%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI712_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 : n007.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 09:33:43 AM UTC 2026
% Result : Theorem 0.30s 2.06s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 15 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 480 ( 0 atm; 410 fun; 70 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 : 11 ( 4 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_3,type,
d: $int ).
tff(f1,axiom,
$sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f22,plain,
0 != $sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))),
inference(flattening,[],[f3]) ).
tff(f23,plain,
0 != $sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
$sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
inference(cnf_transformation,[],[f1]) ).
tff(f26,plain,
0 = $sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$uminus($product($sum($sum($sum(a,b),c),d),$sum(2,c)))),
inference(evaluation,[],[f24]) ).
tff(f27,plain,
0 != $sum($product($product($product($product($product(d,d),d),b),b),a),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$uminus($product(a,a))),b),$product(2,c)),$uminus($product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$uminus($product($product(c,b),a))),$uminus($product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$uminus($product($product(d,b),a))),$product(c,c)),$uminus($product($product($product($product($product(d,c),c),b),a),a))))),
inference(evaluation,[],[f23]) ).
tff(f29,definition,
( spl0_1
<=> ( 0 = $sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$uminus($product($sum($sum($sum(a,b),c),d),$sum(2,c)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f32,plain,
spl0_1,
inference(avatar_split_clause,[],[f26,f29]) ).
tff(f34,definition,
( spl0_2
<=> ( 0 = $sum($product($product($product($product($product(d,d),d),b),b),a),$uminus($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$uminus($product(a,a))),b),$product(2,c)),$uminus($product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$uminus($product($product(c,b),a))),$uminus($product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$uminus($product($product(d,b),a))),$product(c,c)),$uminus($product($product($product($product($product(d,c),c),b),a),a))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f37,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f27,f34]) ).
tff(f38,plain,
$false,
inference(avatar_smt_refutation,[],[f37,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI712_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n007.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.24/0.27 % CPULimit : 300
% 0.24/0.27 % WCLimit : 300
% 0.24/0.27 % DateTime : Mon Sep 28 20:56:10 UTC 2026
% 0.24/0.28 % CPUTime :
% 0.24/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 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
% 0.30/2.06 % (2814950)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.30/2.06 % (2814958)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3202213524:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/2.06 % (2814960)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=684509261:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.30/2.06 % (2814958)First to succeed.
% 0.30/2.06 % (2814958)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2814950"
% 0.30/2.06 % (2814962)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1305108094:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.30/2.06 % (2814959)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2634718076:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.30/2.06 % (2814964)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3508874515:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.30/2.06 % (2814963)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2822212848:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.30/2.06 % (2814961)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3496424739:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/2.06 % (2814962)Instruction limit reached!
% 0.30/2.06 % (2814962)------------------------------
% 0.30/2.06 % (2814962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814962)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814962)Termination reason: Instruction limit
% 0.30/2.06 % (2814962)Termination phase: Saturation
% 0.30/2.06 % (2814962)Time elapsed: 0.005 s
% 0.30/2.06 % (2814962)Peak memory usage: 88 MB
% 0.30/2.06 % (2814962)Instructions burned: 4 (million)
% 0.30/2.06 % (2814961)Instruction limit reached!
% 0.30/2.06 % (2814961)------------------------------
% 0.30/2.06 % (2814961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814961)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814961)Termination reason: Instruction limit
% 0.30/2.06 % (2814961)Termination phase: Saturation
% 0.30/2.06 % (2814961)Time elapsed: 0.008 s
% 0.30/2.06 % (2814961)Peak memory usage: 88 MB
% 0.30/2.06 % (2814961)Instructions burned: 7 (million)
% 0.30/2.06 % (2814963)Also succeeded, but the first one will report.
% 0.30/2.06 % (2814964)Instruction limit reached!
% 0.30/2.06 % (2814964)------------------------------
% 0.30/2.06 % (2814964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814964)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814964)Termination reason: Instruction limit
% 0.30/2.06 % (2814964)Termination phase: Saturation
% 0.30/2.06 % (2814964)Time elapsed: 0.065 s
% 0.30/2.06 % (2814964)Peak memory usage: 117 MB
% 0.30/2.06 % (2814964)Instructions burned: 34 (million)
% 0.30/2.06 % (2814960)Instruction limit reached!
% 0.30/2.06 % (2814960)------------------------------
% 0.30/2.06 % (2814960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814960)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814960)Termination reason: Instruction limit
% 0.30/2.06 % (2814960)Termination phase: Saturation
% 0.30/2.06 % (2814960)Time elapsed: 0.232 s
% 0.30/2.06 % (2814960)Peak memory usage: 114 MB
% 0.30/2.06 % (2814960)Instructions burned: 201 (million)
% 0.30/2.06 % (2814959)Refutation not found, SMT solver inside AVATAR returned Unknown
% 0.30/2.06 % (2814959)------------------------------
% 0.30/2.06 % (2814959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814959)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814959)Termination reason: Refutation not found, SMT solver inside AVATAR returned Unknown
% 0.30/2.06 % (2814959)Time elapsed: 0.176 s
% 0.30/2.06 % (2814959)Peak memory usage: 120 MB
% 0.30/2.06 % (2814959)Instructions burned: 155 (million)
% 0.30/2.06 % (2814959)------------------------------
% 0.30/2.06 % (2814959)------------------------------
% 0.30/2.06 % (2814958)Refutation found. Thanks to Tanya!
% 0.30/2.06 % SZS status Theorem for theBenchmark
% 0.30/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/2.06 % (2814958)------------------------------
% 0.30/2.06 % (2814958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.06 % (2814958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.06 % (2814958)CaDiCaL version: 2.1.3
% 0.30/2.06 % (2814958)Termination reason: Refutation
% 0.30/2.06 % (2814958)Time elapsed: 0.029 s
% 0.30/2.06 % (2814958)Peak memory usage: 116 MB
% 0.30/2.06 % (2814958)Instructions burned: 14 (million)
% 0.30/2.06 % (2814958)------------------------------
% 0.30/2.06 % (2814958)------------------------------
% 0.30/2.06 % (2814950)Success in time 0.828 s
% 0.30/2.06 % Vampire exiting
%------------------------------------------------------------------------------