%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI076_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 : n016.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 09:32:29 AM UTC 2026
% Result : Theorem 2.47s 0.84s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 49 ( 0 atm; 20 fun; 13 num; 16 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X0: $int] : ( $sum(X0,-2) = 3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_n2_3) ).
tff(f2,negated_conjecture,
~ ? [X0: $int] : ( $sum(X0,-2) = 3 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f4,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $int] : ( $sum(X0,$uminus(X0)) = 0 ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f15,plain,
! [X0: $int] : ( $sum(X0,-2) != 3 ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
! [X0: $int] : ( $sum(X0,-2) != 3 ),
inference(cnf_transformation,[],[f15]) ).
tff(f23,plain,
! [X0: $int] : ( 3 != $sum(-2,X0) ),
inference(superposition,[],[f16,f3]) ).
tff(f105,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) ),
inference(superposition,[],[f4,f7]) ).
tff(f124,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f105]) ).
tff(f147,plain,
! [X0: $int] : ( 3 != X0 ),
inference(superposition,[],[f23,f124]) ).
tff(f157,plain,
$false,
inference(equality_resolution,[],[f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI076_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 20:46:48 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.47/0.84 % (3968004)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.47/0.84 % (3968080)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2757603917:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.47/0.84 % (3968080)First to succeed.
% 2.47/0.84 % (3968080)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3968004"
% 2.47/0.84 % (3968073)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3729633201:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.47/0.84 % (3968074)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4126072067:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.47/0.84 % (3968075)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3825982405:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.47/0.84 % (3968079)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2183620424:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.47/0.84 % (3968076)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2770892230:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.47/0.84 % (3968076)Also succeeded, but the first one will report.
% 2.47/0.84 % (3968074)Refutation not found, incomplete strategy
% 2.47/0.84 % (3968074)------------------------------
% 2.47/0.84 % (3968074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.84 % (3968074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.84 % (3968074)CaDiCaL version: 2.1.3
% 2.47/0.84 % (3968074)Termination reason: Refutation not found, incomplete strategy
% 2.47/0.84 % (3968074)Time elapsed: 0.028 s
% 2.47/0.84 % (3968074)Peak memory usage: 112 MB
% 2.47/0.84 % (3968074)Instructions burned: 5 (million)
% 2.47/0.84 % (3968075)Also succeeded, but the first one will report.
% 2.47/0.84 % (3968073)Also succeeded, but the first one will report.
% 2.47/0.84 % (3968079)Refutation not found, incomplete strategy
% 2.47/0.84 % (3968079)------------------------------
% 2.47/0.84 % (3968079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.84 % (3968079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.84 % (3968079)CaDiCaL version: 2.1.3
% 2.47/0.84 % (3968079)Termination reason: Refutation not found, incomplete strategy
% 2.47/0.84 % (3968079)Time elapsed: 0.029 s
% 2.47/0.84 % (3968079)Peak memory usage: 112 MB
% 2.47/0.84 % (3968079)Instructions burned: 5 (million)
% 2.47/0.84 % (3968078)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=201393597:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.47/0.84 % (3968078)Instruction limit reached!
% 2.47/0.84 % (3968078)------------------------------
% 2.47/0.84 % (3968078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.84 % (3968078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.84 % (3968078)CaDiCaL version: 2.1.3
% 2.47/0.84 % (3968078)Termination reason: Instruction limit
% 2.47/0.84 % (3968078)Termination phase: Saturation
% 2.47/0.84 % (3968078)Time elapsed: 0.004 s
% 2.47/0.84 % (3968078)Peak memory usage: 88 MB
% 2.47/0.84 % (3968078)Instructions burned: 6 (million)
% 2.47/0.84 % (3968080)Refutation found. Thanks to Tanya!
% 2.47/0.84 % SZS status Theorem for theBenchmark
% 2.47/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/0.84 % (3968080)------------------------------
% 2.47/0.84 % (3968080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.84 % (3968080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.84 % (3968080)CaDiCaL version: 2.1.3
% 2.47/0.84 % (3968080)Termination reason: Refutation
% 2.47/0.84 % (3968080)Time elapsed: 0.019 s
% 2.47/0.84 % (3968080)Peak memory usage: 112 MB
% 2.47/0.84 % (3968080)Instructions burned: 11 (million)
% 2.47/0.84 % (3968080)------------------------------
% 2.47/0.84 % (3968080)------------------------------
% 2.47/0.84 % (3968004)Success in time 0.308 s
% 2.47/0.84 % Vampire exiting
%------------------------------------------------------------------------------