%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM895_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 : n013.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 12:17:23 PM UTC 2026
% Result : Theorem 5.38s 1.87s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 23 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 0 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 43 ( 0 atm; 25 fun; 0 num; 18 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 : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 12 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_3,type,
sK0: $int ).
tff(func_def_4,type,
sK1: $int ).
tff(func_def_5,type,
sK2: $int ).
tff(f1,conjecture,
! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
=> ( $difference(X2,X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_difference) ).
tff(f2,negated_conjecture,
~ ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
=> ( $difference(X2,X0) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
=> ( $sum(X2,$uminus(X0)) = X1 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
~ ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X1,X2) = X0 )
=> ( $sum(X0,$uminus(X1)) = X2 ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
? [X2: $int,X1: $int,X0: $int] :
( ( $sum(X0,$uminus(X1)) != X2 )
& ( $sum(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
? [X0: $int,X1: $int,X2: $int] :
( ( $sum(X2,$uminus(X1)) != X0 )
& ( $sum(X1,X0) = X2 ) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
( ( $sum(sK2,$uminus(sK1)) != sK0 )
& ( $sum(sK1,sK0) = sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
tff(f8,plain,
$sum(sK1,sK0) = sK2,
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
$sum(sK2,$uminus(sK1)) != sK0,
inference(cnf_transformation,[],[f7]) ).
tff(f11,definition,
( spl3_1
<=> ( $sum(sK1,sK0) = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f14,plain,
spl3_1,
inference(avatar_split_clause,[],[f8,f11]) ).
tff(f16,definition,
( spl3_2
<=> ( $sum(sK2,$uminus(sK1)) = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f19,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f9,f16]) ).
tff(f20,plain,
$false,
inference(avatar_smt_refutation,[],[f19,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM895_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n013.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 21:37:51 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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
% 5.38/1.87 % (575208)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.38/1.87 % (575216)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2781442607:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 5.38/1.87 % (575218)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=42336982:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 5.38/1.87 % (575216)Instruction limit reached!
% 5.38/1.87 % (575216)------------------------------
% 5.38/1.87 % (575216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.87 % (575216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.87 % (575216)CaDiCaL version: 2.1.3
% 5.38/1.87 % (575216)Termination reason: Instruction limit
% 5.38/1.87 % (575216)Termination phase: Saturation
% 5.38/1.87 % (575216)Time elapsed: 0.005 s
% 5.38/1.87 % (575216)Peak memory usage: 88 MB
% 5.38/1.87 % (575216)Instructions burned: 8 (million)
% 5.38/1.87 % (575218)First to succeed.
% 5.38/1.87 % (575218)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-575208"
% 5.38/1.87 % (575214)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3812717773:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 5.38/1.87 % (575215)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3276542240:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 5.38/1.87 % (575219)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=880048930:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 5.38/1.87 % (575217)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=117677399:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 5.38/1.87 % (575213)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3950426498:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 5.38/1.87 % (575217)Instruction limit reached!
% 5.38/1.87 % (575217)------------------------------
% 5.38/1.87 % (575217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.87 % (575217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.87 % (575217)CaDiCaL version: 2.1.3
% 5.38/1.87 % (575217)Termination reason: Instruction limit
% 5.38/1.87 % (575217)Termination phase: Saturation
% 5.38/1.87 % (575217)Time elapsed: 0.007 s
% 5.38/1.87 % (575217)Peak memory usage: 88 MB
% 5.38/1.87 % (575217)Instructions burned: 4 (million)
% 5.38/1.87 % (575214)Also succeeded, but the first one will report.
% 5.38/1.87 % (575213)Also succeeded, but the first one will report.
% 5.38/1.87 % (575219)Also succeeded, but the first one will report.
% 5.38/1.87 % (575215)Also succeeded, but the first one will report.
% 5.38/1.87 % (575222)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1596682382:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.38/1.87 % (575222)Refutation not found, incomplete strategy
% 5.38/1.87 % (575222)------------------------------
% 5.38/1.87 % (575222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.87 % (575222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.87 % (575222)CaDiCaL version: 2.1.3
% 5.38/1.87 % (575222)Termination reason: Refutation not found, incomplete strategy
% 5.38/1.87 % (575222)Time elapsed: 0.001 s
% 5.38/1.87 % (575222)Peak memory usage: 89 MB
% 5.38/1.87 % (575228)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=3938779976:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.38/1.87 % (575228)Instruction limit reached!
% 5.38/1.87 % (575228)------------------------------
% 5.38/1.87 % (575228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.87 % (575228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.87 % (575228)CaDiCaL version: 2.1.3
% 5.38/1.87 % (575228)Termination reason: Instruction limit
% 5.38/1.87 % (575228)Termination phase: Saturation
% 5.38/1.87 % (575228)Time elapsed: 0.024 s
% 5.38/1.87 % (575228)Peak memory usage: 88 MB
% 5.38/1.87 % (575228)Instructions burned: 30 (million)
% 5.38/1.87 % (575218)Refutation found. Thanks to Tanya!
% 5.38/1.87 % SZS status Theorem for theBenchmark
% 5.38/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.87 % (575218)------------------------------
% 5.38/1.87 % (575218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.87 % (575218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.87 % (575218)CaDiCaL version: 2.1.3
% 5.38/1.87 % (575218)Termination reason: Refutation
% 5.38/1.87 % (575218)Time elapsed: 0.042 s
% 5.38/1.87 % (575218)Peak memory usage: 115 MB
% 5.38/1.87 % (575218)Instructions burned: 7 (million)
% 5.38/1.87 % (575218)------------------------------
% 5.38/1.87 % (575218)------------------------------
% 5.38/1.87 % (575208)Success in time 0.659 s
% 5.38/1.87 % Vampire exiting
%------------------------------------------------------------------------------