%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM707^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : Wed Sep 30 08:19:22 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 4 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
pl: nat > nat > nat ).
thf(func_def_3,type,
ts: nat > nat > nat ).
thf(func_def_4,type,
suc: nat > nat ).
thf(f1,axiom,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ ( suc @ X1 ) )
= ( pl @ ( ts @ X0 @ X1 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28b) ).
thf(f2,conjecture,
( ( pl @ ( ts @ x @ y ) @ x )
= ( ts @ x @ ( suc @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28f) ).
thf(f3,negated_conjecture,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(flattening,[],[f3]) ).
thf(f5,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ ( suc @ X1 ) )
= ( pl @ ( ts @ X0 @ X1 ) @ X0 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f6,plain,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f7,plain,
( ( ts @ x @ ( suc @ y ) )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(constrained_superposition,[],[f6,f5]) ).
thf(f8,plain,
$false,
inference(trivial_inequality_removal,[],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM707^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:47:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 % (293361)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (293370)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4112752306:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.26 % (293370)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (293370) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-293361-293370"...
% 0.20/0.26 % (293370)...printing done.
% 0.20/0.26 % (293370)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (293370)------------------------------
% 0.20/0.26 % (293370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (293370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (293370)CaDiCaL version: 2.1.3
% 0.20/0.26 % (293370)Termination reason: Refutation
% 0.20/0.26 % (293370)Time elapsed: 0.001 s
% 0.20/0.26 % (293370)Peak memory usage: 12 MB
% 0.20/0.26 % (293370)Instructions burned: 1 (million)
% 0.20/0.26 % (293361)Success in time 0.031 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------