%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM713^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:18:40 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 112 ( 12 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 25 !; 1 ?; 26 :)
% 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,
z: nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(func_def_5,type,
ts: nat > nat > nat ).
thf(func_def_8,type,
sK0: nat ).
thf(f1,axiom,
~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( ts @ X0 @ ( pl @ X1 @ X2 ) )
= ( pl @ ( ts @ X0 @ X1 ) @ ( ts @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz30) ).
thf(f5,conjecture,
~ ! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz32a) ).
thf(f6,negated_conjecture,
~ ~ ! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f10,plain,
! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(flattening,[],[f6]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ts @ X2 @ ( pl @ X0 @ X1 ) )
= ( pl @ ( ts @ X2 @ X0 ) @ ( ts @ X2 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
? [X0: nat] :
( x
= ( pl @ y @ X0 ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12]) ).
thf(f16,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X2 @ ( pl @ X0 @ X1 ) )
= ( pl @ ( ts @ X2 @ X0 ) @ ( ts @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X0: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X1 @ ( pl @ X0 @ X2 ) )
= ( pl @ ( ts @ X0 @ X1 ) @ ( ts @ X1 @ X2 ) ) ),
inference(superposition,[],[f16,f17]) ).
thf(f41,plain,
! [X0: nat] :
( ( ts @ x @ z )
!= ( ts @ z @ ( pl @ y @ X0 ) ) ),
inference(superposition,[],[f18,f25]) ).
thf(f42,plain,
! [X0: nat] :
( ( ts @ z @ x )
!= ( ts @ z @ ( pl @ y @ X0 ) ) ),
inference(forward_demodulation,[],[f41,f17]) ).
thf(f43,plain,
( ( ts @ z @ x )
!= ( ts @ z @ x ) ),
inference(superposition,[],[f42,f19]) ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM713^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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 12:44:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (700130)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (700138)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=561371540:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (700138)Instruction limit reached!
% 0.21/0.29 % (700138)------------------------------
% 0.21/0.29 % (700138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (700138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (700138)CaDiCaL version: 2.1.3
% 0.21/0.29 % (700138)Termination reason: Instruction limit
% 0.21/0.29 % (700138)Termination phase: Saturation
% 0.21/0.29 % (700138)Time elapsed: 0.002 s
% 0.21/0.29 % (700138)Peak memory usage: 12 MB
% 0.21/0.29 % (700138)Instructions burned: 3 (million)
% 0.21/0.29 % (700140)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=325073676:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (700140) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-700130-700140"...
% 0.21/0.29 % (700140)...printing done.
% 0.21/0.29 % (700140)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (700140)------------------------------
% 0.21/0.29 % (700140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (700140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (700140)CaDiCaL version: 2.1.3
% 0.21/0.29 % (700140)Termination reason: Refutation
% 0.21/0.29 % (700140)Time elapsed: 0.004 s
% 0.21/0.29 % (700140)Peak memory usage: 12 MB
% 0.21/0.29 % (700140)Instructions burned: 4 (million)
% 0.21/0.29 % (700130)Success in time 0.044 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------