%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM865_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 : n026.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 12:17:19 PM UTC 2026
% Result : Theorem 2.80s 1.37s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 27 unt; 0 typ; 13 def)
% Number of atoms : 80 ( 61 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 45 ( 8 ~; 0 |; 25 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 86 ( 0 atm; 44 fun; 0 num; 42 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 : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 11 usr; 11 con; 0-2 aty)
% Number of variables : 42 ( 21 !; 21 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int ).
tff(func_def_5,type,
sK1: $int ).
tff(func_def_6,type,
sK2: $int ).
tff(func_def_7,type,
sK3: $int ).
tff(func_def_8,type,
sK4: $int ).
tff(func_def_9,type,
sK5: $int ).
tff(func_def_10,type,
sK6: $int ).
tff(func_def_11,type,
sF7: $int ).
tff(func_def_12,type,
sF8: $int ).
tff(func_def_13,type,
sF9: $int ).
tff(func_def_14,type,
sF10: $int ).
tff(f1,conjecture,
! [X5: $int,X3: $int,X2: $int,X0: $int,X1: $int,X6: $int,X4: $int] :
( ( ( $sum(X3,X2) = X4 )
& ( $sum(X0,X1) = X3 )
& ( $sum(X1,X2) = X5 )
& ( $sum(X0,X5) = X6 ) )
=> ( X4 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_sum_forall) ).
tff(f2,negated_conjecture,
~ ! [X5: $int,X3: $int,X2: $int,X0: $int,X1: $int,X6: $int,X4: $int] :
( ( ( $sum(X3,X2) = X4 )
& ( $sum(X0,X1) = X3 )
& ( $sum(X1,X2) = X5 )
& ( $sum(X0,X5) = X6 ) )
=> ( X4 = X6 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f15,plain,
~ ! [X3: $int,X0: $int,X1: $int,X2: $int,X6: $int,X4: $int,X5: $int] :
( ( ( $sum(X4,X2) = X0 )
& ( $sum(X3,X4) = X1 )
& ( $sum(X1,X2) = X6 )
& ( $sum(X3,X0) = X5 ) )
=> ( X5 = X6 ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
? [X3: $int,X0: $int,X1: $int,X2: $int,X6: $int,X4: $int,X5: $int] :
( ( X5 != X6 )
& ( $sum(X4,X2) = X0 )
& ( $sum(X3,X4) = X1 )
& ( $sum(X1,X2) = X6 )
& ( $sum(X3,X0) = X5 ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
? [X5: $int,X3: $int,X6: $int,X1: $int,X2: $int,X4: $int,X0: $int] :
( ( $sum(X3,X0) = X5 )
& ( $sum(X1,X2) = X6 )
& ( $sum(X4,X2) = X0 )
& ( X5 != X6 )
& ( $sum(X3,X4) = X1 ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
? [X0: $int,X1: $int,X2: $int,X3: $int,X4: $int,X5: $int,X6: $int] :
( ( $sum(X1,X6) = X0 )
& ( $sum(X3,X4) = X2 )
& ( $sum(X5,X4) = X6 )
& ( X0 != X2 )
& ( $sum(X1,X5) = X3 ) ),
inference(rectify,[],[f17]) ).
tff(f19,plain,
( ( $sum(sK1,sK6) = sK0 )
& ( $sum(sK3,sK4) = sK2 )
& ( sK6 = $sum(sK5,sK4) )
& ( sK2 != sK0 )
& ( $sum(sK1,sK5) = sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f18]) ).
tff(f20,plain,
$sum(sK1,sK5) = sK3,
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
sK2 != sK0,
inference(cnf_transformation,[],[f19]) ).
tff(f22,plain,
sK6 = $sum(sK5,sK4),
inference(cnf_transformation,[],[f19]) ).
tff(f23,plain,
$sum(sK3,sK4) = sK2,
inference(cnf_transformation,[],[f19]) ).
tff(f24,plain,
$sum(sK1,sK6) = sK0,
inference(cnf_transformation,[],[f19]) ).
tff(f25,definition,
sF7 = $sum(sK1,sK6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f26,plain,
$sum(sK1,sK6) = sF7,
inference(reorient_equations,[],[f25]) ).
tff(f27,plain,
sF7 = sK0,
inference(definition_folding,[],[f24,f26]) ).
tff(f28,definition,
sF8 = $sum(sK3,sK4),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
tff(f29,plain,
$sum(sK3,sK4) = sF8,
inference(reorient_equations,[],[f28]) ).
tff(f30,plain,
sK2 = sF8,
inference(definition_folding,[],[f23,f29]) ).
tff(f31,definition,
sF9 = $sum(sK5,sK4),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
tff(f32,plain,
$sum(sK5,sK4) = sF9,
inference(reorient_equations,[],[f31]) ).
tff(f33,plain,
sK6 = sF9,
inference(definition_folding,[],[f22,f32]) ).
tff(f34,definition,
sF10 = $sum(sK1,sK5),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
tff(f35,plain,
$sum(sK1,sK5) = sF10,
inference(reorient_equations,[],[f34]) ).
tff(f36,plain,
sK3 = sF10,
inference(definition_folding,[],[f20,f35]) ).
tff(f38,definition,
( spl11_1
<=> ( sK6 = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
tff(f41,plain,
spl11_1,
inference(avatar_split_clause,[],[f33,f38]) ).
tff(f43,definition,
( spl11_2
<=> ( sK2 = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
tff(f46,plain,
spl11_2,
inference(avatar_split_clause,[],[f30,f43]) ).
tff(f48,definition,
( spl11_3
<=> ( $sum(sK1,sK6) = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
tff(f51,plain,
spl11_3,
inference(avatar_split_clause,[],[f26,f48]) ).
tff(f53,definition,
( spl11_4
<=> ( sK3 = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
tff(f56,plain,
spl11_4,
inference(avatar_split_clause,[],[f36,f53]) ).
tff(f58,definition,
( spl11_5
<=> ( $sum(sK1,sK5) = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
tff(f61,plain,
spl11_5,
inference(avatar_split_clause,[],[f35,f58]) ).
tff(f63,definition,
( spl11_6
<=> ( $sum(sK5,sK4) = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
tff(f66,plain,
spl11_6,
inference(avatar_split_clause,[],[f32,f63]) ).
tff(f68,definition,
( spl11_7
<=> ( sF7 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
tff(f71,plain,
spl11_7,
inference(avatar_split_clause,[],[f27,f68]) ).
tff(f73,definition,
( spl11_8
<=> ( $sum(sK3,sK4) = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
tff(f76,plain,
spl11_8,
inference(avatar_split_clause,[],[f29,f73]) ).
tff(f78,definition,
( spl11_9
<=> ( sK2 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
tff(f81,plain,
~ spl11_9,
inference(avatar_split_clause,[],[f21,f78]) ).
tff(f82,plain,
$false,
inference(avatar_smt_refutation,[],[f81,f76,f71,f66,f61,f56,f51,f46,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM865_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:38:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.80/1.37 % (3225189)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.80/1.37 % (3225200)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1045785870:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.80/1.37 % (3225200)First to succeed.
% 2.80/1.37 % (3225200)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3225189"
% 2.80/1.37 % (3225198)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4109726871:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.80/1.37 % (3225195)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1344858680:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.80/1.37 % (3225197)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3326748231:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.80/1.37 % (3225196)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1024143812:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.80/1.37 % (3225199)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3401124838:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.80/1.37 % (3225194)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1033482002:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.80/1.37 % (3225198)Instruction limit reached!
% 2.80/1.37 % (3225198)------------------------------
% 2.80/1.37 % (3225198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.37 % (3225198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.37 % (3225198)CaDiCaL version: 2.1.3
% 2.80/1.37 % (3225198)Termination reason: Instruction limit
% 2.80/1.37 % (3225198)Termination phase: Saturation
% 2.80/1.37 % (3225198)Time elapsed: 0.003 s
% 2.80/1.37 % (3225198)Peak memory usage: 88 MB
% 2.80/1.37 % (3225198)Instructions burned: 4 (million)
% 2.80/1.37 % (3225197)Also succeeded, but the first one will report.
% 2.80/1.37 % (3225199)Also succeeded, but the first one will report.
% 2.80/1.37 % (3225195)Also succeeded, but the first one will report.
% 2.80/1.37 % (3225194)Also succeeded, but the first one will report.
% 2.80/1.37 % (3225196)Also succeeded, but the first one will report.
% 2.80/1.37 % (3225200)Refutation found. Thanks to Tanya!
% 2.80/1.37 % SZS status Theorem for theBenchmark
% 2.80/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.38 % (3225200)------------------------------
% 2.80/1.38 % (3225200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.38 % (3225200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.38 % (3225200)CaDiCaL version: 2.1.3
% 2.80/1.38 % (3225200)Termination reason: Refutation
% 2.80/1.38 % (3225200)Time elapsed: 0.021 s
% 2.80/1.38 % (3225200)Peak memory usage: 116 MB
% 2.80/1.38 % (3225200)Instructions burned: 12 (million)
% 2.80/1.38 % (3225200)------------------------------
% 2.80/1.38 % (3225200)------------------------------
% 2.80/1.38 % (3225189)Success in time 0.315 s
% 2.80/1.38 % Vampire exiting
%------------------------------------------------------------------------------