sum(d,c)))),
inference(evaluation,[],[f7]) ).
tff(f13,definition,
( spl0_1
<=> ( b = $product($sum(c,$uminus(d)),$sum(c,$uminus(d))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f16,plain,
spl0_1,
inference(avatar_split_clause,[],[f9,f13]) ).
tff(f18,definition,
( spl0_2
<=> ( 0 = $sum($sum(a,b),$uminus($product(2,$sum($product(c,c),$product(d,d))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f21,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f10,f18]) ).
tff(f23,definition,
( spl0_3
<=> ( 0 = $sum(a,$uminus($product($sum(c,d),$sum(d,c)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f26,plain,
spl0_3,
inference(avatar_split_clause,[],[f11,f23]) ).
tff(f27,plain,
$false,
inference(avatar_smt_refutation,[],[f26,f21,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI708_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n006.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 20:57:40 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running first-order theorem proving
% 0.11/0.25 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
% 3.93/1.33 % (190731)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.93/1.33 % (190818)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=679007061:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.93/1.33 % (190818)Instruction limit reached!
% 3.93/1.33 % (190818)------------------------------
% 3.93/1.33 % (190818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190818)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190818)Termination reason: Instruction limit
% 3.93/1.33 % (190818)Termination phase: Saturation
% 3.93/1.33 % (190818)Time elapsed: 0.003 s
% 3.93/1.33 % (190818)Peak memory usage: 88 MB
% 3.93/1.33 % (190818)Instructions burned: 9 (million)
% 3.93/1.33 % (190817)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3729431306:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.93/1.33 % (190820)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=49048990:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.93/1.33 % (190816)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=866849917:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.93/1.33 % (190819)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3489931664:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.93/1.33 % (190821)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2369991926:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.93/1.33 % (190815)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=577338609:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.93/1.33 % (190819)Instruction limit reached!
% 3.93/1.33 % (190819)------------------------------
% 3.93/1.33 % (190819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190819)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190819)Termination reason: Instruction limit
% 3.93/1.33 % (190819)Termination phase: Saturation
% 3.93/1.33 % (190819)Time elapsed: 0.004 s
% 3.93/1.33 % (190819)Peak memory usage: 88 MB
% 3.93/1.33 % (190819)Instructions burned: 6 (million)
% 3.93/1.33 % (190820)First to succeed.
% 3.93/1.33 % (190815)Also succeeded, but the first one will report.
% 3.93/1.33 % (190820)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-190731"
% 3.93/1.33 % (190816)Also succeeded, but the first one will report.
% 3.93/1.33 % (190821)Also succeeded, but the first one will report.
% 3.93/1.33 % (190823)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3065769198:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.93/1.33 % (190823)Refutation not found, incomplete strategy
% 3.93/1.33 % (190823)------------------------------
% 3.93/1.33 % (190823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190823)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190823)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.33 % (190823)Time elapsed: 0.001 s
% 3.93/1.33 % (190823)Peak memory usage: 88 MB
% 3.93/1.33 % (190817)Instruction limit reached!
% 3.93/1.33 % (190817)------------------------------
% 3.93/1.33 % (190817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190817)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190817)Termination reason: Instruction limit
% 3.93/1.33 % (190817)Termination phase: Saturation
% 3.93/1.33 % (190817)Time elapsed: 0.158 s
% 3.93/1.33 % (190817)Peak memory usage: 117 MB
% 3.93/1.33 % (190817)Instructions burned: 201 (million)
% 3.93/1.33 % (190830)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=1687423230:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.93/1.33 % (190830)Instruction limit reached!
% 3.93/1.33 % (190830)------------------------------
% 3.93/1.33 % (190830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190830)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190830)Termination reason: Instruction limit
% 3.93/1.33 % (190830)Termination phase: Saturation
% 3.93/1.33 % (190830)Time elapsed: 0.015 s
% 3.93/1.33 % (190830)Peak memory usage: 88 MB
% 3.93/1.33 % (190830)Instructions burned: 30 (million)
% 3.93/1.33 % (190823)------------------------------
% 3.93/1.33 % (190823)------------------------------
% 3.93/1.33 % (190820)Refutation found. Thanks to Tanya!
% 3.93/1.33 % SZS status Theorem for theBenchmark
% 3.93/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.33 % (190820)------------------------------
% 3.93/1.33 % (190820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.33 % (190820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.33 % (190820)CaDiCaL version: 2.1.3
% 3.93/1.33 % (190820)Termination reason: Refutation
% 3.93/1.33 % (190820)Time elapsed: 0.034 s
% 3.93/1.33 % (190820)Peak memory usage: 115 MB
% 3.93/1.33 % (190820)Instructions burned: 10 (million)
% 3.93/1.33 % (190820)------------------------------
% 3.93/1.33 % (190820)------------------------------
% 3.93/1.33 % (190731)Success in time 0.463 s
% 3.93/1.33 % Vampire exiting
%------------------------------------------------------------------------------