%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI180_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:32:38 AM UTC 2026
% Result : Theorem 2.85s 1.16s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 24 unt; 0 typ; 13 def)
% Number of atoms : 58 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 8 ~; 0 |; 9 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 57 ( 0 atm; 28 fun; 19 num; 10 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 : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 10 ( 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sK1: $int ).
tff(func_def_7,type,
sF2: $int ).
tff(func_def_8,type,
sF3: $int ).
tff(func_def_9,type,
sF4: $int ).
tff(func_def_10,type,
sF5: $int ).
tff(func_def_11,type,
sF6: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( ( ( $sum(X0,X1) = f(X0) )
& ( $difference(X1,f(X0)) = 0 ) )
=> ( X1 = f(0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( ( ( $sum(X0,X1) = f(X0) )
& ( $difference(X1,f(X0)) = 0 ) )
=> ( X1 = f(0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int] :
( ( ( $sum(X0,X1) = f(X0) )
& ( 0 = $sum(X1,$uminus(f(X0))) ) )
=> ( X1 = f(0) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
? [X1: $int,X0: $int] :
( ( f(0) != X1 )
& ( $sum(X0,X1) = f(X0) )
& ( 0 = $sum(X1,$uminus(f(X0))) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
? [X0: $int,X1: $int] :
( ( 0 = $sum(X1,$uminus(f(X0))) )
& ( $sum(X0,X1) = f(X0) )
& ( f(0) != X1 ) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
( ( 0 = $sum(sK1,$uminus(f(sK0))) )
& ( $sum(sK0,sK1) = f(sK0) )
& ( f(0) != sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
tff(f7,plain,
f(0) != sK1,
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
$sum(sK0,sK1) = f(sK0),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
0 = $sum(sK1,$uminus(f(sK0))),
inference(cnf_transformation,[],[f6]) ).
tff(f10,definition,
sF2 = f(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f11,definition,
sF3 = $uminus(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f12,plain,
$uminus(sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
tff(f13,definition,
sF4 = $sum(sK1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f14,plain,
$sum(sK1,sF3) = sF4,
inference(reorient_equations,[],[f13]) ).
tff(f15,plain,
0 = sF4,
inference(definition_folding,[],[f9,f14,f12,f10]) ).
tff(f16,definition,
sF5 = $sum(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f17,plain,
$sum(sK0,sK1) = sF5,
inference(reorient_equations,[],[f16]) ).
tff(f18,plain,
sF5 = sF2,
inference(definition_folding,[],[f8,f10,f17]) ).
tff(f19,definition,
sF6 = f(0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f20,plain,
f(0) = sF6,
inference(reorient_equations,[],[f19]) ).
tff(f21,plain,
sF6 != sK1,
inference(definition_folding,[],[f7,f20]) ).
tff(f23,definition,
( spl7_1
<=> ( sF5 = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f26,plain,
spl7_1,
inference(avatar_split_clause,[],[f18,f23]) ).
tff(f28,definition,
( spl7_2
<=> ( 0 = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f31,plain,
spl7_2,
inference(avatar_split_clause,[],[f15,f28]) ).
tff(f33,definition,
( spl7_3
<=> ( sF6 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f36,plain,
~ spl7_3,
inference(avatar_split_clause,[],[f21,f33]) ).
tff(f38,definition,
( spl7_4
<=> ( f(0) = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f41,plain,
spl7_4,
inference(avatar_split_clause,[],[f20,f38]) ).
tff(f43,definition,
( spl7_5
<=> ( $sum(sK0,sK1) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f46,plain,
spl7_5,
inference(avatar_split_clause,[],[f17,f43]) ).
tff(f48,definition,
( spl7_6
<=> ( sF2 = f(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f51,plain,
spl7_6,
inference(avatar_split_clause,[],[f10,f48]) ).
tff(f53,definition,
( spl7_7
<=> ( $sum(sK1,sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f56,plain,
spl7_7,
inference(avatar_split_clause,[],[f14,f53]) ).
tff(f58,definition,
( spl7_8
<=> ( $uminus(sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
tff(f61,plain,
spl7_8,
inference(avatar_split_clause,[],[f12,f58]) ).
tff(f62,plain,
$false,
inference(avatar_smt_refutation,[],[f61,f56,f51,f46,f41,f36,f31,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI180_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:45:05 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.85/1.16 % (520952)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.85/1.16 % (520958)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1226945891:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.85/1.16 % (520958)First to succeed.
% 2.85/1.16 % (520958)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-520952"
% 2.85/1.16 % (520963)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2745303526:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.85/1.16 % (520960)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1632931583:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.85/1.16 % (520961)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3885429340:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.85/1.16 % (520957)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4092231157:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.85/1.16 % (520959)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1154360644:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.85/1.16 % (520961)Instruction limit reached!
% 2.85/1.16 % (520961)------------------------------
% 2.85/1.16 % (520961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.16 % (520961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.16 % (520961)CaDiCaL version: 2.1.3
% 2.85/1.16 % (520961)Termination reason: Instruction limit
% 2.85/1.16 % (520961)Termination phase: Saturation
% 2.85/1.16 % (520961)Time elapsed: 0.004 s
% 2.85/1.16 % (520961)Peak memory usage: 89 MB
% 2.85/1.16 % (520961)Instructions burned: 5 (million)
% 2.85/1.16 % (520960)Also succeeded, but the first one will report.
% 2.85/1.16 % (520962)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4058717040:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.85/1.16 % (520963)Also succeeded, but the first one will report.
% 2.85/1.16 % (520957)Also succeeded, but the first one will report.
% 2.85/1.16 % (520959)Also succeeded, but the first one will report.
% 2.85/1.16 % (520962)Also succeeded, but the first one will report.
% 2.85/1.16 % (520971)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1656999538:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.85/1.16 % (520971)Refutation not found, incomplete strategy
% 2.85/1.16 % (520971)------------------------------
% 2.85/1.16 % (520971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.16 % (520971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.16 % (520971)CaDiCaL version: 2.1.3
% 2.85/1.16 % (520971)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.16 % (520971)Time elapsed: 0.001 s
% 2.85/1.16 % (520971)Peak memory usage: 89 MB
% 2.85/1.16 % (520958)Refutation found. Thanks to Tanya!
% 2.85/1.16 % SZS status Theorem for theBenchmark
% 2.85/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.16 % (520958)------------------------------
% 2.85/1.16 % (520958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.16 % (520958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.16 % (520958)CaDiCaL version: 2.1.3
% 2.85/1.16 % (520958)Termination reason: Refutation
% 2.85/1.16 % (520958)Time elapsed: 0.021 s
% 2.85/1.16 % (520958)Peak memory usage: 116 MB
% 2.85/1.16 % (520958)Instructions burned: 11 (million)
% 2.85/1.16 % (520958)------------------------------
% 2.85/1.16 % (520958)------------------------------
% 2.85/1.16 % (520952)Success in time 0.314 s
% 2.85/1.16 % Vampire exiting
%------------------------------------------------------------------------------