%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT091_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:47:17 AM UTC 2026
% Result : Theorem 2.51s 0.99s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 30 ~; 15 |; 0 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 74 ( 0 atm; 9 fun; 19 num; 46 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_10,type,
sK0: ( list * $int ) > $int ).
tff(func_def_11,type,
sK1: ( list * $int ) > list ).
tff(func_def_12,type,
sK2: ( list * $int ) > list ).
tff(func_def_13,type,
sK3: ( list * $int ) > $int ).
tff(func_def_14,type,
sK4: ( $int * list ) > list ).
tff(func_def_15,type,
sK5: ( $int * list ) > $int ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f10,axiom,
! [X0: $int,X1: $int,X3: $int,X2: list] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(f11,axiom,
! [X3: $int,X2: list,X1: $int,X0: $int] :
( ( X0 = X1 )
=> ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_4) ).
tff(f15,conjecture,
~ ! [X1: list,X0: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X1: list,X0: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
~ ~ ! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(rectify,[],[f16]) ).
tff(f20,plain,
! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(flattening,[],[f19]) ).
tff(f23,plain,
! [X0: $int,X3: list,X1: $int] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X3)) = count(X0,X3) ) ),
inference(rectify,[],[f10]) ).
tff(f25,plain,
! [X3: $int,X1: list,X2: $int] :
( ( X2 = X3 )
=> ( count(X3,cons(X2,X1)) = $sum(count(X3,X1),1) ) ),
inference(rectify,[],[f11]) ).
tff(f29,plain,
! [X1: list,X2: $int,X3: $int] :
( ( count(X3,cons(X2,X1)) = $sum(count(X3,X1),1) )
| ( X2 != X3 ) ),
inference(ennf_transformation,[],[f25]) ).
tff(f30,plain,
! [X0: $int,X3: list,X1: $int] :
( ( X0 = X1 )
| ( count(X0,cons(X1,X3)) = count(X0,X3) ) ),
inference(ennf_transformation,[],[f23]) ).
tff(f31,plain,
! [X1: list,X0: list] :
( ! [X2: $int] : ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f20]) ).
tff(f32,plain,
! [X0: $int,X1: list,X2: $int] :
( ( X0 = X2 )
| ( count(X0,X1) = count(X0,cons(X2,X1)) ) ),
inference(rectify,[],[f30]) ).
tff(f44,plain,
! [X0: list,X1: list] :
( ! [X2: $int] : ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ),
inference(rectify,[],[f31]) ).
tff(f45,plain,
! [X0: list,X1: $int,X2: $int] :
( ( count(X2,cons(X1,X0)) = $sum(count(X2,X0),1) )
| ( X1 != X2 ) ),
inference(rectify,[],[f29]) ).
tff(f48,plain,
! [X2: $int,X0: $int,X1: list] :
( ( count(X0,X1) = count(X0,cons(X2,X1)) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f51,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f66,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f67,plain,
! [X2: $int,X0: list,X1: list] :
( ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f69,plain,
! [X2: $int,X0: list,X1: $int] :
( ( count(X2,cons(X1,X0)) = $sum(count(X2,X0),1) )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f79,plain,
! [X2: $int,X0: list] : ( count(X2,cons(X2,X0)) = $sum(count(X2,X0),1) ),
inference(equality_resolution,[],[f69]) ).
tff(f86,plain,
! [X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( nil = X1 ) ),
inference(superposition,[],[f67,f51]) ).
tff(f122,plain,
! [X0: $int,X1: list] :
( ( 0 != $sum(count(X0,X1),1) )
| ( cons(X0,X1) = nil ) ),
inference(superposition,[],[f86,f79]) ).
tff(f125,plain,
! [X0: $int,X1: list] : ( 0 != $sum(count(X0,X1),1) ),
inference(forward_subsumption_resolution,[],[f122,f66]) ).
tff(f133,plain,
! [X2: $int,X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( nil = cons(X2,X1) )
| ( X0 = X2 ) ),
inference(superposition,[],[f86,f48]) ).
tff(f137,plain,
! [X2: $int,X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( X0 = X2 ) ),
inference(forward_subsumption_resolution,[],[f133,f66]) ).
tff(f139,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( 0 != 0 ) ),
inference(superposition,[],[f137,f51]) ).
tff(f142,plain,
! [X0: $int,X1: $int] : ( X0 = X1 ),
inference(trivial_inequality_removal,[],[f139]) ).
tff(f193,plain,
! [X0: $int] : ( 0 != $sum(X0,1) ),
inference(superposition,[],[f125,f142]) ).
tff(f208,plain,
$false,
inference(forward_subsumption_resolution,[],[f193,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT091_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:08:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.51/0.99 % (3623270)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.51/0.99 % (3623280)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1602385642:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.51/0.99 % (3623280)First to succeed.
% 2.51/0.99 % (3623280)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3623270"
% 2.51/0.99 % (3623276)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=49032939:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.51/0.99 % (3623275)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4070046332:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.51/0.99 % (3623277)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=742941312:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.51/0.99 % (3623279)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=600325767:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.51/0.99 % (3623278)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2543468900:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.51/0.99 % (3623278)Also succeeded, but the first one will report.
% 2.51/0.99 % (3623279)Instruction limit reached!
% 2.51/0.99 % (3623279)------------------------------
% 2.51/0.99 % (3623279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/0.99 % (3623279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.99 % (3623279)CaDiCaL version: 2.1.3
% 2.51/0.99 % (3623279)Termination reason: Instruction limit
% 2.51/0.99 % (3623279)Termination phase: Saturation
% 2.51/0.99 % (3623279)Time elapsed: 0.029 s
% 2.51/0.99 % (3623279)Peak memory usage: 88 MB
% 2.51/0.99 % (3623279)Instructions burned: 17 (million)
% 2.51/0.99 % (3623281)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1846852602:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.51/0.99 % (3623275)Refutation not found, incomplete strategy
% 2.51/0.99 % (3623275)------------------------------
% 2.51/0.99 % (3623275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/0.99 % (3623275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.99 % (3623275)CaDiCaL version: 2.1.3
% 2.51/0.99 % (3623275)Termination reason: Refutation not found, incomplete strategy
% 2.51/0.99 % (3623275)Time elapsed: 0.062 s
% 2.51/0.99 % (3623275)Peak memory usage: 112 MB
% 2.51/0.99 % (3623275)Instructions burned: 6 (million)
% 2.51/0.99 % (3623276)Also succeeded, but the first one will report.
% 2.51/0.99 % (3623281)Also succeeded, but the first one will report.
% 2.51/0.99 % (3623277)Also succeeded, but the first one will report.
% 2.51/0.99 % (3623280)Refutation found. Thanks to Tanya!
% 2.51/0.99 % SZS status Theorem for theBenchmark
% 2.51/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/0.99 % (3623280)------------------------------
% 2.51/0.99 % (3623280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/0.99 % (3623280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.99 % (3623280)CaDiCaL version: 2.1.3
% 2.51/0.99 % (3623280)Termination reason: Refutation
% 2.51/0.99 % (3623280)Time elapsed: 0.021 s
% 2.51/0.99 % (3623280)Peak memory usage: 116 MB
% 2.51/0.99 % (3623280)Instructions burned: 13 (million)
% 2.51/0.99 % (3623280)------------------------------
% 2.51/0.99 % (3623280)------------------------------
% 2.51/0.99 % (3623270)Success in time 0.321 s
% 2.51/0.99 % Vampire exiting
%------------------------------------------------------------------------------