%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT020_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:47:07 AM UTC 2026
% Result : Theorem 2.42s 0.72s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 37 ( 15 ~; 15 |; 6 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 46 ( 0 atm; 0 fun; 34 num; 12 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f4,axiom,
! [X0: $int,X2: $int,X1: collection] :
( in(X0,add(X2,X1))
<=> ( ( X0 = X2 )
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f6,conjecture,
~ in(4,add(1,add(3,add(5,empty)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ~ in(4,add(1,add(3,add(5,empty)))),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f9,plain,
in(4,add(1,add(3,add(5,empty)))),
inference(flattening,[],[f7]) ).
tff(f14,plain,
! [X0: $int,X2: $int,X1: collection] :
( ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) )
& ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f15,plain,
! [X0: $int,X2: $int,X1: collection] :
( ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) )
& ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
! [X0: $int,X1: $int,X2: collection] :
( ( in(X0,add(X1,X2))
| ( ( X0 != X1 )
& ~ in(X0,X2) ) )
& ( ( X0 = X1 )
| in(X0,X2)
| ~ in(X0,add(X1,X2)) ) ),
inference(rectify,[],[f15]) ).
tff(f18,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f23,plain,
in(4,add(1,add(3,add(5,empty)))),
inference(cnf_transformation,[],[f9]) ).
tff(f24,plain,
! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,add(X1,X2))
| in(X0,X2)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f31,plain,
( ( 4 = 1 )
| in(4,add(3,add(5,empty))) ),
inference(resolution,[],[f24,f23]) ).
tff(f34,plain,
in(4,add(3,add(5,empty))),
inference(evaluation,[],[f31]) ).
tff(f35,plain,
( ( 4 = 3 )
| in(4,add(5,empty)) ),
inference(resolution,[],[f34,f24]) ).
tff(f36,plain,
in(4,add(5,empty)),
inference(evaluation,[],[f35]) ).
tff(f37,plain,
( ( 4 = 5 )
| in(4,empty) ),
inference(resolution,[],[f36,f24]) ).
tff(f38,plain,
in(4,empty),
inference(evaluation,[],[f37]) ).
tff(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT020_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 00:05:19 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 2.42/0.72 % (3914252)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.42/0.72 % (3914258)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3229319976:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.42/0.72 % (3914261)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=564047525:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.42/0.72 % (3914259)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=647948395:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.42/0.72 % (3914262)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1173012347:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.42/0.72 % (3914257)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2017948651:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.42/0.72 % (3914263)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2935968288:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.42/0.72 % (3914260)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1630539503:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.42/0.72 % (3914261)First to succeed.
% 2.42/0.72 % (3914260)Refutation not found, incomplete strategy
% 2.42/0.72 % (3914260)------------------------------
% 2.42/0.72 % (3914260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.72 % (3914260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.72 % (3914260)CaDiCaL version: 2.1.3
% 2.42/0.72 % (3914260)Termination reason: Refutation not found, incomplete strategy
% 2.42/0.72 % (3914260)Time elapsed: 0.001 s
% 2.42/0.72 % (3914260)Peak memory usage: 88 MB
% 2.42/0.72 % (3914260)Instructions burned: 2 (million)
% 2.42/0.72 % (3914261)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3914252"
% 2.42/0.72 % (3914259)Also succeeded, but the first one will report.
% 2.42/0.72 % (3914257)Refutation not found, incomplete strategy
% 2.42/0.72 % (3914257)------------------------------
% 2.42/0.72 % (3914257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.72 % (3914257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.72 % (3914257)CaDiCaL version: 2.1.3
% 2.42/0.72 % (3914257)Termination reason: Refutation not found, incomplete strategy
% 2.42/0.72 % (3914257)Time elapsed: 0.018 s
% 2.42/0.72 % (3914257)Peak memory usage: 114 MB
% 2.42/0.72 % (3914257)Instructions burned: 6 (million)
% 2.42/0.72 % (3914262)Also succeeded, but the first one will report.
% 2.42/0.72 % (3914258)Also succeeded, but the first one will report.
% 2.42/0.72 % (3914263)Also succeeded, but the first one will report.
% 2.42/0.72 % (3914260)------------------------------
% 2.42/0.72 % (3914260)------------------------------
% 2.42/0.72 % (3914261)Refutation found. Thanks to Tanya!
% 2.42/0.72 % SZS status Theorem for theBenchmark
% 2.42/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.72 % (3914261)------------------------------
% 2.42/0.72 % (3914261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.72 % (3914261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.72 % (3914261)CaDiCaL version: 2.1.3
% 2.42/0.72 % (3914261)Termination reason: Refutation
% 2.42/0.72 % (3914261)Time elapsed: 0.001 s
% 2.42/0.72 % (3914261)Peak memory usage: 89 MB
% 2.42/0.72 % (3914261)Instructions burned: 1 (million)
% 2.42/0.72 % (3914261)------------------------------
% 2.42/0.72 % (3914261)------------------------------
% 2.42/0.72 % (3914252)Success in time 0.312 s
% 2.42/0.72 % Vampire exiting
%------------------------------------------------------------------------------