%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT031_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:47:59 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 15 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 68 ( 14 atm; 0 fun; 37 num; 17 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 : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 23 !; 4 ?; 27 :)
% 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(func_def_12,type,
sK0: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f2,axiom,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax2) ).
tff(f4,axiom,
! [X0: $int,X1: collection,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 ) )
<=> in(X0,add(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f6,conjecture,
! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( $lesseq(20,X1)
& $lesseq(X1,40)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( $lesseq(20,X1)
& $lesseq(X1,40)
& in(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection] :
( ( X0 = add(10,add(30,add(50,empty))) )
=> ? [X1: $int] :
( ~ $less(X1,20)
& ~ $less(40,X1)
& in(X1,X0) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f21,plain,
? [X0: collection] :
( ! [X1: $int] :
( $less(X1,20)
| $less(40,X1)
| ~ in(X1,X0) )
& ( X0 = add(10,add(30,add(50,empty))) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f22,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 )
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ~ in(X0,X1)
& ( X0 != X2 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f23,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( in(X0,X1)
| ( X0 = X2 )
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ~ in(X0,X1)
& ( X0 != X2 ) ) ) ),
inference(flattening,[],[f22]) ).
tff(f26,plain,
( ! [X1: $int] :
( $less(X1,20)
| $less(40,X1)
| ~ in(X1,sK0) )
& ( add(10,add(30,add(50,empty))) = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
tff(f28,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f2]) ).
tff(f31,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f36,plain,
add(10,add(30,add(50,empty))) = sK0,
inference(cnf_transformation,[],[f26]) ).
tff(f37,plain,
! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) ),
inference(cnf_transformation,[],[f26]) ).
tff(f229,plain,
! [X0: $int] :
( ~ in(X0,add(30,add(50,empty)))
| in(X0,sK0) ),
inference(superposition,[],[f31,f36]) ).
tff(f241,plain,
in(30,sK0),
inference(resolution,[],[f229,f28]) ).
tff(f250,plain,
( $less(40,30)
| $less(30,20) ),
inference(resolution,[],[f241,f37]) ).
tff(f251,plain,
$false,
inference(evaluation,[],[f250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT031_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:06:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24 % (2479509)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (2479516)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3603357751:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.24 % (2479516) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2479509-2479516"...
% 0.08/0.24 % (2479516)...printing done.
% 0.08/0.24 % (2479516)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24 % (2479516)------------------------------
% 0.08/0.24 % (2479516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (2479516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (2479516)CaDiCaL version: 2.1.3
% 0.08/0.24 % (2479516)Termination reason: Refutation
% 0.08/0.24 % (2479516)Time elapsed: 0.003 s
% 0.08/0.24 % (2479516)Peak memory usage: 12 MB
% 0.08/0.24 % (2479516)Instructions burned: 6 (million)
% 0.08/0.24 % (2479509)Success in time 0.027 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------